Abstract:
A system and method for reconstructing an image acquired by delivering an irradiating dose of radiation to a subject includes acquiring imaging data using a dose of irradiating radiation and selecting at least one of a plurality of mechanisms for reducing the dose that could be delivered to the subject to acquire additional imaging data. Noise is inserted into the imaging data to simulate the at least one of the plurality of mechanisms for reducing the dose that could be applied to acquire the additional imaging data to thereby generate simulated imaging data at a reduced dose of irradiating radiation. A simulated reduced dose image is reconstructed from the simulated imaging data. A method is provided for utilizing a non-local means filter adapted using a map of local noise to produce denoised medical imaging data reflecting reduced local nose levels from those in originally-acquired medical imaging data.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is based on, claims priority to, and incorporates herein by reference in its entirety U.S. Provisional Patent Application No. 61/595,999, filed Feb. 7, 2012, and entitled “SYSTEM AND METHOD FOR CONTROLLING RADIATION DOSE FOR RADIOLOGICAL APPLICATIONS.” 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to medical imaging and, more particularly, to systems and methods for controlling radiation doses delivered when performing imaging processes using ionizing radiation. 
         [0003]    In a computed tomography system, an x-ray source projects a beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system, termed the “imaging plane.” The x-ray beam passes through the object being imaged, such as a medical patient or other non-medical patient or object, such as in industrial CT imaging, and impinges upon an array of radiation detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the x-ray beam by the object and each detector produces a separate electrical signal that is a measurement of the beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce the transmission profile at a particular view angle. 
         [0004]    The source and detector array in a conventional CT system are rotated on a gantry within the imaging plane and around the object so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements from the detector array at a given angle is referred to as a “view”, and a “scan” of the object comprises a set of views acquired at different angular orientations during one revolution of the x-ray source and detector. In a 2D scan, data is processed to construct an image that corresponds to a two dimensional slice taken through the object. The prevailing method for reconstructing an image from 2D data is referred to in the art as the filtered backprojection technique, however, other image reconstruction processes are also well known. This process converts the attenuation measurements from a scan into integers called “CT numbers” or “Hounsfield units”, which are used to control the brightness of a corresponding pixel on a display. 
         [0005]    The drastically increased use of CT in modern clinical settings has generated serious public health concerns regarding the cancer risks associated with the radiation exposure from CT. However, lowering radiation dose alone generally produces a noisier image and may degrade diagnostic performance. Thus, the current guiding principle in CT clinical practice is to use radiation dose levels as low as reasonably achievable while maintaining acceptable diagnostic accuracy. 
         [0006]    Despite the tremendous effort in the CT community to minimize radiation dose, scanning protocols and radiation doses still vary widely among different CT practices, which poses substantial risks to patient safety. The substantial variation in protocols and radiation dose is largely attributable to the lack of an efficient and widely available approach to optimizing CT protocols. 
         [0007]    Clinical evaluation by interpreting physicians is the most commonly used approach to determining the lowest possible radiation dose in CT protocols. To do the evaluation, one can gradually decrease the scanning technique until the image quality approaches the minimum acceptable limit. This approach requires exploratory low-dose scans on a number of patients, which is tedious and can potentially result in diagnostically compromised image. A more elegant approach is to use a noise insertion tool to simulate images at reduced dose levels from “standard dose” existing exams. A range of simulated dose levels can be generated and the diagnostic quality comparisons can be done across the same patient, removing patient-specific variables. This approach enables radiologists to determine the lowest acceptable dose level without risk of compromising a patient scan, which has been used for optimizing CT scanning protocols. Due to the proprietary nature of the CT raw data, the noise-insertion tools for clinical use have often been developed by manufacturers and distributed to very few users under research agreement. The technical details of the tools are not publicly available and the accuracy is usually out of the users&#39; control, which makes their applications rather limited. 
         [0008]    Even assuming that a reduced dose is appropriately selected by a clinician, the clinical value of the image may be correspondingly reduced by the introduction of additional noise. Accordingly substantial efforts have been made to create denoising mechanisms for CT image and, as a result, there is increasing evidence that state-of-the-art denoising algorithms may allow dose to be reduced by up to 50% in many clinical scans without compromising diagnostic performance. However, the effectiveness of denoising mechanisms are widely variable and, more troubling, can make substantial and varied changes to the images. That is, ineffective or overly aggressive denoising mechanisms can reduce the clinical usefulness and credibility of the images acquired. In doing so, the difficulty of controlling radiation dose to the patient can be compounded by the need to perform subsequent data acquisitions to replace overly-noisy images. 
         [0009]    Accordingly, it would be desirable to have a system and method for determining a desirable or optimized radiation dose that is not limited to particular clinical applications or specialized hardware or proprietary software that cannot be readily extended across various manufacturers and platforms of CT imaging systems. Furthermore, it would be desirable to have a highly flexible, yet robust, denoising mechanism. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention overcomes the aforementioned drawbacks by providing a system and method for simultaneously determining both the noise-level and spatial-frequency content in lower-dose images from existing “standard dose” CT data. In particular, a noise insertion method is provided that incorporates several important physical factors of a CT scanner that have been determined to potentially present a significant affect on the characteristics of image noise, including x-ray beam bowtie filter, automatic exposure control (AEC), and electronic noise. Furthermore, the present invention overcomes the aforementioned drawbacks by providing a non-local means filter adapted using a map of local noise to produce denoised medical imaging data reflecting reduced local nose levels from those in originally-acquired medical imaging data. 
         [0011]    In accordance with one aspect of the invention, a method for reconstructing an image acquired by delivering an irradiating dose of radiation to a subject is disclosed that includes obtaining a set of medical imaging data acquired using a dose of irradiating radiation delivered to a subject, and selecting at least one of a plurality of mechanisms for reducing the dose of irradiating radiation that could be delivered to the subject to acquire an additional set of medical imaging data. The method also includes inserting noise into the medical imaging data to simulate the at least one of the plurality of mechanisms for reducing the dose of irradiating radiation that could be applied to acquire the additional set of medical imaging data to thereby generate a simulated set of medical imaging data at a reduced dose of irradiating radiation. The method further includes reconstructing a simulated reduced dose image from the simulated set of medical imaging data. 
         [0012]    In accordance with another aspect of the invention, a computed tomography (CT) imaging system is disclosed that includes an x-ray source configured to emit x-rays toward an object to be imaged, a detector configured to receive x-rays that are attenuated by the object, and a data acquisition system (DAS) connected to the detector to receive an indication of received x-rays. The system also includes a computer system coupled to the DAS to receive the indication of the received x-rays and programmed to obtain a set of medical imaging data acquired using a dose of irradiating radiation delivered by the x-ray source to a subject positioned between the x-ray source and the detector. The computer system is also programmed to select at least one of a plurality of mechanisms for reducing the dose of irradiating radiation that could be delivered to the subject to acquire an additional set of medical imaging data. The computer system is further programmed to insert noise into the medical imaging data to simulate the at least one of the plurality of mechanisms for reducing the dose of irradiating radiation that could be applied to acquire the additional set of medical imaging data to thereby generate a simulated set of medical imaging data at a reduced does of irradiating radiation. The computer system is also configured to reconstruct a simulated reduced dose image from the simulated set of medical imaging. 
         [0013]    In accordance with yet another aspect of the invention, a method for reconstructing an image acquired by delivering an irradiating dose of radiation to a subject is disclosed that includes obtaining a set of medical imaging data using the irradiating dose of radiation, obtaining a map of local noise level in the medical imaging data, utilizing a non-local means filter adapted using the map of local noise to produce denoised medical imaging data reflecting reduced local nose levels from those in the medical imaging data, and providing a medical image of the subject from the denoised medical imaging data. 
         [0014]    In accordance with still another aspect of the invention, a computed tomography (CT) imaging system is disclosed that includes an x-ray source configured to emit x-rays toward an object to be imaged, a detector configured to receive x-rays that are attenuated by the object, a data acquisition system (DAS) connected to the detector to receive an indication of received x-rays, and a computer system coupled to the DAS to receive the indication of the received x-rays. The computer system is programmed to obtain a set of medical imaging data using the irradiating dose of radiation, obtain a map of local noise level in the medical imaging data, utilize a non-local means filter adapted using the map of local noise to produce denoised medical imaging data reflecting reduced local nose levels from those in the medical imaging data, and provide a medical image of the subject from the denoised medical imaging data. 
