Patent Publication Number: US-11026642-B2

Title: Apparatuses and a method for artifact reduction in medical images using a neural network

Description:
TECHNICAL FIELD 
     This disclosure relates to using neural networks to reduce artifacts in reconstructed medical images. 
     BACKGROUND 
     The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure. 
     Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices (also referred to as sections) through a subject&#39;s body. A radiation source, such as an X-ray source, irradiates the body from one side. At least one detector on the opposite side of the body receives radiation transmitted through the body. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector. 
     A CT sinogram indicates attenuation through the body as a function of position along a detector array and as a function of the projection angle between the X-ray source and the detector array for various projection measurements. In a sinogram, the spatial dimensions refer to the position along the array of X-ray detectors. The time/angle dimension refers to the projection angle of X-rays, which changes as a function of time during a CT scan. The attenuation resulting from a portion of the imaged object (e.g., a vertebra) will trace out a sine wave around the vertical axis. Performing an inverse Radon transform—or any other image reconstruction method—reconstructs an image from the projection data in the sinogram. X-ray CT has found extensive clinical applications in cancer, heart, and brain imaging. In some X-ray CT scans (e.g., cone-beam CT using a large cone angle), the reconstructed images have imaging artifacts. These artifacts can degrade the image quality and impede clinical applications of the reconstructed images. Accordingly, better method for reducing the imaging artifacts are desired. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of this disclosure is provided by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
         FIG. 1A  shows an exemplary method  110  to form a training dataset and to train a neural network, according to an embodiment of the disclosure; 
         FIG. 1B  shows an exemplary method  150  to reduce imaging artifacts using a trained neural network, according to an embodiment of the disclosure; 
         FIG. 2A  shows an example of a feedforward neural network, according to an embodiment of the disclosure; 
         FIG. 2B  shows an example of a convolution neural network (CNN), according to an embodiment of the disclosure; 
         FIG. 2C  shows an example of implementing a convolution layer, according to an embodiment of the disclosure; 
         FIG. 2D  shows an example of a method to train a neural network, according to an embodiment of the disclosure; 
         FIG. 3  shows an example of a method to generate data in a training dataset, according to an embodiment of the disclosure; 
         FIG. 4A  shows an example of a coronal view of a reconstructed image from a cone-beam CT (CBCT) scan that exhibits a cone-beam artifact, according to an embodiment of the disclosure; 
         FIG. 4B  shows an example of an axial view of the reconstructed image from the CBCT scan, according to an embodiment of the disclosure; 
         FIG. 4C  shows an example of a coronal view of a reconstructed image from a helical CT scan that does not exhibit the cone-beam artifact, according to an embodiment of the disclosure; 
         FIG. 4D  shows an example of an axial view of the reconstructed image from the helical CT scan, according to an embodiment of the disclosure; 
         FIG. 5  shows an example of pixels in a large image down-sampled into four small sub-images, according to an embodiment of the disclosure; and 
         FIG. 6  shows a schematic of an implementation of a CT scanner, according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The apparatuses and methods described herein achieve several advantages over related methods. These advantages include: reducing computational time and hardware costs, and improving image quality of medical images, such as images generated by X-ray computed tomography. Further, the examples provided herein of applying these methods are non-limiting, and the methods described herein can benefit other medical imaging modalities such as single-photon emission computed tomography (SPECT), and the like, by adapting the framework proposed herein. Accordingly, the apparatuses and methods herein described herein are provided as non-limiting example implementations of the present disclosure. As will be understood by those skilled in the art, the present disclosure may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Accordingly, the detailed description is intended to be illustrative, but not limiting of the scope of the disclosure. The disclosure, including any readily discernible variants of the teachings herein, defines, in part, the scope of the foregoing claim terminology such that no inventive subject matter is dedicated to the public. 
     In some embodiments of CT, such as volumetric CT, to reduce imaging time and an X-ray dose, a relatively thick section (or a volume) of an object is scanned (i.e., imaged) in a single rotation of a CT source and with respect to the object OBJ being imaged. In some examples, volumetric CT, such as circular cone-beam CT (CBCT), is implemented using an X-ray beam that has a relatively larger cone angle (e.g., a cone angle that is greater than a predefined angle threshold) and scans a volume of an object in one scan. Accordingly, a three-dimensional (3D) image that shows internal features of the volume being imaged is reconstructed based on a signal from the detector. The signal corresponding to the detected radiation of the X-ray beam after having traversed the object OBJ being imaged is referred to as “projection data.” The reconstructed 3D image reconstructed from a CBCT scan can be susceptible to cone-beam artifacts, i.e., undesirable characteristics that degrade image quality due to a large cone angle of the X-ray beam. The cone-beam artifacts can be mitigated using a slower scanning method such as a helical scan with a small cone angle. Other imaging artifacts besides cone-beam artifacts can also result from various aspects of the san and reconstruction processes. 
     To mitigate imaging artifacts, an artificial neural network (often simplified as “neural network”), such as a deep neural network, a convolutional neural network (CNN), and the like, can be trained using pairs of images including an input image that exhibits the imaging artifacts and a target image that does not exhibit the imaging artifacts. The network is trained such that applying the input image to the neural network produces a result approximately matching the target image. Then the trained neural network can be used to reduce imaging artifacts associated with volumetric CT scans, such as cone-beam artifacts. 
