Patent Publication Number: US-2015065854-A1

Title: Joint estimation of attenuation and activity information using emission data

Description:
BACKGROUND 
     Positron emission tomography (PET) finds use in generating images that represent a distribution of positron-emitting nuclides, for example, within a patient&#39;s body. During PET imaging, a radionuclide is injected into the patient. As the radionuclide decays, positrons are emitted that collide with electrons, resulting in an annihilation event, which converts the entire mass of the positron-electron pair into two 511 kilo-electron volt (keV) photons emitted in substantially opposite directions along a line of response (LOR). In a PET system, detectors placed along the LOR on a detector ring detect the annihilation photons. Particularly, the detectors detect a coincidence event if the photons arrive and are detected at the detector elements within a coincidence timing window. The PET system uses the detected coincidence information along with other acquired image data for ascertaining localized concentrations of the radionuclide for use in generating a functional diagnostic image. 
     However, during PET imaging, photon-electron interactions may result in attenuation of emitted photons, which in turn, may lead to degraded image quality and inaccurate PET quantitation. Accordingly, PET imaging is often combined with X-ray computed tomography (CT) imaging to correct for such attenuation. CT produces transmission data of high statistical quality, which often yields an essentially noise-free attenuation map. However, CT imaging may have limited soft-tissue contrast and involve administration of substantial radiation to a patient. 
     Accordingly, in certain imaging scenarios, non-radiation based imaging, such as magnetic resonance imaging (MRI) may be used in conjunction with PET imaging for generating high-quality images useful for diagnosis and/or treatment. To that end, MRI and PET scans may be performed sequentially in separate scanners or simultaneously in a combined PET/MRI scanner. The unmatched soft tissue contrast that MRI provides along with functional imaging options, such as spectroscopy and functional MRI, complements the molecular information that PET offers with high-sensitivity tracking of biomarkers. Particularly, simultaneous acquisition of PET and MRI data provides unique opportunities to study biochemical processes through fusion of complementary information from the orthogonal MRI and PET imaging modalities. 
     MRI, however, may not provide a direct transformation of magnetic resonance (MR) images into PET attenuation values. The MR images reflect distribution of hydrogen nuclei with relaxation properties rather than electron density, which is related to PET attenuation. Accordingly, certain conventional approaches employ a segmentation-based approach, where an MR image is segmented into a number of regions and then a predetermined attenuation value is assigned to each segment. Certain other approaches are based on an atlas that includes a template MR image and a corresponding attenuation map, where a patient-specific MR image is registered to the template MR image and the template attenuation map is warped using the same spatial transformation as used for the registration to produce a corresponding patient-specific attenuation map. Other approaches are drawn to joint estimation of PET attenuation and activity maps from PET emission projection data, where all voxels/pixels are initially unknown. 
     Although bones/metal implants and lungs/air have substantially different PET attenuation values, MRI typically does not discriminate well between bone/metal implants and air/lungs. Use of conventional segmentation-based approaches for estimation of PET attenuation and activity, thus, may result in inaccurate attenuation correction, particularly in and/or near bones and lungs. The atlas-based approaches may require sophisticated data processing techniques such as pattern recognition and machine learning to address significant inter-patient variation in anatomy particularly for patient body parts other than heads. Moreover, conventional joint estimation approaches for reconstructing all voxels/pixels in PET attenuation and activity maps from only PET emission projection data may result in cross-talk artifacts and incorrect scaling, thus leading to inaccurate attenuation correction, because of under-determinedness and ill-conditionedness of the corresponding inverse problem. 
     Further, in certain scenarios, MRI may provide only a truncated field of view (FOV) and may not provide information corresponding to extra-patient components such as beds and coils. The truncated part and the extra-patient components may contribute to photon attenuation, which may lead to degraded image quality and inaccurate PET quantitation. 
     BRIEF DESCRIPTION 
     Certain aspects of the present disclosure are drawn to methods, systems and non-transitory computer readable media for imaging are disclosed. To that end, emission projection data corresponding to a target region of a subject is acquired using an emission tomography system. Additionally, one or more magnetic resonance images of the target region are generated using a magnetic resonance imaging system operatively coupled to the emission tomography system. A partially-determined attenuation map is determined by identifying one or more regions in the partially-determined attenuation map with a designated confidence level based on the magnetic resonance images. Further, a complete attenuation map and/or a complete activity map are reconstructed from the emission projection data using the partially-determined attenuation map as a constraint. One or more images corresponding to the target region are then generated based on the partially-determined attenuation map, the complete attenuation map and/or the complete activity map. 