         [0015]    Various other features of the present invention will be made apparent from the following detailed description and the drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]      FIG. 1A  is a CT imaging system in which the present invention may be employed. 
           [0017]      FIG. 1B  is block schematic diagram of the CT imaging system of  FIG. 1A . 
           [0018]      FIG. 2  is a flow chart setting forth the steps of a processes for creating a noise map. 
           [0019]      FIG. 3  is a flow chart setting forth the steps for estimating noise in accordance with the present invention. 
           [0020]      FIG. 4  a graph of tube current as a function of table position illustrating one example of automatic exposure control (AEC) with respect to a chest/abdomen/pelvis exam. 
           [0021]      FIG. 5  is a schematic illustration of a scanning configuration using a bowtie filter to reduce the incident x-ray intensity in the peripheral region of the x-ray fan-beam. 
           [0022]      FIG. 6  is a graph illustrating the noise equivalent quanta as a function of detector bin along a single detector row. 
           [0023]      FIG. 7  is a graph of bar plots of noise levels comparing noise in acquired images and simulated images when different electronic noise levels were used in the simulation. 
           [0024]      FIG. 8  is a graph of noise level as a function of slice location plotted for each mAs setting and for both acquired and simulated images. 
           [0025]      FIG. 9  is a graph showing the percent differences in noise level between the simulated and acquired low dose images. 
           [0026]      FIG. 10  is an illustration of a bowtie filter in a CT scanner and an associated distribution of a incident number of photons along one detector row. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0027]    With initial reference to  FIGS. 1A and 1B , a computed tomography (CT) imaging system  110  includes a gantry  112  representative of at least a “third generation” CT scanner. In the illustrated example, the gantry  112  has a pair of x-ray sources  113  that each project a fan beam or cone beam of x-rays  114  toward a detector array  116  on the opposite side of the gantry  112 . The detector array  116  is formed by a number of detector elements  118  that together sense the projected x-rays that pass through a medical patient  115 . During a scan to acquire x-ray projection data, the gantry  112  and the components mounted thereon rotate about a center of rotation  119  located within the patient  115  to acquire attenuation data. 
         [0028]    The rotation of the gantry  112  and the operation of the x-ray source  113  are governed by a control mechanism  120  of the CT system  110 . The control mechanism  120  includes an x-ray controller  122  that provides power and timing signals to the x-ray sources  113  and a gantry motor controller  123  that controls the rotational speed and position of the gantry  112 . A data acquisition system (DAS)  124  in the control mechanism  120  samples analog data from detector elements  118  and converts the data to digital signals for subsequent processing. An image reconstructor  125 , receives sampled and digitized x-ray data from the DAS  124  and performs high speed image reconstruction. The reconstructed image is applied as an input to a computer  126  that stores the image in a mass storage device  128 . 
         [0029]    The computer  126  also receives commands and scanning parameters from an operator via console  130  that has a keyboard. An associated display  132  allows the operator to observe the reconstructed image and other data from the computer  126 . The operator supplied commands and parameters are used by the computer  126  to provide control signals and information to the DAS  124 , the x-ray controller  122 , and the gantry motor controller  123 . In addition, computer  126  operates a table motor controller  134  that controls a motorized table  136  to position the patient  115  in the gantry  112 . 
         [0030]    In CT scans, image noise is highly correlated to the number of photons received. Thus, lower noise in a resulting image is achieved when more x-ray photons are used to create the image. Thus, traditional notions of CT imaging focus including all usable x-ray information to minimize the tradeoff between does delivery and image noise. However, if a clinician were able to prospectively determine and consider whether the increased noise associated with a decreased dose would be acceptable to a given clinical application, the clinician would be empowered to determine whether additional dose reductions would be acceptable to the given clinical application. The present invention provides a system and method for achieving this objective. 
         [0031]    Noise in CT images originates from data noise in the projection measurement, which has two principal sources. Namely, noise in CT images is generally attributable to quantum noise and electronic noise. The electronic noise is the result of electronic fluctuation in the detector photodiode and other electronic components. The quantum noise is due to the limited number of photons collected by the detector. 
         [0032]    Non-local means (NLM) filtering utilizes an estimate of the noise level in the data. NLM expresses the redundancy present in most images in terms of similarities between small regions of an image, and generalizes the notion of finite differences to include a measure of difference between nearby image patches. This allows NLM to preserve a high degree of image texture and fine detail. The present invention recognizes that, in CT imaging, the noise level varies within and across slices, often by 2× within a slice and as much as 3× across slices. Therefore, the present invention further recognizes that this spatial variation in noise implies that NLM denoising based on a single noise level may be too weak in some places (accomplishing little), too strong in others (blurring fine detail), or both. Hence, as will be described with respect to  FIG. 2 , the present invention provides an image processing technique that includes modified NLM methodologies to adapt to the local noise level. As will be described, the present invention accomplishes this with a NLM algorithm that adds little computational cost. This NLM algorithm, adapting to the local noise level, effectively handles the widely different noise levels in different slices or within a slice. 
         [0033]    With an analytical solution to noise distribution, the image noise distribution can, in principle, be derived analytically, by propagating a noise model through the reconstruction equations. This has been implemented in simple fan-beam CT, where variance and covariance at each location of image space are analytically derived, assuming a simple CT noise model. However, to analytically derive the noise formula in multi-slice helical CT, accurate knowledge of the image reconstruction process implemented in the scanner is required, which is currently or typically not available. In addition, the noise model in the measured data has to be accurate before it is used in the analytical solution of the noise image, as will be described below. 
         [0034]    Referring to  FIG. 2 , the process begins by obtaining “full-dose” CT data at process block  150 . In the context of noise modeling and reconstruction, because the exact analytical formula of noise distribution is not readily available, one alternative for obtaining full-dose CT data is to reconstruct noisy data using the reconstruction algorithm on the scanner. However, other alternatives are provided hereafter. 
         [0035]    At process block  152 , a noise-insertion tool in accordance with the present invention is applied. As will be described, the present invention provides a highly-accurate “noise-insertion” tool that can be used with “full-dose” scans to simulate “reduced-dose” scans, based on knowledge of the physical characteristics of the scanners. 
         [0036]    The noise model used in this noise insertion tool may incorporate the effects of the bowtie filter, automatic exposure control, and electronic noise. Although most CT detectors in current operation are not a photon-counting (PC) elements, but so-called energy integrating detectors that generate a signal proportional to the total energy deposited in the detector, a photon-counting (PC) model is still a satisfactory approximation and maybe used for characterizing noise properties of the CT data. More accurate noise models for energy-integrating detector systems may also be used, such as the compound Poisson model that takes into account the polychromatic x-ray beam and energy integration. The actual residual error introduced by a PC model is only a few percent for typical photon flux level in clinical CT protocols. The impact from the bowtie filter and tube current modulation on noise characteristics of CT data is more significant than the noise model itself. Therefore, for simplicity, a PC model and can be considered to include the effect of a bowtie filter and tube current modulation. 
         [0037]    The effect of the bowtie filter may be characterized by measuring a map of noise-equivalent number of photons along the detector row from a set of air scans. The tube current modulation may be included by extracting the reference signal from each projection angle. The electronic noise may be included in the noise model and calibrated from a set of low-dose scans. This powerful technique accesses and manipulates the raw CT projection data. The noise insertion tool enables the effective acquisition reduced-dose scans without having to re-expose patients and eliminates uncertainty in the results due to scan-to-scan variation. 
         [0038]    Accurate noise distributions in image space can be created at process block  154  by taking the difference of the full-dose CT data and the low-dose images simulated using the noise-insertion tool, which is an instantiation (a specific instance) of noise that is distributed according to the noise model assumed in the noise insertion (and is proportional to it by a known scaling factor). The noise distribution can be determined with such difference data sets, by generating many (for example, 100) different noise instantiations of a low-dose image. Accordingly, at process block  156 , a noise map is yielded that shows the noise level at each pixel at a very high resolution. This noise map can then be used in an NLM filtering process applied at process block  158  to reduce noise. As will be described below, the NLM filtering process applied at process block  158  may be an adaptive NLM filtering process in accordance with the present invention. 
         [0039]    Specifically, NLM may utilize an estimate of the noise level in the data. However, in CT the noise level varies within and across slices, often by 2× within a slice and as much as, for example, 3 times across slices. This implies that NLM denoising based on a single noise level may be too weak in some places (accomplishing little), too strong in others (blurring fine detail), or both. Therefore, the NLM mechanism has been modified to adapt to the local noise level. This is accomplished by an NLM algorithm that is specifically designed to be adaptive, but that adds little computational cost. This modified NML algorithm, adapting to the local noise level, is referred to herein as an adaptive NLM algorithm or process and is very effective at handling the widely different noise levels in different slices or within a slice. 