     That is, the neural network is trained using a training dataset including artifact-exhibiting data and artifact-minimized data that has less imaging artifacts than the artifact-exhibiting data. In some embodiments, artifact-exhibiting data is obtained from corresponding artifact-minimized data using simulation (e.g., forward projecting the artifact-minimized data using a large cone angle configuration to generate the artifact-exhibiting data). 
     Referring now to the drawings, where like reference numerals designate identical or corresponding parts throughout the several views,  FIG. 1A  shows a method  110  to form a training dataset and to train a neural network according to an embodiment of the disclosure. The method  110  starts at S 111 , and proceeds to S 112 . 
     At S 112 , the training dataset having imaging artifacts associated with volumetric CT scans is obtained. In general, imaging artifacts refer to undesirable characteristics that degrade image quality. Imaging artifacts can be reduced using image processing. In some embodiments, imaging artifacts, such as cone-beam artifacts, occur due to a large cone angle of an X-ray beam used in a CBCT scan. A large cone angle refers to a cone angle that is greater than a predefined angle threshold, and a small cone angle refers to a cone angle that is less than or equal to the predefined angle threshold. For example, the predefined angle threshold can be determined empirically based on observations regarding how large the cone angles can become for a particular anatomical or diagnostic application before it becomes a hindrance to clinical practice. Cone-beam artifacts often arise because for some views of the CT scan the X-ray beam does not pass through certain volume pixels (also referred to as voxels) in the reconstructed image, resulting in insufficient data/sampling for these volume pixels to be properly reconstructed. Consequently, cone-beam artifacts, such as low-frequency shading artifacts, streaking cone-beam artifacts, and the like, can be observed in these under-sampled regions. 
     Often a 3D reconstructed image is viewed using two-dimensional slices in one of the axial, sagittal, or coronal planes. That is, 2D images can be used to illustrate different cross-sections (or views) of internal features of an object. For example, 2D images can have coronal views, sagittal views, axial views, and the like. In some embodiments, axial views are perpendicular to the axis of rotation, and coronal views and sagittal views are parallel to the axis of rotation. In some examples, imaging artifacts vary with different views. For example, cone-beam artifacts can be more pronounced in certain views, such as coronal and sagittal views, than other views, such as an axial view, as shown in  FIGS. 4A-4D . In some examples, a training dataset includes 2D images having coronal and sagittal views, 3D images, and the like. 
     In general, a training dataset includes artifact-exhibiting data and artifact-minimized data. In an example, artifact-exhibiting data have imaging artifacts above a certain threshold, and artifact-minimized data have imaging artifacts below the certain threshold. In some examples, artifact-exhibiting data is a reconstructed CT image referred to as an artifact-exhibiting image. In some examples, artifact-minimized data is a reconstructed CT image referred to as an artifact-minimized image. In some examples, artifact-exhibiting data and corresponding artifact-minimized data form a data pair, and imaging artifacts are more pronounced in the artifact-exhibiting data than in the respective artifact-minimized data. 
     In various embodiments, a training dataset can also be tailored to different CT scanning methods, protocols, applications, conditions, and the like, for example, to train various neural networks in reducing imaging artifacts associated with respective CT scanning methods, protocols, applications, conditions, and the like. As a result, the trained neural networks can be customized and tailored to certain CT scanning methods, protocols, applications, conditions, and the like. For example, a trained neural network can be tailored to reduce imaging artifacts associated with certain anatomical structures or region of a body being imaged. Further, a trained neural network is tailored to reduce cone-beam artifacts associated with circular CBCT scans that use an X-ray beam having the large cone angle. 
     Artifacts-exhibiting data and artifact-minimized data can be generated using any suitable methods. In some embodiments, artifact-exhibiting data and artifact-minimized data are obtained by scanning objects under different scanning conditions, protocols, and the like. In some embodiments, artifact-minimized data can be generated using a process, such as a scanning method, a protocol, and a suitable condition, that maintains imaging artifacts below a certain threshold, for example, using optimized scanning conditions, having a high X-ray dose, a small cone angle X-ray beam, and the like. On the other hand, artifact-exhibiting data can be obtained using scanning conditions exhibiting relatively large artifacts, such as an X-ray beam having a large cone angle, and the like. 
     In certain implementations, the artifact-exhibiting data is obtained by scanning an object using a circular CBCT scan with an X-ray beam having the large cone angle, and the corresponding artifact-minimized data are obtained by scanning the same object using a helical CT scan with an X-ray beam having the small cone angle. Accordingly, the images obtained using helical CT scans can have image artifacts below a certain threshold, making them effective as artifact-minimized data. 
     Additional image processing methods can be included in S 112  to reduce a training time in S 114 . For examples, certain imaging artifacts, such as cone-beam artifacts, have low-frequency components. According to aspects of the disclosure, an image where imaging artifacts vary slowly with respect to space can be down-sampled to obtain multiple sub-images, as described in  FIG. 5 . The sub-images can be used to form respective data pairs. 
     In some embodiments, artifact-exhibiting data, such as a 3D image having cone-beam artifacts, is obtained from corresponding artifact-minimized data using simulation, image processing, and the like. Alternatively, artifact-minimized data can also be obtained from corresponding artifact-exhibiting data using simulation, image processing, and the like. 
     In some examples, a neuronal network is trained using a training dataset, validated using a validation dataset, and further tested using a test dataset. Therefore, in some embodiments, additional datasets, such as a validation dataset and a test dataset, are formed from additional artifact-exhibiting data and artifact-minimized data. 