    
    
     
       DRAWINGS 
       These and other features and aspects of embodiments of the present technique will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a pictorial view of an embodiment of a hybrid PET/MRI system configured to obtain attenuation-corrected PET and PET/MR images, in accordance with an aspect of the present disclosure; 
         FIG. 2  is a flowchart depicting an exemplary method for enhanced tomographic imaging, in accordance with aspects of the present disclosure; 
         FIG. 3  is a schematic representation of an embodiment of an undetermined PET attenuation map; and 
         FIG. 4  is a schematic representation of an embodiment of an MR image; 
         FIG. 5  is a schematic representation of another embodiment of an MR image with one or more regions identified with a designated confidence level, in accordance with aspects of the present disclosure; 
         FIG. 6  is a schematic representation of an embodiment of a partially-determined attenuation map based on information derived from the regions identified from one or more MR images, in accordance with aspects of the present disclosure; 
         FIG. 7  is a schematic representation of embodiments of a true attenuation map and a true activity map; 
         FIG. 8  is a schematic representation of another embodiment of a partially-determined attenuation map, in accordance with aspects of the present disclosure; and 
         FIG. 9  is a schematic representation of embodiments of a complete attenuation map and a complete activity map, in accordance with aspects of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The following description presents exemplary systems and methods for attenuation correction in nuclear images using MR data. Particularly, embodiments illustrated hereinafter disclose hybrid PET/MRI systems and methods that allow for enhanced PET imaging by simultaneously generating an emission activity map and an attenuation map from emission data and a partially-determined attenuation map. 
     Although exemplary embodiments of the present technique are described in the context of correction of PET and/or PET/MR images, the approaches described herein are also applicable to attenuation correction and/or image modification in other modalities, such as single photon emission computed tomography (SPECT). Therefore, while hybrid PET/MR imaging is presently discussed, it should be noted that the disclosed techniques are also applicable to hybrid SPECT/MR, SPECT image modification and/or attenuation correction, and any other imaging modality in which attenuation correction or attenuation-based modifications may be desirable. Further, in addition to medical imaging, embodiments of the systems and methods discussed herein may be used in pharmacological and pre-clinical research for the development and evaluation of innovative tracer compounds. 
     It may also be noted that the embodiments of image data acquisition described herein may be performed sequentially, such as by first obtaining PET image data followed by the acquisition of MR image data, or vice versa. Alternatively, the image data acquisition may be performed substantially simultaneously via simultaneous acquisition of PET and MR image data. The acquisition of both types of image data may enable the generation of images having spatial resolution and structural data associated with MR scans, while also including functional data produced by PET scans. Accordingly, in certain implementations, a PET image produced from a given PET scan may be attenuation-corrected using MR data collected at substantially the same time as the PET scan. An exemplary environment that is suitable for practicing various implementations of the present disclosure is discussed in the following sections with reference to  FIG. 1 . 
       FIG. 1  illustrates an exemplary imaging system  100  for enhanced nuclear imaging of a subject of interest. In one embodiment, the system  100  corresponds to a hybrid PET/MR system configured to generate an emission activity map and an attenuation map from emission data and a partially-determined attenuation map. Although the embodiment, illustrated in  FIG. 1  illustrates an integrated PET/MR system, in certain embodiments, independent PET and MR systems may be employed for imaging the subject. 
     To that end, in one embodiment, the hybrid PET/MR imaging system  100  includes a scanner  102 , a system controller  104  and an operator interface  106  communicatively coupled to each other over a communications link and/or a communications network  107 . In certain embodiments, the system controller  104  may be configured to perform MR and PET imaging, for example, using imaging sequences capable of generating in-phase, out-of-phase, water, fat, and functional PET images. In one embodiment, the PET/MR system  100  may be configured to generate at least the MR images within the same repetition time (TR). Particularly, the PET/MR system  100  may be configured to perform sequences such as Liver Acquisition with Volume Acquisition (LAVA) and LAVA flex sequences, and/or use reconstruction techniques such as Dixon and/or Iterative Decomposition of water and fat with Echo Asymmetry and Least squares estimation (IDEAL) techniques. Additionally, in certain embodiments, the MRI contrast may be T1-weighted (T1w), proton density weighted (PDw), T2 weighted (T2w), and/or may be optimized for segmenting a particular tissue type and/or to avoid certain artifacts. 
     Although the embodiment illustrated in  FIG. 1  depicts a full body scanner  102 , in certain embodiments, the MRI system  100  may include any suitable MRI scanner based on specific imaging and/or examination requirements. Further, a presently contemplated configuration of the MRI system  100  is drawn to a horizontal cylindrical bore imaging system employing a superconducting primary field magnet assembly. Certain other embodiments, however, may employ various other system configurations based on specific imaging mandates. The MRI system  100 , for example, may include scanners employing vertical fields generated by superconducting magnets, permanent magnets and/or electromagnets. 
     Additionally, while  FIG. 1  illustrates a closed MRI system  100 , certain embodiments of the present disclosure may also be used in an open MRI system designed to allow access to a physician, such as during interventional imaging. It may also be noted that in certain embodiments, the MRI system  100  may include any suitable MRI scanner configuration in lieu of the full body scanner  102  illustrated in  FIG. 1  based on specific imaging and/or examination requirements. 