         [0040]    As described above, the denoising may be based on a noise map, which is effective at handling the widely different noise levels in different slices or within a slice. However, as explained above, this may rely on a map of the local noise level, which in turn may rely upon developing a way to efficiently estimate such a map of the local noise level in CT data. To do so, the image noise distribution can be estimated or calculated using many different approaches. 
         [0041]    One approach is through Monte Carlo simulation. Since the noise contained in each reconstructed image (volume) is one single realization, the measurement of noise in small neighborhood pixels based on one reconstructed image (volume) may result in substantial errors, especially in heterogeneous regions with complicated anatomical structures. One could repeat scans multiple times for the same object and then calculate the statistical information from reconstructed images, which is ideal but almost impossible to implement in practice. 
         [0042]    One alternative is to simulate multiple realizations of CT data and reconstruct multiple realizations of CT images, which can be achieved by virtually projecting the reconstructed images into the CT data domain, then adding simulated noise multiple times and reconstructing the corresponding images for each noise simulation. This Monte-Carlo type method to calculate a noise map requires a large number of repeated noise simulations and reconstructions, which is time consuming, and the results may still suffer from statistical fluctuation due to practical limits on the number of calculations. 
         [0043]    Another approach is to derive the noise distribution analytically by propagating a noise model through the reconstruction algorithms. This method can be used in fan-beam CT, where variance and covariance at each location of image space were analytically derived, assuming a simple CT noise model and can be extended beyond fan-beam CT. In multi-slice helical CT, given the analytical formula of the reconstruction algorithms and exact knowledge of noise properties of CT data, in principle, the noise on the reconstructed images can be derived. However, there are two obstacles to practical implementation. First, the image reconstruction algorithms implemented in the CT scanner vary significantly among different manufacturers and scanner models, and they usually are not available to the CT users. Second, the noise properties in CT data before reconstruction can be estimated if the original raw data is available, but for an image-based method that aims to denoise images without the need to access CT raw data, obtaining the noise information in CT data can be challenging. These issues, of course, are negated when the present invention is integrated with a given CT system or manufacturing line. 
         [0044]    Nevertheless, as described above, an approximate method to estimate the noise map distribution in CT images can be used that does not require the access to CT raw data and is computationally efficient. A basic process includes (1) calculating the linear attenuation coefficient from the CT image; (2) generating CT sinogram data using a virtual CT geometry; (3) estimating the noise distribution of the sinogram data, incorporating the effect of the bowtie filter and automatic tube current modulation; and (4) applying the analytical formula to reconstruct the noise map in the final reconstructed images. Step (1) is quite common to CT imaging and, steps (2)-(4) are further described below. 
         [0045]    As for the generation of CT sinogram data, in principle, this requires an accurate knowledge of the CT acquisition geometry. For simplicity, a 2D fan-beam geometry, with fan-angle and focal length consistent with the clinical scanner or other geometry, can be used. A standard ray-driven or distance-driven forward projection method can be employed to generate the CT sinogram. 
         [0046]    When addressing noise modeling in sinogram data, although common CT detectors are generally energy integrating and not photon-counting elements, and, thus, generate a signal proportional to the total energy deposited in the detector, a photon-counting model is still a good approximation of quantum noise and is widely used for characterizing noise properties of CT data. It is known that the bowtie filter may have a greater effect on the noise characteristics of CT data than the noise model itself. Therefore, for simplicity, a photon-counting model may be used, and the effect of bowtie filter and tube current modulation considered. 
         [0047]    The effect of the bowtie filter can be characterized by measuring a map of noise-equivalent number of photons along the detector row from a set of air scans, such as illustrated in  FIG. 10 . The tube current modulation can be estimated based on the attenuation level along each projection angle and modulation strategy described in, for example, Gies et al. 1999. Therefore, the incident number of photons is a function of both detector bin index and projection angle. 
         [0048]    Turning to the analytical calculation of noise in reconstructed images, the derivation of the analytical formula of noise variance and covariance in the reconstructed images generally requires an accurate knowledge of reconstruction algorithms, which typically involve a rebinning process to convert cone-beam data to quasi-parallel-beam data and a weighted 3D filtered backprojection (FBP) process. Due to the complicated numerical operations in the reconstruction process, an accurate derivation of noise in the final image may be difficult. For example, it is noted that an accurate calculation of a noise map through multiple realizations of noise may not be feasible in clinical settings. Alternatively, a single instantiation of noise can be analyzed by calculating the standard deviation over small neighborhoods to get an approximate, smoothed noise map. For the purpose of denoising using an NLM filter, this approximation of the noise map may already be sufficient, as noise in CT images varies quite smoothly in the image space. Although less computationally intensive, one single instantiation of noise may still be impractical to perform within the clinical workflow, and requires access to the raw data, which is not available to the general user. Hence, the present invention provides a system and method that can make a reasonable approximation to the noise map quickly, and without relying on the raw data. Rather, the system and method may utilize the image data alone. 
         [0049]    For the purpose of image-based NLM denoising adaptive to local noise level, it is sufficient to assume a simple CT geometry and reconstruction process. Therefore, the analytical noise map may be calculated based on a simple 2D fan-beam geometry and a rebinning FBP reconstruction. If desired for further simplification and efficiency, the correlation introduced in the rebinning step may also neglected. These simplifications still yield a reasonably accurate noise map estimate, but can be implemented very efficiently, which is important in clinical use of the technique. The analytical formula is similar to those described in Pan et al. (Pan, et al. “Image reconstruction with shift-variant filtration and its implication for noise and resolution properties in fan-beam computed tomography.” Med Phys 30(4): 590-600.) and Wunderlich et al. (Wunderlich, A et al. “Image covariance and lesion detectability in direct fan-beam x-ray computed tomography.” Phys Med Biol 53(10): 2471-93.), which are incorporated herein by reference in their entirety. 
         [0050]    Simply performing a 2D fan-beam x-ray projection on individual slices of the image (ignoring the true 3D cone-beam nature of the acquisition), estimating noise based on photon statistics that incorporate some of the important physical effects (in particular, the bowtie filter and automatic tube current modulation), and using the analytical formula to estimate the noise map in final images can lead to a good approximation to the true noise map. This approach is highly parallelizable and can be made computationally efficient. Since the noise map varies smoothly and can utilize a reasonable approximation, it is possible to be performed only once every several slices. 
         [0051]    Referring to  FIG. 3 , the steps of a process for approximating a noise map without the need for the above-described intensive procedure or access to raw data are illustrated. First, at process block  160 , a 2D Radon transform is performed on individual slices of the image (ignoring the true 3D cone-beam nature of the acquisition in the case of a cone-beam acquisition). At process block  162 , noise is inserted based on photon statistics that incorporate some of the important physical effects experienced using CT imaging systems, such as effects caused by the bowtie filter and automatic tube current modulation. Finally, at process block  164 , an image at a simulated dose is reconstructed, for example, using the filtered-backprojection (FBP) method to provide a fairly good approximation to the true noise map obtained with the intensive procedure described above. Hence, the process described above with respect to  FIG. 3  can be used to provide a noise map estimate, thereby substituting the potentially-burdensome process steps of  FIG. 2  described above with respect to process blocks  154  and  156 . It should be noted that the map of local noise level estimated from the above methods can also be used in many other filters to improve the noise reduction, and is not just limited to NLM filters, such as applied at process block  158  of  FIG. 2 . 
         [0052]    To implement the above-described modeling, a number of constructs and models are provided. First, consider mechanisms for incorporating the effect of bowtie filter and automatic exposure control (AEC). 
         [0053]    Considering the bowtie filter, it is recognized that a bowtie filter is usually used in clinical CT scanners to reduce the incident x-ray intensity in the peripheral region so that the radiation dose to the patient, especially the skin dose, can be minimized. As a consequence, the x-ray intensity incident to the patient is highly non-uniform across the fan-beam, which will affect the noise properties in the measured CT data. The effect of the bowtie filter can be quantified by measuring the variance of the transmission from an air scan. The inverse of the variance is the noise-equivalent quanta, which can be used to estimate the incident number of photons across the x-ray beam, as will be explained and given below with respect to Eqn. 8. 
         [0054]    For a given attenuating ray path in the imaged subject, denote the incident and the penetrated photon numbers as N 0 (k,l,m) and N(k,l,m), respectively, where k and l denote the index of detector bins along axial and longitudinal directions, respectively, and m denotes the index of projection angle. In the presence of noise, the measured data should be considered as a stochastic process. Ideally the line integral along the attenuating path is given by: 
         [0000]        P   i =−ln( N   i   /N   0i )   Eqn. 1.
 