     At S 114 , the neural network is trained based on the training dataset obtained at S 112 . In some embodiments, the neural network is trained offline, and then stored in memory to be used later when a new CT scan is performed and artifact reduction is desired. 
     In general, a neural network can learn and perform a task from examples, such as a training dataset including artifact-exhibiting data and artifact-minimized data, without task specific instructions. A neural network can be based on a computational model including nodes. The nodes, also referred to as neurons, interconnected by connections, can perform computational tasks. In an embodiment, a neural network can be characterized by a computational model and parameters. In an example, the parameters can include weights and thresholds associated with connections and nodes in the neural network. 
     In an embodiment, a neural network can be organized in multiple layers where different layers can perform different kinds of computations. The multiple layers can include an input layer having input nodes, an output layer having output nodes, and hidden layers between the input layer and the output layer. In an embodiment, the input layer can receive an input signal originated from outside of the neural network. In an example, the input signal is artifact-exhibiting data such as an image having cone-beam artifacts. The output layer can send a result to outside of the neural network. In an example, the result is an image having reduced cone-beam artifacts. In some embodiments, a neural network can be a deep neural network that has, for example, a relatively larger number of hidden layers than that of a shallow neural network. In an example, a neural network can be a CNN. 
     In various embodiments, a computational model of a neural network can be determined by search algorithms, and the like. Subsequently, the neural network can be trained using examples related to a certain task, such as reducing image artifacts. As a result, the parameters are modified repetitively when additional examples are used. In an embodiment, a large number of examples can be organized into multiple independent datasets, such as a training dataset and a validation dataset, to train and validate a neural network to obtain an optimal neural network. 
     In an embodiment, neural networks having various computational models can be trained using multiple training methods based on a training dataset including data pairs. A data pair includes having an input signal, such as artifact-exhibiting data, and an expected output signal, such as artifact-minimized data. An input layer of a neural network can receive the input signal, and the neural network can subsequently generate a result via the output layer. The result can be compared with the expected output signal. The parameters of the neural network are modified or optimized to minimize a difference between the result and the expected output signal. 
     In some embodiments, the neural network is trained using the training dataset obtained in S 112  to optimize parameters of the neural network. Neural networks can be trained using respective training methods to have optimized parameters. An optimal neural network is obtained by further applying a validation dataset on the trained neural networks, analyzing the results and the expected output signals associated with the validation dataset. The optimal neural network can then be deployed to perform a certain task. In addition, performance of the optimal neural network can be further assessed by a test dataset. In an example, the test dataset is independent from other datasets, such as the training dataset and the validation dataset. 
     In some embodiments, the neural network can be repetitively trained when additional artifact-exhibiting data and artifact-minimized data are available. For example, steps S 112  and S 114  can be implemented repetitively. 
     In some embodiments, the neural network is trained to reduce imaging artifacts, such as cone-beam artifacts associated with volumetric CT scans including CBCT scans, when the training dataset includes artifact-exhibiting images and artifact-minimized images. The method  110  then proceeds to S 119 , and terminates. 
       FIG. 1B  shows a method  150  according to an embodiment of the disclosure. In some embodiments, the method  150  is used to reduce image artifacts, such as cone-beam artifacts, of an input image by using a suitable neural network, such as the neural network trained using the method  110 . The method  150  starts at S 151 , and proceeds to S 152 . 
     At S 152 , input data to the neural network is obtained. In an embodiment, the input data is an input image, a reconstructed CT image having imaging artifacts associated with volumetric CT scans, such as cone-beam artifacts. In some examples, the input image is a 3D image, for example, reconstructed from corresponding projection data obtained using a circular CBCT scan, a 2D image, such as a coronal view or a sagittal view of a respective 3D image having imaging artifacts, and the like. 
     In some embodiments, imaging artifacts of an original image have certain features. The original image can be processed based on the features to generate the input data to the neural network to make the method  150  more efficient. For example, the imaging artifacts vary slowly with respect to space, i.e., the imaging artifacts are dominated by low spatial frequency components. Therefore, the original image can be Fourier transformed into a spatial frequency domain and includes a low-frequency component and a high-frequency component. Further, the original image can be low pass filtered in the spatial frequency domain to obtain the low-frequency component. The low-frequency component is selected to be the input data to the neural network at S 152 . Further, the low-frequency component can be downsampled to decrease the size of the input data that is applied to the neural network at S 152 , improving the computational efficiency of training and then using the neural network at S 152 . That is, when input data is smaller (i.e., has fewer pixels), applying the input data to the neural network at S 152  can be performed using fewer computations. 
     In certain implementations, other methods of obtaining the low-frequency component can be used without departing from the spirit of the methods described herein, as would be understood by a person of ordinary skill in the art. For example, the low-frequency component can be generated by averaging (e.g., averaging N-by-M blocks) or by downsampling by factors of N and M in respective directions of the original image. In certain implementations N and M can be equal (e.g., in  FIG. 5  N=M=2). Once, the low-frequency component is generated the high-frequency component can be generated in various way, as would be understood by a person of ordinary skill in the art, including, e.g., by subtracting the low-frequency component from the original image. Thus, all of the information in the original image can be preserved in the combination of the low-frequency component together with the high-frequency component. When the artifacts are predominantly in the low-frequency component (e.g., in cone-beam artifacts), applying the low-frequency component, which is downsampled (e.g., by a factor N in a first direction and M in a second directions), to the neural network the artifact can be efficiently mitigated, and then the resolution of the original image can be restored by combining the result of the neural network  152  with the high-frequency component, which has not been applied to the neural network  152 . 