     Further, in certain embodiments, the scanner  102  may include a patient bore  108  into which a table  110  may be positioned for disposing the subject such as a patient  112  in a desired position for scanning. Moreover, the scanner  102  may also include a series of associated coils for imaging the patient  112 . Particularly, in one embodiment, the scanner  102  includes a primary magnet coil  114 , for example, energized via a power supply  116  for generating a primary magnetic field generally aligned with the patient bore  108 . The scanner  102  may further include a series of gradient coils  118 ,  120  and  122  grouped in a coil assembly for generating accurately controlled magnetic fields, the strength of which vary over a designated field of view (FOV) of the scanner  102 . 
     Particularly, the gradient coils  118 ,  120  and  122  may have different physical configurations adapted for different functions in the MRI system  100 . For example, in one embodiment, the gradient coils  118 ,  120  and  122  are configured to produce magnetic field gradients used for spatially encoding acquired signals. In certain embodiments, the gradient coils  118 ,  120  and  122  may have mutually orthogonal axes, allowing a linear field gradient to be imposed in any desired direction using an appropriate combination of the three gradient coils  118 ,  120  and  122 . The field gradient may then be employed for various functions such as slice selection, frequency encoding and/or phase encoding during MR imaging. 
     Further, the scanner  102  may include an RF coil  124  for generating RF pulses for exciting a gyromagnetic material of interest, typically bound in tissues (gyromagnetic tissue material) of the patient  112 . In certain embodiments, the RF coil  124  may also serve as a receiving coil. Accordingly, the RF coil  124  may be operationally coupled to transmit-receive circuitry  126  in passive and active modes for receiving emissions from the gyromagnetic tissue material and for applying RF excitation pulses, respectively. Alternatively, the MRI system  100  may include various configurations of receiving coils different from the RF coil  124 . Such receiving coils may include structures specifically adapted for target anatomies, such as head, knee and/or chest coil assemblies. Moreover, receiving coils may be provided in any suitable physical configuration, such as including phased array coils. 
     In certain embodiments, the system controller  104  controls operation of the associated MR coils for generating desired magnetic field and RF pulses. To that end, in one embodiment, the system controller  104  may include a pulse sequence generator  128 , timing circuitry  130  and a processing subsystem  132  for generating and controlling imaging gradient waveforms and RF pulse sequences employed during patient examination. In one embodiment, the system controller  104  may also include amplification circuitry  134  and interface circuitry  136  for controlling and interfacing between the pulse sequence generator  128  and the coils of the scanner  102 . The amplification circuitry  134  may include one or more amplifiers that process the imaging gradient waveforms for supplying desired drive current to each of the gradient coils  118 ,  120  and  122  in response to control signals received from the processing subsystem  132 . In certain embodiments, the amplification circuitry  134  may also amplify and couple the generated RF pulses to the RF coil  124  for transmission. 
     In one embodiment, the RF coil  124  receives response signals emitted by excited nuclei in the tissues of the patient  112 . To that end, the RF coil  124  may be tuned to an imaging resonant frequency of the patient nuclei, for example, to about 63.5 MHz for hydrogen in a 1.5 Tesla magnetic field. In such embodiments, where the RF coil  124  serves both to emit the RF excitation pulses and to receive MR response signals, the interface circuitry  136  may also include a switching device (not shown in  FIG. 1 ) for toggling the RF coil  124  between active/transmitting mode and passive/receiving mode. Additionally, the interface circuitry  136  may include additional amplification circuitry for driving the RF coil  124  and for amplifying the response signals for further processing. In certain embodiments, the amplified response signals may be transmitted to the processing subsystem  132  for determining information for use in image reconstruction. 
     To that end, the processing subsystem  132 , for example, may include one or more application-specific processors, graphical processing units (GPUs), digital signal processors (DSPs), microcomputers, microcontrollers, Application Specific Integrated Circuits (ASICs) and/or Field Programmable Gate Arrays (FPGAs). In one embodiment, the processing subsystem  132  may be configured to use a specific imaging protocol for customizing scan sequences and generating data indicative of the timing, strength and shape of the RF and gradient pulses produced. Additionally, the processing subsystem  132  may ascertain the timing and length of a data acquisition window in the imaging pulse sequence using the timing circuitry  130 . The processing subsystem  132  may then process the response signals emitted by excited patient nuclei in response to the RF pulses. 
     By way of example, in one embodiment, the processing subsystem  132  may be configured to demodulate, filter and/or digitize the response signals for determining the image reconstruction information. To that end, the processing subsystem  132  may be configured to apply analytical routines to the processed information for deriving features of interest, such as location of a stenosis and structural and/or functional parameters such as blood flow in the target ROI. The processing subsystem  132  may be configured to transmit this information to an image reconstruction unit  138  to allow reconstruction of desired images of the target ROI. Additionally, the processing subsystem  132  may be configured to receive and process patient data from a plurality of sensors (not shown in  FIG. 1 ), such as electrocardiogram (ECG) signals from electrodes attached to the patient  112  for display and/or storage. 