         [0055]    Herein, for expression simplicity, a single discrete index, I, is used to represent the data index (k,l,m). A bold letter and the corresponding normal letter denote a stochastic process and its mean, respectively. 
         [0056]    Assuming that data collected on each detector bin is uncorrelated, it can be shown that, to a very good approximation that the mean of P is −ln(N i /N 0i ) and the covariance of P i  is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0057]    where δ ii′  denotes the Kronecker delta function. This model is consistent with the noise model obtained from repeated measurements on a CT scanner. The scaling factor included in traditional models, such as included in Harrison H. Barrett and W. Swindell, “Radiological Imaging: The Theory of Image Formation, Detection, and Processing,” (1981) and J. Wang, T. Li, H. Lu and Z. Liang, “Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography,” IEEE Trans Med Imaging. 25, 1272-83 (2006), which are incorporated herein by reference, is incorporated in Eqn. 2, which can be determined experimentally to incorporate the effect of bowtie filter and AEC, as will be described below. 
         [0058]    For a given tube potential and detector collimation, the data measured with the original tube current setting can be expressed as P A =−ln(N A /N 0A ), where N 0A  and N A  are the incident and penetrated number of photons along a given ray path indexed by i, respectively, and N 0A  is proportional to the value of the tube current setting, expressed as tube current (mA), tube current time product (mAs), or effective mAs (mAs/pitch). Herein, the index i will be neglected for simplicity. Under typical clinical conditions, the detected number of photons N A  exceeds 20 and the measured data can thus be considered normally distributed which can be expressed as: 
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         [0059]    where p is the mean value of the data, and x a normally distributed stochastic process with a zero mean and a unit variance. If the tube current setting is reduced to a lower level with a scaling factor of a, 0&lt;a&lt;1, the corresponding incident number of photons is N 0B =aN 0A  and the measured data can be expressed as: 
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                     A 
                   