     At S 154 , a suitable neural network is determined to process the input data, such as an input image. In some examples, a neural network trained to reduce imaging artifacts associated with volumetric CT scans, such as cone-beam artifacts, is selected to process the input data. In some examples, as described above, neural networks can be customized and tailored to certain CT scanning methods, protocols, applications, conditions, and the like by using respective training datasets. Therefore, in some examples, the neural network is determined based on characteristics of the input data. In an example, a neural network trained with 3D images is selected to reduce imaging artifacts of the input data, such as a 3D image. In an example, a neural network trained with images having imaging artifacts that vary slowly with respect to space is selected to reduce imaging artifacts of the input data having similar property. 
     At S 156 , the input data is processed using the determined neural network and output data having reduced artifacts is generated. 
     At S 158 , an output image is obtained based on the output data. In various embodiments, the output data, such as a 2D or 3D image, can be further processed by suitable image processing methods to generate the output image. In some examples, as described in step S 152 , the original image is low pass filtered in the spatial frequency domain to obtain the low-frequency component that is processed by the neural network. Accordingly, at S 158 , the output data is combined with the corresponding high-frequency component of the original image to form the output image. 
     In some examples, step S 158  is omitted, and the output image is the output data. The method then proceeds to S 159 , and terminates. 
       FIG. 2A  shows an exemplary feedforward neural network  201  according to an embodiment of the disclosure. For example, the neural network  201  has N inputs, K hidden layers, and three outputs. Each layer is made up of nodes, and each node performs a weighted sum of the inputs and compares a result of the weighted sum to a threshold to generate an output (also referred to as a result). Neural networks make up a class of functions for which the members of the class are obtained by varying thresholds, connection weights, or specifics of the architecture such as the number of nodes and/or their connectivity. In an example, a relatively simple neural network, such as an autoencoder, has three layers. A deep neural network generally has more than three layers of neurons, and has as many outputs neurons as input neurons, where N, for example, is a number of pixels in an reconstructed image. In some examples, the connections between neurons store values called “weights” (also interchangeably referred to as “coefficients” or “weighting coefficients”) that manipulate data in the calculations. The outputs of the neural network depend on three types of parameters: (i) the interconnection pattern between the different layers of neurons, (ii) the learning process for updating the weights of the interconnections, and (iii) the activation function that converts a neuron&#39;s weighted input to the output activation. 
     Mathematically, a neuron&#39;s network function m(x) is defined as a composition of other functions n i (x), which can further be defined as a composition of other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between variables, as shown in  FIGS. 2A-2C . For example, the neural network can use a nonlinear weighted sum, m(x)=K(Σ i w i n i (x)), where K (commonly referred to as the activation function) is certain predefined function, such as the hyperbolic tangent. 
     In  FIG. 2A  (and similarly in  FIG. 2B ), the neurons are depicted by circles around a threshold function or circles. For the non-limiting example shown in  FIG. 2A , the inputs are depicted as circles around a linear function, and the arrows indicate directed connections between neurons. In certain implementations, the neural network trained in S 114  is a feedforward network as exemplified in  FIGS. 2A and 2B  (e.g., it can be represented as a directed acyclic graph). 
     The neural network operates to achieve a specific task, such as reducing imaging artifacts, by searching within the class of functions F to learn, using a set of observations, to find m*∈F which solves the specific task in certain optimal sense (e.g., the stopping criteria used in step S 260  in the method  200  described below). For example, in certain implementations, this can be achieved by defining a cost function C: F→  such that, for the optimal solution m*, C(m*)≤C(m)∀m∈F (i.e., no solution has a cost less than the cost of the optimal solution).   refers to the set of real numbers. The cost function C is a measure of how far away a particular solution is from an optimal solution to the problem to be solved (e.g., the error). Learning algorithms iteratively search through the solution space to find a function that has the smallest possible cost. In certain implementations, the cost is minimized over a sample of the data (i.e., the training dataset). 
       FIG. 2B  shows an exemplary CNN  202  according to an embodiment of the disclosure. In some embodiments, CNNs have beneficial properties for image processing, thus, are relevant for applications of reducing imaging artifacts. In various embodiments, CNNs use feed-forward neural networks where the connectivity pattern between neurons can represent convolutions in image processing. For example, CNNs can be used for image processing optimization by using multiple layers of small neuron collections which process portions of an input image, called “receptive fields”, also referred to as “perception fields.” The outputs of these collections can then tiled so that they overlap, to obtain a better representation of the original image. This processing pattern can be repeated over multiple layers having alternating convolution and pooling layers. 
       FIG. 2C  shows an example  203  of implementing a convolution layer according to an embodiment of the disclosure. Referring to  FIG. 2C , a 4×4 kernel  204  is applied to map values from an input layer representing a 2D image to a first hidden layer, which is a convolution layer. The kernel maps respective 4×4 pixel regions  204  to corresponding neurons  205  of the first hidden layer. In the non-limiting example illustrated in  FIG. 2C , for example, the receptive/perception field is 4 pixels by 4 pixels. 
     Following a convolutional layer, a CNN can include local and/or global pooling layers, which combine the outputs of neuron clusters in the convolution layers. Additionally, in certain implementations, the CNN can also include various combinations of convolutional and fully connected layers, with pointwise nonlinearity applied at the end of or after each layer. 