     Accordingly, in certain embodiments, the system controller  104  may further include a storage repository  140  for storing the acquired data, reconstructed images and/or information derived therefrom. The storage repository  140  may also store physical and logical axis configuration parameters, examination pulse sequence descriptions and/or programming routines for use during the scanning sequences implemented by the scanner  102 . In certain embodiments, the storage repository  140  may further include programming code for implementing one or more algorithms capable of performing PET image reconstruction based on acquired MR data in accordance with an aspect of the present disclosure. To that end, the storage repository  140  may include devices such as a hard disk drive, a floppy disk drive, a compact disk-read/write (CD-R/W) drive, a Digital Versatile Disc (DVD) drive, a flash drive and/or a solid-state storage device. 
     In one embodiment, the system controller  104  may include interface components  142  for exchanging the stored information such as scanning parameters and image data with the operator interface  106 , for example for use during PET and/or MR imaging. Further, in certain embodiments, the operator interface  106  may allow an operator  144  to specify commands and scanning parameters for use during the interventional procedure. To that end, the operator interface  106  may include at least one operator  144  to configure the system controller  104  to control imaging parameters such as table motion, patient and table orientation, and/or shape and timing of the RF pulse sequences. 
     Moreover, in certain embodiments, the operator interface  106  may also include output devices  148  such as a display  150  including one or more monitors and/or printers  152 . The display  150 , for example, may be integrated into wearable eyeglasses, or may be ceiling or cart mounted to allow the interventional practitioner  144  to observe the reconstructed images, data derived from the images and other relevant information such as scanning time throughout the procedure. In one embodiment, the display  150  includes an interactive user interface that may allow selection and display of scanning modes, FOV and prior exam data. The interactive user interface on the display  150  may also allow on-the-fly access to patient data such as respiration and heart rate, scanning parameters and selection of an ROI for subsequent imaging. 
     As previously noted, during a medical examination, MRI allows determination of structural and/or functional information of the target ROI for diagnosis and/or treatment. In certain embodiments, the structural information derived from MRI images may be used for determining attenuation coefficients for use in PET image reconstruction. To that end, the PET data may be acquired sequentially and/or substantially simultaneously with the MR data acquisition. Particularly, in one embodiment, a positron emitter or a radiotracer may be administered to the patient  112  that targets specific ROIs or tissues of the patient&#39;s body. 
     The PET/MRI system  100 , in certain embodiments, may include a detector ring assembly  154  disposed about a patient bore  108  configured to detect radiation events corresponding to the target ROI. The detector ring assembly  154  may include multiple detector rings that are spaced along the central axis to form the detector ring assembly  154 . The detector rings, in turn, may be formed of detector modules  156  that include, for example, a 6×6 array of individual bismuth germanate (BGO) detector crystals. The detector crystals detect gamma radiation emitted from a patient, and in response, produce photons. 
     In one embodiment, the array of detector crystals is positioned in front of a plurality of photomultiplier tubes (PMTs). The PMTs produce analog signals when a scintillation event occurs at one of the detector crystals, for example, when a gamma ray emitted from the patient is received by one of the detector crystals. Further, a set of acquisition circuits  158  in the PET/MRI system  100  receive the analog signals and generate corresponding digital signals indicative of the location and the energy associated with the detected radiation event. 
     Particularly, in one embodiment, the PET/MRI system  100  includes a data acquisition system (DAS)  160  that periodically samples the digital signals produced by the acquisition circuits  158 . The DAS  160 , in turn, includes event locator circuits  162  that assemble information corresponding to each valid radiation event into an event data packet. The event data packet, for example, includes a set of digital numbers that precisely indicate the time of the radiation event and the position of the detector crystal that detected the event. Further, the event locator circuits  162  communicate the assembled event data packets to a coincidence detector  164  for determining coincidence events. The coincidence detector  164  determines coincidence event pairs if time and location markers in two event data packets are within certain designated thresholds. 
     In certain embodiments, the PET/MRI system  100  stores the determined coincidence event pairs in the storage repository  140 . The storage repository  140 , in one embodiment, includes a sorter  166  to sort the coincidence events in a 3D projection plane format, for example, using a look-up table. Particularly, the sorter  166  orders the detected coincidence event data using one or more parameters such as radius or projection angles for storage. In one embodiment, the processing subsystem  132  processes the stored data to determine time-of-flight (TOF) and/or non-TOF information. The TOF information may allow the PET/MRI system  100  to estimate a point of origin of the electron-positron annihilation with greater accuracy, thus improving event localization. 
     In certain embodiment, the event localization information may be used to further enhance the quality of PET images reconstructed by the image reconstruction unit  138 . In one embodiment, the image reconstruction unit  138  may be an independent device communicatively coupled to the PET/MRI system  100 . In another embodiment, the image reconstruction unit  138  may be an integral part of the processing subsystem  132 . Alternatively, the processing subsystem  132  may perform one or more functions of the image reconstruction unit  138 , including generating one or more PET and/or MR images from the acquired data. 