                   = 
                   
                     
                       P 
                       + 
                       
                         
                           1 
                           
                             
                               N 
                               A 
                             
                           
                         
                         · 
                         x 
                       
                     
                     = 
                     
                       P 
                       + 
                       
                         
                           
                             
                               1 
                               
                                 
                                   aN 
                                   
                                     0 
                                      
                                     A 
                                   
                                 
                                  
                                 
                                   exp 
                                    
                                   
                                     ( 
                                     
                                       - 
                                       P 
                                     
                                     ) 
                                   
                                 
                               
                             
                             · 
                             x 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   4. 
                 
               
             
           
         
       
     
         [0060]    It should be noted that the true value of p is unknown. So P B  is also unknown without a direct measurement. However, if the data P A  measured at a higher tube current setting is available, then one can obtain an approximation of Pg by adding noise to P A . The level of noise added will have to make the simulated data {tilde over (P)} B  to have the same mean a standard deviation as P B . The following expression satisfies this requirement: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       ~ 
                     
                     B 
                   
                   = 
                   
                     
                       P 
                       A 
                     
                     + 
                     
                       
                         
                           
                             
                               1 
                               
                                 N 
                                 B 
                               
                             
                             - 
                             
                               
                                 1 
                                 
                                   N 
                                   A 
                                 
                               
                               · 
                               x 
                             
                           
                           = 
                           
                             
                               P 
                               A 
                             
                             + 
                           
                         
                       
                        
                       
                         
                           
                             ( 
                             
                               
                                 1 
                                 
                                   N 
                                   
                                     0 
                                      
                                     B 
                                   
                                 
                               
                               - 
                               
                                 1 
                                 
                                   N 
                                   
                                     0 
                                      
                                     A 
                                   
                                 
                               
                             
                             ) 
                           
                           · 
                           exp 
                         
                       
                        
                       
                         
                           ( 
                           P 
                           ) 
                         
                         · 
                         
                           x 
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   5. 
                 
               
             
           
         
       
     
         [0061]    Because P A  is acquired with a higher tube current setting, one can use P A  to approximately represent the true value P and Eqn. 5 can be approximately expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             ~ 
                           
                           B 
                         
                         ≈ 
                           
                          
                         
                           
                             P 
                             A 
                           
                           + 
                           
                             
                               
                                 
                                   
                                     1 
                                     
                                       N 
                                       B 
                                     
                                   
                                   - 
                                   
                                     
                                       1 
                                       
                                         N 
                                         A 
                                       
                                     
                                     · 
                                     exp 
                                   
                                 
                                 = 
                                 
                                   ( 
                                   
                                     P 
                                     A 
                                   
                                   ) 
                                 
                               
                             
                             · 
                             x 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                             A 
                           
                           + 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         1 
                                         - 
                                         a 
                                       
                                       a 
                                     
                                     · 
                                     
                                       
                                         exp 
                                          
                                         
                                           ( 
                                           
                                             P 
                                             A 
                                           
                                           ) 
                                         
                                       
                                       
                                         N 
                                         
                                           0 
                                            
                                           A 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                               
                             
                              
                             
                               x 
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   6. 
                 
               
             
           
         
       
     
         [0062]    As can be seen from Eqn. 6, in order to simulate the CT data with a reduced mAs setting from the existing data acquired with a higher mAs setting (N 0B =aN 0A , 0&lt;a&lt;1), one has to determine the incident number of photons, N 0A , in the existing data along each ray path. 
         [0063]    The incident number of photons can be determined in terms of the number of photons that provides the same noise as in the measurement if assuming a quantum limit condition. An example of such a method is suggested in B. R. Whiting, P. Massoumzadeh, O. A. Earl, J. A. O&#39;Sullivan, D. L. Snyder and J. F. Williamson, “Properties of preprocessed sinogram data in x-ray computed tomography,” Med Phys. 33, 3290-303 (2006), which is incorporated herein by reference, to estimate the noise-equivalent quanta. 
         [0064]    The variance of the transmission data is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     var 
                      
                     
                       { 
                       
                         exp 
                          
                         
                           ( 
                           
                             - 
                             P 
                           
                           ) 
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       var 
                        
                       
                         { 
                         
                           N 
                           
                             N 
                             0 
                           
                         
                         } 
                       
                     
                     ≈ 
                     
                       
                         N 
                         
                           N 
                           0 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   7. 
                 
               
             
           
         
       
     
         [0065]    Therefore, for air scan the variance of the transmission data is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     var 
                      
                     
                       { 
                       
                         exp 
                          
                         
                           ( 
                           
                             - 
                             
                               P 
                               air 
                             
                           
                           ) 
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       1 
                       
                         N 
                         0 
                       
                     
                     . 
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   8. 
                 
               
             
           
         
       
     
         [0066]    One can perform an air scan and calculate the variance of the transmission data to obtain the noise-equivalent incident quanta at a given mAs level. The incident number of photons at other mAs levels can be readily derived based on this calibration. 
         [0067]    At each angle, the x-ray projection covers a 2D detector area. Along each detector row, the use of the bowtie filter changes the incident number of photons. In addition, the tube current modulation is often used, which changes the incident number of photons for different projection angles. Therefore, to quantify the incident number photons, one should incorporate both of these two effects. 
         [0068]    Turing now to AEC, it is noted that AEC is widely used for dose reduction in CT. Referring now to  FIG. 4 , one example of AEC is illustrated with respect to a chest/abdomen/pelvis exam. CAREDose4D, the AEC software on Siemens&#39; CT scanners, was used during the exemplary exam used to generate the data reflected in  FIG. 4 . The curve represents the tube current as a function of table position. As can be seen, the tube current oscillates during the gantry rotation in order to adapt to the attenuation of the patient along different orientations. This automatic tube current modulation leads to substantial changes in the incident x-ray intensity, which will also affect the noise characteristics of the CT data. This effect can be incorporated into the noise insertion algorithm by extracting the reference signal from each projection frame and then estimating the corresponding incident number of photons. The calibration curves determined from the bowtie filter can be used for this estimation. 
         [0069]    When the detected number of photons is low, the electronic noise cannot be neglected. A typical way to express the electronic noise is to assume that the variance of the detected number of photons follows: 
         [0000]      var{ N}=σ   e   2 +σ q   2   =N   e   +N,    Eqn. 9;
 