     CNNs have several advantages for image processing. To reduce the number of free parameters and improve generalization, a convolution operation on small regions of input is introduced. One significant advantage of certain implementations of CNNs is the use of shared weight in convolutional layers. Therefore, the same filter (weights bank) is used as the coefficients for each pixel in the layer, thus, reducing memory footprint and improving performance. Compared to other image-processing methods, CNNs advantageously use relatively little pre-processing. This means that the neural network is responsible for learning the filters that in traditional algorithms were hand-engineered. The lack of dependence on prior knowledge and human effort in designing features is a major advantage for CNNs. 
     In certain implementations, the neural network trained in S 114  includes multiple neural networks that are suitably connected to perform a task, such as reducing imaging artifacts. 
       FIG. 2D  shows a method  200  according to an embodiment of the disclosure. In some embodiments, the method  200  is an implementation of S 114  of the method  110  for training the neural network using the training dataset obtained in S 112 . In an example,  FIG. 2D  shows one implementation of supervised learning used to train the neural network in S 114  according to an embodiment of the disclosure. In supervised learning, a training dataset including artifact-exhibiting data and artifact-minimized data is obtained, and the neural network is iteratively updated to reduce the error, such that a result from the neural network based on the artifact-exhibiting data closely matches the artifact-minimized data. In other words, the neural network infers the mapping implied by the training dataset, and the cost function produces an error value related to the mismatch between the artifact-minimized data and the result produced by applying a current incarnation of the neural network to the artifact-exhibiting data. For example, in certain implementations, the cost function can use the mean-squared error to minimize the average squared error. In the case of a of multilayer perceptrons (MLP) neural network, the backpropagation algorithm can be used for training the neural network by minimizing the mean-squared-error-based cost function using a gradient descent method. 
     In some embodiments, training a neural network model refers to selecting one model from a set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost criterion (i.e., the error value calculated using the cost function). Generally, the neural network can be trained using any of numerous algorithms for training neural network models (e.g., by applying optimization theory and statistical estimation). 
     For example, the optimization method used in training neural networks can use some form of gradient descent, using backpropagation to compute the actual gradients. This is done by taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a gradient-related direction. The backpropagation training algorithm can be: a steepest descent method (e.g., with variable learning rate, with variable learning rate and momentum, and resilient backpropagation), a quasi-Newton method (e.g., Broyden-Fletcher-Goldfarb-Shannon, one step secant, and Levenberg-Marquardt), or a conjugate gradient method (e.g., Fletcher-Reeves update, Polak-Ribiére update, Powell-Beale restart, and scaled conjugate gradient). Additionally, evolutionary methods, such as gene expression programming, simulated annealing, expectation-maximization, non-parametric methods and particle swarm optimization, can also be used for training the neural networks. 
     Referring to  FIG. 2D , the method  200  starts at S 211 , and proceeds to S 210 . The training dataset can include an image exhibiting imaging artifacts. For example, an imaging artifact can arise from a certain method of reconstruction, or arise from a method used for acquiring projection data (e.g., a large-angle cone-beam scan), and the like. In some embodiments, the training dataset includes artifact-exhibiting data and artifact-minimized data. 
     At S 210 , a neural network being trained is initialized. In some examples, an initial guess is generated for coefficients of the neural network. For example, the initial guess can be based on a priori knowledge of an object being imaged. Additionally, the initial guess can be based on a neural network trained on a training dataset related to a different CT scan method. 
     At S 220 , an error (e.g., a cost function) is calculated between the artifact-minimized data and a result generated from the neural network based on the artifact-exhibiting data. The error can be calculated using any known cost function or distance measure between image (or projection data), including the cost functions described above. 
     At S 230 , a change in the error as a function of the change in the neural network can be calculated (e.g., an error gradient), and the change in the error can be used to select a direction and step size for a subsequent change to the weights/coefficients of the neural network. Calculating the gradient of the error in this manner is consistent with certain implementations of a gradient descent optimization method. In certain other implementations, as would be understood by one of ordinary skill in the art, this step can be omitted and/or substituted with another step in accordance with another optimization algorithm (e.g., a non-gradient descent optimization algorithm like simulated annealing or a genetic algorithm). 
     At S 240 , a new set of coefficients are determined for the neural network. For example, the weights/coefficients can be updated using the change calculated in S 230 , as in a gradient descent optimization method or an over-relaxation acceleration method. 
     At S 250 , a new error value is calculated using the updated weights/coefficients of the neural network. In various embodiments, a new error value is calculated between the artifact-minimized data and a new result generated by the updated neural network based on the artifact-exhibiting data. 
     At S 260 , predefined stopping criteria are used to determine whether the training of the neural network is complete. For example, the predefined stopping criteria can evaluate whether the new error and/or the total number of iterations performed exceed predefined values. For example, the stopping criteria can be satisfied if either the new error falls below a predefined threshold or if a maximum number of iterations is reached. When the stopping criteria is not satisfied, the method  200  will continue back to the start of the iterative loop by returning and repeating S 230  using the new weights and coefficients (the iterative loop includes steps S 230 , S 240 , S 250 , and S 260 ). When the stopping criteria are satisfied, the method  200  terminates at S 299 . 
     In addition to the implementation for error minimization shown in  FIG. 2D , the method  200  can use one of many other known minimization methods, including, e.g., local minimization methods, convex optimization methods, and global optimization methods. 