     Conventional PET imaging entails reconstruction of a PET activity map that defines a spatial distribution of a radiotracer in the patient body based on the emitted 511 keV photons measured by detector modules  156 . The emitted photons that travel through different regions of the patient body or extra-patient components such as tissue, lungs, air, beds and/or MR coils, and thus experience different attenuations. Typically, these attenuation values are corrected for accurate PET quantitation in the activity maps by a segmentation-based approach and/or an atlas-based approach. However, as previously noted, such conventional approaches may result in inaccurate attenuation correction in and/or near bones, metal implants and lungs or may require very sophisticated data processing techniques. 
     Unlike such conventional approaches, the image reconstruction unit  138  may use embodiments of the present disclosure that allows joint estimation of an emission activity map and an attenuation map from emission data and a partially-determined attenuation map. The partially-determined attenuation map, in turn, may be determined based on acquired MR data. Particularly, in one embodiment, the partially-determined attenuation map may be determined by identifying high-confidence regions with known attenuation values such as water or fat tissue from MR images. The high-confidence regions may be identified, for example, using thresholding, segmentation, atlas-based methods, machine learning and/or using unconventional MR sequences such as ultra-short echo time (UTE) and/or zero echo time (ZTE), followed by assigning determined PET attenuation values to each identified region. 
     The partially-determined attenuation map and the acquired PET projection data may then be used for reconstructing both the complete emission activity map and the undetermined region of the attenuation map simultaneously. The PET activity map and the attenuation maps may then allow reconstruction of high quality TOF and/or non-TOF PET images and/or provide the operator  144  with corresponding diagnostic information. Further, the reconstructed images may be transmitted to one or more of the output devices  148 , such as a display, an audio and/or a video device, for example, coupled to the operator interface  106  in real-time or retrospectively. Communicating the image quality and/or diagnostic information allows a medical practitioner to assess a health condition of the patient  112  and whether values computed from the reconstructed image can be trusted, thus leading to a more informed diagnosis. 
     It may be noted that the specific arrangements depicted in  FIG. 1  are exemplary. Further, the PET/MRI system  100  may be configured or customized for additional functionality, different imaging applications and scanning protocols. Accordingly, in certain embodiments, the PET/MRI system may be coupled to multiple displays, printers, workstations, and/or similar devices located either locally or remotely, for example, within an institution or hospital, or in an entirely different location via one or more configurable wired and/or wireless networks such as the Internet, cloud computing and virtual private networks. 
     In one embodiment, for example, the PET/MRI system  100  includes, or is coupled to, a picture archiving and communications system (PACS). Particularly, in one exemplary implementation, the PACS is further coupled to a remote system, radiology department information system, hospital information system and/or to an internal or external network to allow operators at different locations to supply commands and parameters and/or gain access to the attenuation corrected PET image data. Certain exemplary methods for improving emission tomographic imaging using joint estimation will be described in greater detail with reference to  FIG. 2 . 
       FIG. 2  illustrates a flow chart  200  depicting an exemplary method for improved nuclear imaging. The exemplary method may be described in a general context of computer executable instructions stored and/or executed on a computing system or a processor. Generally, computer executable instructions may include routines, programs, objects, components, data structures, procedures, modules, functions, and the like that perform particular functions or implement particular abstract data types. The exemplary method may also be practiced in a distributed computing environment where optimization functions are performed by remote processing devices that are linked through a wired and/or wireless communication network. In the distributed computing environment, the computer executable instructions may be located in both local and remote computer storage media, including memory storage devices. 
     Further, in  FIG. 2 , the exemplary method is illustrated as a collection of blocks in a logical flow chart, which represents operations that may be implemented in hardware, software, or combinations thereof. The various operations are depicted in the blocks to illustrate the functions that are performed, for example, during data acquisition, attenuation and activity map estimation, and image reconstruction phases of the exemplary method. In the context of software, the blocks represent computer instructions that, when executed by one or more processing subsystems, perform the recited operations. 
     The order in which the exemplary method is described is not intended to be construed as a limitation, and any number of the described blocks may be combined in any order to implement the exemplary method disclosed herein, or an equivalent alternative method. Additionally, certain blocks may be deleted from the exemplary method or augmented by additional blocks with added functionality without departing from the spirit and scope of the subject matter described herein. For discussion purposes, the exemplary method will be described with reference to the elements of  FIG. 1 . 
     Generally, tomographic imaging such as PET or SPECT imaging is used to generate two-dimensional (2D) and/or three-dimensional (3D) images for various diagnostic and/or prognostic purposes. Conventional imaging techniques allow for a tradeoff between various imaging criteria such as image quality, spatial resolution, noise, contrast dose and total scanning time. Certain clinical applications, however, entail use of images with high spatial resolution or contrast ratio for investigating minute features within a subject, such as in and around a human heart. Particularly, clinical decisions regarding diagnosis and treatment of detected disease conditions are made based on certain image-derived parameters. Typically, clinical decisions entail use of high quality images that accurately characterize the functional and structural parameters of an ROI for use in diagnosis and treatment. Reconstruction of high quality images involves accurate reconstruction of the PET activity map, which in turn, depends upon accurate attenuation correction of PET data. 