         [0070]    where σ q  represents the quantum noise, σ e  represents the standard deviation of the electronic noise floor of the detection system (the noise equivalent quanta of this noise floor is given by N e =σ e   2 ). Therefore, to the first order approximation, the variance of data P can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     var 
                      
                     
                       { 
                       P 
                       } 
                     
                   
                   = 
                   
                     
                       var 
                        
                       
                         { 
                         
                           ln 
                            
                           
                               
                           
                            
                           
                             
                               N 
                               0 
                             
                             N 
                           
                         
                         } 
                       
                     
                     ≈ 
                     
                       
                         
                           
                             N 
                             e 
                           
                           + 
                           N 
                         
                         
                           N 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   
                     Eqn 
                     . 
                     
                         
                     
                      
                     10 
                   
                   ; 
                 
               
             
           
         
       
     
         [0071]    Using the above equation, the data to approximate P B  by adding noise can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           B 
                         
                         = 
                           
                          
                         
                           
                             P 
                             A 
                           
                           + 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       1 
                                       
                                         N 
                                         B 
                                       
                                     
                                     - 
                                     
                                       1 
                                       
                                         N 
                                         A 
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         N 
                                         e 
                                       
                                       
                                         N 
                                         A 
                                       
                                     
                                     + 
                                     
                                       
                                         N 
                                         e 
                                       
                                       
                                         N 
                                         B 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                             x 
                           
                         
                       
                     
                   
                   
                     
                       
                         ≈ 
                           
                          
                         
                           
                             P 
                             A 
                           
                           + 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             1 
                                             
                                               N 
                                               
                                                 0 
                                                  
                                                 B 
                                               
                                             
                                           
                                           - 
                                           
                                             1 
                                             
                                               N 
                                               
                                                 0 
                                                  
                                                 A 
                                               
                                             
                                           
                                         
                                         ) 
                                       
                                       · 
                                       
                                         exp 
                                          
                                         
                                           ( 
                                           
                                             P 
                                             A 
                                           
                                           ) 
                                         
                                       
                                       · 
                                     
                                   
                                 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         + 
                                         
                                           
                                             N 
                                             e 
                                           
                                           
                                             
                                               N 
                                               
                                                 0 
                                                  
                                                 A 
                                               
                                             
                                              
                                             
                                               exp 
                                                
                                               
                                                 ( 
                                                 
                                                   - 
                                                   
                                                     P 
                                                     A 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             N 
                                             e 
                                           
                                           
                                             
                                               N 
                                               
                                                 0 
                                                  
                                                 B 
                                               
                                             
                                              
                                             
                                               exp 
                                                
                                               
                                                 ( 
                                                 
                                                   - 
                                                   
                                                     P 
                                                     A 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                              
                             x 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                             A 
                           
                           + 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         1 
                                         - 
                                         a 
                                       
                                       a 
                                     
                                     - 
                                     
                                       
                                         exp 
                                          
                                         
                                           ( 
                                           
                                             P 
                                             A 
                                           
                                           ) 
                                         
                                       
                                       
                                         N 
                                         
                                           0 
                                            
                                           A 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         
                                           1 
                                           + 
                                           a 
                                         
                                         a 
                                       
                                       · 
                                       
                                         
                                           
                                             N 
                                             e 
                                           
                                           · 
                                           
                                             exp 
                                              
                                             
                                               ( 
                                               
                                                 P 
                                                 A 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           N 
                                           
                                             0 
                                              
                                             A 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               x 
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   11. 
                 
               
             
           
         
       
     