     When the cost function (e.g., the error) has local minima that are different from the global minimum, a robust stochastic optimization process is beneficial to find the global minimum of the cost function. Examples of optimization method for finding a local minimum can be one of a Nelder-Mead simplex method, a gradient-descent method, a Newton&#39;s method, a conjugate gradient method, a shooting method, or other known local optimization method. There are also many known methods for finding global minima including: genetic algorithms, simulated annealing, exhaustive searches, interval methods, and other conventional deterministic, stochastic, heuristic, and metaheuristic methods. In some embodiments, the above methods can be used to optimize the weights and coefficients of the neural network. Additionally, neural networks can be optimized using a back-propagation method. 
       FIG. 3  shows a method  300  according to an embodiment of the disclosure. In some embodiments, the method  300  is used to implement step S 112  in the method  110 . For example, the method  300  generates a training dataset including a data pair having artifact-exhibiting data and artifact-minimized data. The method  300  starts at S 301 , and proceeds to S 310 . 
     At S 310 , a first projection data is obtained. The first projection data represents radiation data obtained in one or more CT scans. In some embodiments, the first projection data is measured under optimal conditions, such as using helical CT scans having the small cone angle. 
     At S 320 , a first image is generated based on the first projection data, for example, by image reconstruction. In some embodiments, the first image is artifact-minimized data that has minimal imaging artifacts, such as below the certain threshold. In some examples, the first image is a 3D reconstructed image. In some examples, the first image is a 2D reconstructed image. In some examples, the first image is a 2D coronal view or a 2D sagittal view. In some examples, an intermediate 3D image is reconstructed from the first projection data. Referring to  FIGS. 4A-4D , the first image is obtained using certain view(s) that show more pronounced imaging artifacts, such as a coronal view, than other view(s), such as an axial view, of the intermediate 3D image, thus, the first image is a 2D image showing the coronal view. 
     The image reconstruction can be performed using a back-projection method, a filtered back-projection method, a Fourier-transform based image reconstruction method, an iterative image reconstruction method (e.g., algebraic reconstruction technique), a matrix inversion image reconstruction method, a statistical image reconstruction method, and the like. 
     At S 330 , a second projection data is generated from the first image. In some embodiments, the second projection data is generated using a forward projection method. In various examples, the second projection data is obtained using simulation under a simulation condition that can produce relatively large imaging artifacts, such as a circular CBCT scan configuration that uses an X-ray beam having the large cone angle. 
     In some examples, multiple second projection data are simulated from the same first image under different simulation conditions that can produce relatively large imaging artifacts. For example, the multiple second projection data can be simulated to represent various values of one or more scanning parameters. These scanning parameters can include, e.g., a scanning protocol, and a diagnostic application. In some cases, the different scanning parameters can correspond to different first images, such as when the scanning parameters are anatomic structure to be imaged or a diagnostic application. In certain implementations, the multiple second projection data are obtained using different cone angles that are greater than the angle threshold. Further, different neural networks can be optimized for specific values of the one or more scanning parameters. For example, a given neural network can be trained to be used for a first cone angle and a first anatomical structure to be imaged (e.g., a head). Another neural network can be trained to be used for the first cone angle and a second anatomical structure to be imaged (e.g., a torso). A third neural network can be trained to be used for a second cone angle and the first anatomical structure to be imaged, and so forth. For each neural network, the choice of the scanning parameters for the first images and the scanning parameters for the simulation of the corresponding second images will be chosen based on the designation of the neural network. 
     At S 340 , a second image is obtained based on the second projection data, for example, by image reconstruction. In some embodiments, the second image is artifact-exhibiting data that has relatively large imaging artifacts, such as above the certain threshold. In some examples, the second image has a same dimension, such as 2D, 3D, and the like, as that of the first image. In some examples, the second image has a same view, such as a coronal view, a sagittal view, and the like, as that of the first image. The image reconstruction can be similar or identical to the image reconstruction described in S 320 . 
     At S 350 , a training dataset is generated. In some embodiments, the training dataset includes the first image and the second image that form a data pair. In some embodiments, the training dataset includes the first image and multiple second images that correspond to the first image. For example, as discussed above, the same first image can be forward projected using different values for the scanning parameters, such as different cone angles, and each of these different values can be used to reconstruct a respective second image. In this case, each of the respective second images would be paired with the first image in a respective training dataset to train a neural network designated by the respective values of the scanning parameters. Further, steps S 310 , S 320 , S 330 , S 340 , and S 350  can be repeated to generate additional data pairs, each including a first image and a second image, and the like to be included in the training dataset. In some examples, a validation dataset and a testing dataset are generated using additional first images and respective second images. The method  300  proceeds to S 399 , and terminates. 
     In some embodiments, a neural network can also be trained using 2D images, for example, because training a neural network with 2D images can be faster. As described above, imaging artifacts vary with different views. For example, cone-beam artifacts can be more pronounced in certain views, such as coronal and sagittal views as compared with an axial view, as shown below in  FIGS. 4A-4D . In some examples, suitable views, such as coronal views and sagittal views that have relatively large imaging artifacts are included in the training dataset in S 112 . 
       FIGS. 4A-4D  show exemplary images  410 ,  415 ,  420 , and  425  according to an embodiment of the disclosure.  FIGS. 4A and 4B  show the first coronal view  410  and a second coronal view  415  of a first object, for example, a first region of a body. In some embodiments, the first coronal view  410  is generated under optimal imaging conditions using an X-ray beam having the small cone angle and corresponds to artifact-minimized data. The second coronal view  415  is generated using an X-ray beam having the large cone angle and corresponds to artifact-exhibiting data. For example, areas  411  and  412  illustrate pronounced cone-beam artifacts that are not detectable in the first coronal view  410 . 