     Accordingly, embodiments of the present method describe an image reconstruction technique that allows for simultaneous estimation of activity and attenuation maps from projection data acquired from an emission-based tomographic system and certain determined information. For discussion purposes, an exemplary embodiment of the present method will be described with reference to attenuation correction of PET images. 
     At step  202 , projection data corresponding to a target region of a subject is acquired using an emission tomography system such as the PET/MRI system  100  of  FIG. 1 . To that end, a radiopharmaceutical agent (hereinafter referred to as “radiotracer”), for example Fluorodeoxyglucose (FDG), may be administered to the patient for imaging a target ROI of the patient. The radiotracer, for example, may be selected so as to target the specific ROI for imaging. In certain embodiments, the PET/MRI system  100  may acquire the PET projection data corresponding to the target ROI during an estimated decay period of the radiotracer. Specifically, the projection data may provide an estimate of a target specificity of the radiotracer based on measured values representative of tissue radiotracer uptake distribution as a function of time. The measured distribution, in turn, may be used to assess one or more functional and/or physiological parameters, such as blood flow, in the target ROI for use in clinical diagnosis. 
     Accordingly, in one embodiment, the projection data may be stored as time-of-flight (TOF) information corresponding to a measured difference in time between arrivals of each pair of gamma photons from each annihilation event for reconstructing 2D and/or 3D TOF images with high signal-to-noise ratio (SNR). In another embodiment, the PET/MRI system  100  stores the acquired projection data as non-TOF information. In certain other embodiments, the acquired data may be stored in list-mode format or the acquired data may be gated according to respiratory and/or cardiac gating. The projection data may then be used to reconstruct an emission map and an attenuation map, which in turn, may be used to reconstruct an emission activity map, which defines a spatial distribution of the radiotracer in the patient body based on measurements corresponding to the emitted 511 keV photons. 
     The emitted photons travel through different regions in the patient body and/or extra-patient components such as beds and MR coils, and thus, experience attenuation. The different regions, for example, bones, tissue, lungs and air have different PET attenuation values that may be represented using the PET attenuation map. A schematic representation of an embodiment of an undetermined PET attenuation map  302  illustrated in  FIG. 3 . As illustrated in the attenuation map  302 , typically, bones  304  have a high PET attenuation value, tissue regions  306  have a medium PET attenuation value, lungs  308  have a low PET attenuation value and background air  310  has zero PET attenuation value. For quantitatively accurate PET imaging, these attenuation values are taken into account when reconstructing PET emission activity maps. Particularly, in one embodiment, the PET attenuation map may be reconstructed using MR images and acquired PET projection data. 
     With returning reference to  FIG. 2 , at step  204 , one or more MR images of the target ROI may be generated using an MRI system, such as the PET/MRI system  100 . To that end, the PET/MRI system  100  may scan the target ROI for acquiring MR data before, after or during the PET data acquisition. In one embodiment, the MR data acquisition may entail one or more localization scans, registration scans, and/or pre-processing of MR data, including three-dimensional gradient linearity correction. Further, the MRI scan may acquire one or a combination of in-phase (I i ), out-of-phase (I o ), water (I w ), and fat (I f ) images. 
     In one embodiment, the MR data acquisition performed within a single TR may obtain all four images for a particular slice selection, and may be extended for generating MR images of the whole body of the patient. The MR images may provide anatomical information with high spatial resolution. MR images, however, have low signal values in bones, lungs and air. Particularly, unlike PET images in which the bones, and air and/or lungs have significantly different PET attenuation values, in MR images bones, lungs and air have similar low signal values, and thus, are difficult to differentiate. 
       FIG. 4 , for example, illustrates a schematic representation of an embodiment of an MR image  402 . As illustrated in the MR image  402 , soft tissue regions  404  have high MR signal values, whereas bones  406  and lungs  408  have similar low signal values, and thus, it is difficult to differentiate between bones and lungs in the MR image  402 . If the MR image  402  could be segmented into fat, water, bones and lungs accurately, a complete PET attenuation map could be generated by assigning determined PET attenuation values to each segment. MR and PET systems, however, employ different imaging principles. Conventionally, transformation of MR images into PET attenuation maps, thus, is not straightforward. 
     Embodiments of the present disclosure, however, allow for use of the MR images along with the PET projection data in reconstructing accurate PET attenuation maps. To that end, in certain embodiments, the generated MR images may be transformed by image registration or a determined geometrical calibration such that the MR images and the PET attenuation and activity maps are in a common spatial coordinate system, particularly when MR and PET scans are sequentially performed using separate scanning devices. 