         [0072]    In a typical clinical setting and a simulation at not too low of a dose, the impact of electronic noise is negligible. For example, when scanning an average-sized patient with a lateral width of 36 cm using a technique of 120 kV and 240 mAs, the number of detected photons in terms of noise equivalent quanta is about 1.4*10 5  per detector reading, and the detected number of photons is 1.4*10 5 *exp(−0.2 cm −1 *36 cm)=104. To simulate a 50 percent mAs level from the original 240 mAs, the detected number of photons is 52, which is still much higher than the electronic noise floor. Assuming N e  is 5, the electronic noise term only contributes about 6 percent of the overall noise. Only when the simulated mAs level is too low, and the detected number of photons is approaching the electronic noise floor, the term of electronic noise has a greater impact on the image noise. For example, if simulating a 30 mAs level from the original 240 mAs data for the same patient, the detected number of photons would be only about 12. In this situation, the contribution from electronic noise is much greater and cannot be neglected. 
         [0073]    The present invention provides a method for calibration and to estimate N e . A cylindrical water phantom with a diameter of 30 cm was scanned at four effective mAs levels (240, 120, 60, 30) on a 128 slice scanner (Definition Flash, Siemens Healthcare) with a tube potential of 120 kV and a detector collimation of 128×0.6 mm (z flying focal spot is on). Noise was introduced to the raw data acquired at 240 mAs based on Eqn. 11 to simulate the three lower mAs levels. Different values of N e  (0, 5, 10, 15) were used in simulation of each mAs level. Noise was measured on images from each acquired image and simulated image. A linear model was fitted based on the value of N e  and the noise measured in simulated images at each mAs level. The calibrated electronic noise floor was obtained by interpolation using the noise level measured on the actually acquired image in the fitted linear model. 
         [0074]    To validate the accuracy of the developed noise insertion tool in adult body CT, an anthropomorphic phantom was scanned on a dual-source 128 slice scanner (Definition Flash, Siemens Healthcare). The routine adult abdominal protocol was used (120 kV, quality reference mAs 240, 128×0.6 mm collimation, rotation time 0.5 second, helical pitch 0.6). AEC was on (CARE Dose4D, Siemens Healthcare). Images were reconstructed at B40 kernel with a slice thickness of 5 mm and an interval of 5 mm. In addition to the 240 mAs scan, three scans were also performed with lower mAs settings: 120, 60, and 30. All scans were from top of the shoulder to upper abdomen. The raw data of the 240 mAs scan were used to simulate the scans at 120, 60, and 30 mAs. Simulated raw data were uploaded to the scanner for image reconstruction using exactly the same parameters. Noise were measured every 4 cm from neck to abdomen on both acquired and simulated images. Regions of interest (ROI) on exactly the same location was used for noise measurement. Three ROIs per each slice were measured, yielding an average noise level per each slice. The noise level in the simulated low-dose images was compared with images measured at the corresponding dose levels. 
         [0075]    The noise insertion tool was validated in pediatric body CT using a series of acrylic cylindrical phantoms (8.7 cm, 10.1 cm, 12.7 cm, 14 cm in diameter) simulating the attenuation level of a newborn, 4 months, 1 year old, and 2 year old child. For each phantom, CT scans were acquired at three mAs levels: effective mAs 80, 40, and 20, with a tube potential of 120 kV, a rotation time of 0.33 second and a helical pitch of 0.5. The raw data from the 80 mAs level were processed by the noise insertion tool to simulate images acquired with 40 mAs and 20 mAs. The noise level was measured and compared on five ROIs (each averaged over 10 contiguous slices) in the simulated and measured low-dose images, respectively. 
         [0076]    Noise level only represents the first order noise properties of CT images. Diagnostic performance is also critically dependent on the spatial correlation of the noise. Hence, the NPS is a more complete representation of the noise properties of the image. In addition to the validation on noise level, the NPS in the simulated and acquired low-dose images were calculated and compared using the images of the 14 cm acrylic phantom acquired with the pediatric CT protocol. The calculation of NPS follows the process of 21 K. L. Boedeker, V. N. Cooper and M. F. McNitt-Gray, “Application of the noise power spectrum in modern diagnostic MDCT: part I. Measurement of noise power spectra and noise equivalent quanta,” Phys Med Biol. 52, 4027-46 (2007), which is incorporated herein by reference, and averaged over 20 images for each dose level. 
         [0077]    Under an approved Institutional Research Board (IRB) protocol, 24 adult chest/abdomen/pelvic cases and 105 pediatric body cases were collected. All adult cases were acquired with 120 kV and 240 quality reference mAs. The pediatric body cases were acquired following a weight-based kV/mAs technique chart, including 26 cases at 80 kV, 40 cases at 100 kV, and 39 cases at 120 kV. For each exam, we simulated three additional mAs levels (75 percent, 50 percent, and 25 percent for adults and 70 percent, 50 percent, and 30 percent for pediatric). Noise was measured on images of all four mAs levels for each case on exactly the same ROI. Three ROIs were measured and averaged for each case. The noise level measured on the simulated images was compared with the theoretical noise levels predicted from the full mAs image according to the inverse square root relation between noise and mAs level (noise is inversely proportional to the square root of the mAs level). A validation method, such as described in M. W. Ciaschini, E. M. Remer, M. E. Baker, M. Lieber and B. R. Herts, “Urinary calculi: radiation dose reduction of 50 percent and 75 percent at CT—effect on sensitivity,” Radiology. 251, 105-11 (2009) and incorporated herein by reference, was used due to the lack of ground truth at lower mAs levels in patient exams. 
         [0078]    Calibration of the Incident Number of Photons 
         [0079]    Air scans without any attenuating object inside the field of view were performed at different tube potentials (80 kV, 100 kV, 120 kV, 140 kV) at a mAs level of 40. Referring to  FIG. 5 , a scanning configuration  200  is illustrated that provides an x-ray source  202  with a bowtie filter  204  and flat filter  206  located within the beam field  208  to reduce the incident x-ray intensity in the peripheral region of the x-ray fan (or cone) beam  208 . Thus, as the beam  208  is directed toward the detector  210  and through the field subject  212  in the field of view, the periphery of the subject  212 , w  here the subject is less dense/thick, receives a reduced dose of radiation. 
         [0080]    Using Eqn. 8, the noise-equivalent quanta was calculated as the inverse of the variance of the transmission data. Referring to  FIG. 6 , the noise equivalent quanta as a function of detector bin along a single detector row is illustrated. By fitting the data with third-order Gaussian curves, a calibration curve of the incident number of photons for each of the four tube potentials was obtained. One can see that the incident number of the photons decreases by a factor of approximately 8 from center to peripheral region of the x-ray beam. For any other mAs level, these curves can be scaled to obtain the incident number of photons used in the noise insertion tool. 
         [0081]    Table I compares noise levels measured on 5 different ROI locations (each averaged over 10 contiguous slices) for acquired images, simulated images with bowtie filter, and simulated images without bowtie filter. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE I 
               
             
             
               
                   
                   
               
               
                   
                   
                 Simulated 
                 Simulated 
               
               
                   
                 Measured 
                 (bowtie) 
                 (no bowtie) 
               
             
          
           
               
                   
                 Noise 
                   
                 Noise 
                   
                 Noise 
                   
               
               
                   
                 level 
                 std. dev. 
                 level 
                 std. dev. 
                 level 
                 std. dev. 
               
               
                 ROI 
                 (HU) 
                 (HU) 
                 (HU) 
                 (HU) 
                 (HU) 
                 (HU) 
               
               
                   
               
             
          
           
               
                 1 
                 20.1 
                 0.3 
                 19.9 
                 0.2 
                 19.8 
                 0.2 
               
               
                 2 
                 16.2 
                 0.8 
                 16.3 
                 0.9 
                 15.1 
                 0.9 
               
               
                 3 
                 16.6 
                 0.9 
                 16.3 
                 0.6 
                 15.0 
                 0.7 
               
               
                 4 
                 17.6 
                 0.7 
                 17.5 
                 1.1 
                 15.9 
                 0.9 
               
               
                 5 
                 16.8 
                 0.8 
                 16.8 
                 0.7 
                 15.4 
                 0.7 
               
               
                 mean 
                 17.4 
                 0.7 
                 17.4 
                 0.7 
                 16.2 
                 0.7 
               
               
                   
               
             
          
         
       
     