       FIGS. 4C and 4D  show a first axial view  420  and a second axial view  425  of a second object, for example, a second region of a body. In some embodiments, the first axial view  420  is generated under optimal imaging conditions an X-ray beam having using the small cone angle. The second axial view  425  is generated using an X-ray beam having the large cone angle. For example, area  421  illustrates cone-beam shading artifacts that are not detectable in the first axial view  420 . Referring to  FIGS. 4B and 4D , however, the cone-beam artifacts illustrated by the areas  411  and  412  in the coronal view are more pronounced than the cone-beam artifacts illustrated by the area  421  in the axial view. According to embodiments of the disclosure, 2D coronal views, such as the first coronal view  410  and the second coronal view  415  corresponding to the artifact-minimized data and the artifact-exhibiting data are included in a training dataset in step S 112 . In some examples, the first axial view  420  and the second axial view  425  are excluded from a training dataset in step S 112 . Further, in some embodiments, 2D sagittal views corresponding to artifact-exhibiting data and artifact-minimized data are also included in a training dataset in step S 112 . 
     Additional image processing methods can be included, for example, in the methods  110  and  300  to reduce training time. Certain imaging artifacts, such as cone-beam artifacts, vary slowly with respect to space, i.e., have low spatial frequency components. When the neural network trained in the method  110  is a CNN, a relatively large receptive field is used, for example, to account for the low spatial frequency components. According to aspects of the disclosure, an image is split into multiple sub-images that have a smaller number of pixels while a receptive field of each sub-image is comparable to a receptive field of the image. In some examples, the image is down-sampled to obtain the multiple sub-images, as described below. The respective sub-images are included in a training dataset, such as the training dataset generated using the method  110 . 
       FIG. 5  shows a non-limiting example of pixels in an image  550  being down-sampled and subdivided into four smaller sub-images  521 - 524 , according to an embodiment of the disclosure. For example, image  550  can be a 2D slice of a reconstructed image in a sagittal or coronal plane. In  FIG. 5 , the image  550  is down-sampled by a factor  2  in a first direction and a factor  2  in the second direction. In general, image  550  can be down-sampled by a factor N in a first direction and a factor M in the second direction, in which case N×M sub-images would be generated. When the image  550  is to be applied to a CNN (e.g., to train the CNN), the pixels can be grouped into respective 2-by-2 blocks, such as the first block  551 , and the pixels within each block given an index from  1  to  4 . All of the pixels having the same index are combined to form respective sub-images. For example, the pixel  551 ( 1 ) from the pixel group  551  is shown in sub-image  521 , and the pixel  551 ( 2 ) from the pixel group  551  is shown in sub-image  522 . Further, the pixel  551 ( 3 ) from the pixel group  551  is shown in sub-image  523 , and the pixel  551 ( 4 ) from the pixel group  551  is shown in sub-image  524 . Accordingly, all of the information from image  550  is preserved in the sub-images  521 - 524 . 
     In addition to decreasing the number of pixels per sub-image by a factor of N×M (e.g., in  FIG. 5 , N=M=2), down-sampling also decreases the number of pixels per receptive field by a factor of N×M, resulting in a total decrease by a factor of N 2 ×M 2  for the number of multiplications to perform a convolutional layer on a sub-image as opposed to the original image. For example,  FIG. 5  shows a 6-by-6 receptive field  552  for image  550 . For sub-images  521 - 524 , however, the corresponding receptive fields  552 ( 1 )-( 4 ) each have dimensions of 3-by-3 (i.e., ¼ th  the number of pixels as in image  552 ). When each sub-image can be applied to a neural network for down-sampled image, much fewer calculations are required. Further, during training, the neural network can converge more quickly to the optimal weighting coefficients between layers. 
     Accordingly, the image  550  is down-sampled into the four sub-images  521 - 524  having a lower image resolution than an image resolution of the image  550 . In various embodiments, image resolution has a unit of mm 2  per pixel in a 2D image and mm 3  per pixel in a 3D image, where 1 mm is 1 millimeter. The sub-images  521 - 524  include the respective pixels indexed by 1, 2, 3, or 4. Referring to  FIG. 5 , a number of pixels in each second receptive field is ¼ of a number of pixels in the first receptive field  552 , thus, training a CNN with sub-images is faster. Note that the second receptive field  552  in the original image  550 , although including four time more pixels, represents a same physical area as is represented by each of the receptive field  552 ( 1 )-( 4 ) in the sub-images  521 - 524 . 
       FIG. 6  shows a schematic of an implementation of a CT scanner according to an embodiment of the disclosure. Referring to  FIG. 6 , a radiography gantry  500  is illustrated from a side view and further includes an X-ray tube  501 , an annular frame  502 , and a multi-row or two-dimensional-array-type X-ray detector  503 . The X-ray tube  501  and X-ray detector  503  are diametrically mounted across an object OBJ on the annular frame  502 , which is rotatably supported around a rotation axis RA (or an axis of rotation). A rotating unit  507  rotates the annular frame  502  at a high speed, such as 0.4 sec/rotation, while the object OBJ is being moved along the axis RA into or out of the illustrated page. 