     Returning to  FIG. 2 , at step  206 , a partially-determined attenuation map may be determined by identifying one or more regions in the attenuation map with a designated level of confidence using the MR images. Typically, the MR images provide anatomical information with high spatial resolution and soft tissue contrast. Accordingly, water or fat tissues may be identified from the MR images. In one embodiment, for example, a particular region may be identified as a tissue region if MR signals corresponding to the particular region exceed a designated threshold. The designated threshold, in certain embodiments, may be chosen to be conservative such that the identified tissue region is unlikely to include bones, lungs and air, whereas remaining regions in the MR image with signal values smaller than the designated threshold are likely to be bones, lungs, air and certain tissues. Therefore, in these embodiments, larger the designated threshold, larger is a corresponding confidence level used for reliable determination of the identified regions. As previously noted, in certain embodiments, the LAVA flex sequence or IDEAL MRI technique may be used to partially determine water and fat regions in the PET attenuation map with the desired confidence level. 
       FIG. 5  illustrates a schematic representation of another embodiment of an MR image  502  including a region  504  identified as a tissue with a high confidence level. In certain embodiments, PET/MRI system  100  assigns a pre-determined tissue attenuation value to the region  504  identified as tissue in the MR image  502 . Moving to  FIG. 6 , the PET/MRI system  100  generates a partially-determined attenuation map  602  based on the information derived from the regions identified from the MR image  502  of  FIG. 5 . The PET/MRI system  100  may determine the complete PET attenuation map, or only a portion thereof. 
     Particularly, in one embodiment, the PET/MRI system  100  determines only a portion  604  of the attenuation map  602  corresponding to those regions  504  in the MR image  502  of  FIG. 5  that were identified with high confidence. For example, in  FIG. 6 , tissue regions  606  proximal to low MR signal regions  608 , representative of bones and lungs, are excluded from the tissue region  604  identified with a high confidence level as there may be some uncertainty or error in boundary regions  606  between the tissue regions  604  and the low MR signal regions  608 . Although, a presently contemplated embodiment describes the use of thresholding for identifying the tissue regions  604 , in certain embodiments, one or more other regions including tissues may be identified using certain other techniques. 
     For example, in certain embodiments, regions such as bone, air and lungs may be identified by segmentation methods, atlas-based methods, machine learning methods and/or using unconventional MR sequences such as ultra-short echo time (UTE) and zero echo time (ZTE) sequences. Further, predetermined PET attenuation values may be assigned to each of these identified regions. However, regions  610  that may not be determined with a high confidence level, such as boundary regions  606  between identified regions, may remain undetermined in the partial attenuation map  602 . 
     Returning to  FIG. 2 , at step  208 , the complete attenuation map and a complete activity map are reconstructed from the emission projection data using the partially-determined attenuation map as a constraint. Particularly, in one embodiment, the undetermined regions in the attenuation map and the activity map may be reconstructed from the PET projection data using penalized-likelihood (also known as maximum a posteriori) with a constraint of the partially-determined attenuation map. In penalized-likelihood, an objective function may be chosen. The chosen objective function may include a Poisson log-likelihood function and a regularization function or a penalty function. Further, voxel/pixel values corresponding to an undetermined region of the partially-determined attenuation map and the activity map that maximize the objective function may be determined In one example, the penalized-likelihood objective function with a Gaussian quadratic penalty function may be defined using equation (1), 
       φ(λ, μ)= L (λ, μ)−β 1   R   1 (λ)−β 2   R   2 (μ)  (1)
 
     where λ and μ correspond to column vectors representing the emission activity map and the attenuation map, respectively, L corresponds to the Poisson log-likelihood function, R 1  and R 2  correspond to regularization functions for the activity map and the attenuation map, respectively, and β 1  and β 2  correspond to regularization parameters. 
     For TOF PET projection data, the Poisson log-likelihood function, for example, may be defined using equation (2), 
         L (λ, μ)=Σ i,k   y   ik  log(exp(−Σ j   p   ij μ j )Σ j   a   ij   8 λ j   +r   ik ) −(exp(−Σ j   p   ij μ j )Σ j   a   ij   k λ j   +r   ik )  (2)
 
     where i and k correspond to sinogram bin index and TOF bin index, respectively, y is representative of the TOF PET projection data, p ij  corresponds to a geometric forward projection, a ij   k  corresponds to a TOF forward projection including normalization and detector blurring point spread functions, and r ik  corresponds to a mean background contribution of scatter and random coincidences. Although equation (2) illustrates use of TOF PET projection data, in an alternative embodiment, non-TOF PET projection data may be used, and accordingly, the TOF bin index k in equation (2) may be disregarded. 
     Further, the Gaussian quadratic penalty functions, for example, may be defined using equation (3), 
         R   1 (λ)=Σ j,k    w   jk (λ j −λ k ) 2   , R   2 (μ)=Σ j,k    w   jk (μ j −μ k ) 2   (3)
 
     where w jk  corresponds to weights that are non-zero only if voxels j and k are neighbors. 