         [0082]    It can be seen that the simulated image without bowtie filter had the same noise level in the center ROI, but lower estimated the noise in peripheral ROIs by 7 percent, compared to the acquired image. The simulated image with bowtie filter had the same noise level in both center and peripheral ROIs. 
         [0083]    Calibration of Electronic Noise 
         [0084]    An example image acquired using the cylindrical water phantom can be acquired and 5 ROIs designated for noise measurements. Noise, as a standard deviation of the CT number in each ROI, was averaged over 10 contiguous slices (totally 50 ROIs) for each of electronic noise level and mAs level. Referring to  FIG. 7 , bar plots of noise levels comparing noise in acquired images and simulated images when different electronic noise levels were used in the simulation. The electronic noise N e  was estimated to be 7.3, 9.7, and 7.6 for mAs levels of 120, 60, and 30, respectively. An average electronic noise of 8.2 was therefore obtained. 
         [0085]    Validation of the developed noise insertion tool using phantom studies 
         [0086]    Due to the use of AEC, the tube current varies during the scan, as shown in  FIG. 4 . The effect of tube current modulation was incorporated into the noise insertion tool in accordance with the present invention. Noise level as a function of slice location was plotted for each mAs setting and for both acquired and simulated images, as illustrated in  FIG. 8 . One can see that the noise measured on the simulated images matches excellently to that measured on the acquired images at each mAs setting and each slice location. The percentage error was 2.0 percent±1.5 percent, 1.9 percent±1.0 percent, and 2.1 percent±1.3 percent for the simulated images at 120 mAs (50 percent dose), 60 mAs (25 percent dose), and 30 mAs (12.5 percent dose), respectively. 
         [0087]    Pediatric Body CT 
         [0088]    The noise level and percent difference between the simulated and acquired low dose images were compared for all four phantom sizes. As shown in  FIG. 9 , the percent differences in noise level between the simulated and acquired low dose images were below 3.2 percent for all phantom sizes. 
         [0089]    Noise Power Spectra (NPS) 
         [0090]    In a comparison of NPS between simulated lower-dose images and measured lower-dose images, the peak noise power occurred at about 3 lp/cm and was maintained with different dose levels. The shape and magnitude of NPS from the simulated 40 mAs and 20 mAs images matched very closely with those from the measured 40 mAs and 20 mAs images. 
         [0091]    Validation of the Noise Insertion Tool Using Patient Cases 
         [0092]    Tables II and III show the differences between the noise measured in simulated images and theoretically predicted noise level at each mAs level for 105 pediatric body exams and 24 adult chest/abdomen/pelvic exams, respectively. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE II 
               
               
                   
                   
               
               
                   
                 mAs level* 
                 70% 
                 50% 
                 30% 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Average difference** 
                 3.5% 
                 6.1% 
                 9.4% 
               
               
                   
                 Standard deviation*** 
                 3.5% 
                 5.4% 
                 7.6% 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE III 
               
               
                   
                   
               
               
                   
                 mAs level* 
                 75% 
                 50% 
                 25% 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Average difference** 
                 2.0% 
                 4.6% 
                 9.7% 
               
               
                   
                 Standard deviation*** 
                 1.7% 
                 3.4% 
                 9.2% 
               
               
                   
                   
               
             
          
         
       
     
         [0093]    The noise difference increases with the decrease of the simulated mAs level, with an average percentage difference of 2.0 percent±1.7 percent, 4.6 percent±3.4 percent, and 9.7 percent±9.2 percent for adult exams when the simulated mAs level was 75 percent, 50 percent and 25 percent of the original level, respectively. The average percentage difference was 3.5 percent±3.5 percent, 6.1 percent±5.4 percent, and 9.4 percent±7.6 percent for pediatric exams when the simulated mAs level was 70 percent, 50 percent and 30 percent of the original level, respectively.  FIGS. 10 and 11  show two examples of low-dose simulation, one from a pediatric abdominal exam and the other from an adult chest exam. The higher percentage difference observed in patient cases than in phantom studies was probably due to the lack of the “ground truth” of noise level in lower-mAs patient exams. The inverse square root relation between noise and mAs was used to generate the “true” noise values at lower-mAs levels, which may have a small bias, especially when the simulated mAs level is low and the influence of electronic noise increases. 
         [0094]    The noise insertion methods of the present invention use a photon counting noise model, with the incident number of photons determined in terms of noise equivalent quanta measured in air scans. A unique method is used to incorporate the effect of electronic noise, which was calibrated by directly comparing the noise level in the simulated images with that in the acquired images at low dose levels. The methods were validated using both phantom and patient studies, and comparing both noise levels and noise spatial correlation with NPS. 
         [0095]    One difficulty of simulating very low-dose exams is the photon starvation artifacts. When the mAs level is too low for the scanned patient size, the detected number of photons may approach the electronic noise floor, resulting in some types of photon starvation artifacts in the actually acquired image (e.g. ripples or rings in the central region of the image, streakings in the shoulder region). In this situation, the inclusion of electronic noise in a simple form like Eqn. 11 may become insufficient. First, CT manufactures usually introduce additional non-linear filters on the measured data when the detected signal is low. This technique was to reduce the streaking artifacts in the non-uniformly attenuated region such as shoulder. In order to simulate accurately the noise properties in this situation, one has to have the access to the raw data prior to the non-linear filtering, which is not usually available, making the simulation of very low-dose images difficult.  FIG. 12  compares an acquired image and a simulated image at a very low dose level (80 kV, 25 percent of the original dose, CTDI vol =1.0 mGy) for an anthropomorphic phantom. One can see that, although the streaking artifacts in the shoulder region were simulated quite well, the simulated streakings have a sharper appearance than in the actually acquired image, which is probably due to the smoothing effect of the non-linear filter. Second, the photon starvation artifacts caused by very low dose and high attenuation are quite complicated. The proposed method does not appear to be able to simulate images in extremely low-dose situation. For extremely low dose level, the severe photon starvation artifacts appearing in the actually-acquired image cannot be simulated despite that the noise level is still similar. Because of these two reasons, the noise insertion tool should be used cautiously when the simulated dose level is too low that could result in severe photon starvation artifacts. In validation using the anthropomorphic phantom, a mAs level was simulated as low as 12.5 percent of the routine mAs level used clinically and still achieved an high accuracy within 2.1 percent. This tool has been applied in several different clinical areas, including pediatric body and head, adult abdomen, interventional, and brain perfusion. After clinical evaluation, a typical dose reduction was around 25 percent-50 percent compared to our clinical routine protocols. Therefore, the accuracy of developed tool is sufficient for most of the clinical need for optimizing CT scanning protocols. 
         [0096]    The noise insertion tool of the present invention may use a calibration for different scanner models and scanning modes when different bowtie filters or tube potentials are used. The calibration curve (noise equivalent quanta versus detector bins at a given mAs in air) at each scanning mode can be saved in a data library. In addition, the tool may use the access to CT raw data. 
         [0097]    A practical technique for simulating low-dose CT images from existing data acquired with a standard dose level has been developed. The technique incorporates the effect of bowtie filter, automatic tube current modulation, and electronic noise. Validation studies using both phantom and patient cases shows accurate simulation results on noise level distribution and spatial frequency content. This tool can be used to retrospectively optimize CT scanning techniques for specific diagnostic tasks. 
         [0098]    Finally, it should be noted that the map of local noise level estimated from the above methods can also be used in many other filters to improve the noise reduction, and is not just limited to NLM filters. The method can be adopted to utilize a simple approximation to analytically calculate the noise map. Other methods can also be implemented to calculate the noise map, including incorporation of realistic CT geometry and reconstruction algorithms. 
         [0099]    The present invention has been described in accordance with the embodiments shown, and one of ordinary skill in the art will readily recognize that there could be variations to the embodiments, and any variations would be within the spirit and scope of the present invention. Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the spirit and scope of the appended claims.