     X-ray CT apparatuses include various types of apparatuses, e.g., a rotate/rotate-type apparatus in which an X-ray tube and X-ray detector rotate together around an object to be examined, and a stationary/rotate-type apparatus in which many detection elements are arrayed in the form of a ring or plane, and only an X-ray tube rotates around an object to be examined. The present disclosure can be applied to either type. The rotate/rotate type will be used as an example for purposes of clarity. 
     The multi-slice X-ray CT apparatus further includes a high voltage generator  509  that generates a tube voltage applied to the X-ray tube  501  through a slip ring  508  so that the X-ray tube  501  generates X-rays. The X-rays are emitted towards the object OBJ, whose cross sectional area is represented by a circle. For example, the X-ray tube  501  having an average X-ray energy during a first scan that is less than an average X-ray energy during a second scan. Thus, two or more scans can be obtained corresponding to different X-ray energies. The X-ray detector  503  is located at an opposite side from the X-ray tube  501  across the object OBJ for detecting the emitted X-rays that have transmitted through the object OBJ. The X-ray detector  503  further includes individual detector elements or units. 
     The CT apparatus further includes other devices for processing the detected signals from X-ray detector  503 . A data acquisition circuit or a Data Acquisition System (DAS)  504  converts a signal output from the X-ray detector  503  for each channel into a voltage signal, amplifies the signal, and further converts the signal into a digital signal. The X-ray detector  503  and the DAS  504  are configured to handle a predetermined total number of projections per rotation (TPPR). 
     The above-described data is sent to a preprocessing device  506 , which is housed in a console outside the radiography gantry  500  through a non-contact data transmitter  505 . The preprocessing device  506  performs certain corrections, such as sensitivity correction on the raw data. A memory  512  stores the resultant data, which is also called projection data at a stage immediately before reconstruction processing. The memory  512  is connected to a system controller  510  through a data/control bus  511 , together with a reconstruction device  514 , input device  515 , and display  516 . The system controller  510  controls a current regulator  513  that limits the current to a level sufficient for driving the CT system. 
     The detectors are rotated and/or fixed with respect to the patient among various generations of the CT scanner systems. In one implementation, the above-described CT system can be an example of a combined third-generation geometry and fourth-generation geometry system. In the third-generation system, the X-ray tube  501  and the X-ray detector  503  are diametrically mounted on the annular frame  502  and are rotated around the object OBJ as the annular frame  502  is rotated about the rotation axis RA. In the fourth-generation geometry system, the detectors are fixedly placed around the patient and an X-ray tube rotates around the patient. In an alternative embodiment, the radiography gantry  500  has multiple detectors arranged on the annular frame  502 , which is supported by a C-arm and a stand. 
     The memory  512  can store the measurement value representative of the irradiance of the X-rays at the X-ray detector unit  503 . Further, the memory  512  can store a dedicated program for executing, for example, various steps of the methods  110 ,  150 ,  200 , and  300  for training a neural network and reducing imaging artifacts. 
     The reconstruction device  514  can execute various steps of the methods  110 ,  150 ,  200 , and  300 . Further, reconstruction device  514  can execute pre-reconstruction processing image processing such as volume rendering processing and image difference processing as needed. 
     The pre-reconstruction processing of the projection data performed by the preprocessing device  506  can include correcting for detector calibrations, detector nonlinearities, and polar effects, for example. 
     Post-reconstruction processing performed by the reconstruction device  514  can include filtering and smoothing the image, volume rendering processing, and image difference processing as needed. The image reconstruction process can implement various of the steps of methods  110 ,  150 ,  200 , and  300  in addition to various CT image reconstruction methods. The reconstruction device  514  can use the memory to store, e.g., projection data, reconstructed images, calibration data and parameters, and computer programs. 
     The reconstruction device  514  can include a CPU (processing circuitry) that can be implemented as discrete logic gates, as an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Complex Programmable Logic Device (CPLD). An FPGA or CPLD implementation may be coded in VHDL, Verilog, or any other hardware description language and the code may be stored in an electronic memory directly within the FPGA or CPLD, or as a separate electronic memory. Further, the memory  512  can be non-volatile, such as ROM, EPROM, EEPROM or FLASH memory. The memory  512  can also be volatile, such as static or dynamic RAM, and a processor, such as a microcontroller or microprocessor, can be provided to manage the electronic memory as well as the interaction between the FPGA or CPLD and the memory. 
     Alternatively, the CPU in the reconstruction device  514  can execute a computer program including a set of computer-readable instructions that perform the functions described herein, the program being stored in any of the above-described non-transitory electronic memories and/or a hard disk drive, CD, DVD, FLASH drive or any other known storage media. Further, the computer-readable instructions may be provided as a utility application, background daemon, or component of an operating system, or combination thereof, executing in conjunction with a processor, such as a Xenon processor from Intel of America or an Opteron processor from AMD of America and an operating system, such as Microsoft VISTA, UNIX, Solaris, LINUX, Apple, MAC-OS and other operating systems known to those skilled in the art. Further, CPU can be implemented as multiple processors cooperatively working in parallel to perform the instructions. 
     In one implementation, the reconstructed images can be displayed on a display  516 . The display  516  can be an LCD display, CRT display, plasma display, OLED, LED or any other display known in the art. 
     The memory  512  can be a hard disk drive, CD-ROM drive, DVD drive, FLASH drive, RAM, ROM or any other electronic storage known in the art. 
     While certain implementations have been described, these implementations have been presented by way of example only, and are not intended to limit the teachings of this disclosure. Indeed, the novel methods, apparatuses and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods, apparatuses and systems described herein may be made without departing from the spirit of this disclosure.