     In one embodiment, S may correspond to a set of indices for attenuation map voxels determined at step  206 . Particularly, for j S, the attenuation value for voxel j may be determined as μ j =μ j   known . Furthermore, the reconstructed activity map λ recon  and the reconstructed attenuation map μ recon  may be determined by maximizing the penalized-likelihood objective function φ(λ, μ) with a constraint {μ j =μ j   known : j S} on the attenuation map. Thus, λ recon  and μ recon  may be determined by solving a constrained optimization problem, for example, defined using equation (4), 
       maximize φ(λ, μ) subject to λ j ≧0 and μ j ≧0 for all j, and μ j =μ j   known  for j S  (4)
 
     For regularization functions, for example, including non-quadratic non-Gaussian penalty functions having edge-preserving properties such as Huber and log cosh functions, generalized Gaussian and relative difference penalty functions may be used. In certain embodiments, uni-modal or multi-modal distribution functions that represent a probability distribution of the attenuation values may be used for the regularization functions. In certain further embodiments, a combination of aforementioned regularization functions may be used. Alternatively, a zero function may be used for the regularization functions, and in such a scenario, penalized-likelihood estimation reduces to maximum-likelihood estimation. For maximum-likelihood estimations, regularization techniques such as terminating early numerical algorithms, sieves and post-smoothing may be used. In certain other embodiments, weighted least squares may be used instead of the Poisson log-likelihood; in which case, penalized-likelihood estimation becomes penalized weighted least squares estimation of the emission activity map and the undetermined part of the attenuation map. 
     In a presently contemplated embodiment, the partially-determined attenuation map from  104  may be used as a hard constraint for the optimization problem for reconstructing the emission activity map and the undetermined part of the attenuation map. In an alternative embodiment, however, the partially-determined attenuation map may be used as a soft constraint. Accordingly, a penalty function that penalizes a deviation from the constraint may be added to the penalized-likelihood objective function. In one example, such a penalty function may be defined using equation (5), 
         R   soft constraint (μ)=βΣ j    s (μ j −μ j   known ) 2   (5)
 
     In certain embodiments, alternative dissimilarity measures for the distance between μ j  and μ j   known  including norms, seminorm, mutual information and cross entropy may be used. 
     In certain embodiments, the penalized-likelihood estimates of the emission activity map and the undetermined part of the attenuation map may be determined by solving the constrained optimization problem by using a numerical optimization algorithm. In one embodiment, for example, the activity map and the undetermined part of the attenuation map may be updated alternately until one or more designated criteria are satisfied. To that end, the activity map may be updated, for example, by De Pierro&#39;s modified expectation maximization (EM) algorithm, whereas the undetermined part of the attenuation map can be updated, for example, by separable paraboloidal surrogates (SPS) algorithm. Additionally, in certain embodiments, only a subset of the acquired PET projection data may be used for each update for accelerating the convergence of the optimization algorithm that allows estimation of the emission activity map and the undetermined part of the attenuation map. In certain other embodiments, the activity map and the attenuation map may be updated using preconditioned conjugate gradient (PCG), ordered subsets expectation and maximization (OSEM), or block sequential regularized expectation maximization (BSREM) algorithm. 
     Further, at step  210 , one or more images corresponding to the target region may be reconstructed using the partially-determined attenuation map, the complete attenuation map and/or the complete activity map. In one embodiment, for example, the emission activity map may be re-reconstructed from the acquired PET projection data using the reconstructed attenuation map and emission tomography image reconstruction algorithms such as OSEM, BSREM, PCG, SPS and its ordered subsets (OS) version and/or De Pierro&#39;s modified expectation maximization and its OS version. 
       FIG. 7  illustrates a true attenuation map  702  and a true activity map  704 , which were used to generate simulated TOF PET projection data. Further,  FIG. 8  illustrates a partially-determined attenuation map  802  generated from one exemplary implementation of the present method. In the partially-determined attenuation map  802 , as previously noted, a tissue region  804  was identified and a pre-determined tissue attenuation value was assigned to the identified tissue region  804 . The undetermined region  806  in the attenuation map  802  included bones, lungs and even tissue. The partially-determined attenuation map  802  was then used to generate a complete attenuation map  902  and a complete activity map  904  illustrated in  FIG. 9 . 
     Specifically, the complete attenuation map  902  and the complete activity map  904  were obtained by maximizing a penalized-likelihood objective function with a constraint of the partially-determined attenuation map  802  by alternating between an update of the activity map  904  using De Pierro&#39;s modified expectation maximization and an update of the undetermined part of the attenuation map  802  of  FIG. 8  using separable paraboloidal surrogates algorithm. Use of embodiments of the present method allowed accurate recovery of bones and lungs as illustrated by the completed attenuation map  902 . 
     Embodiments of the present systems and methods, thus, describe a nuclear imaging technique for simultaneous estimation of the PET emission activity and PET attenuation maps from PET emission projection data and a partially-determined PET attenuation map that is obtained from MR images. Particularly, embodiments described herein allow identification of bones, metal implants, air and lungs in the patient PET attenuation map and corresponding heterogeneous regions, typically indistinguishable in MR images. Additionally, embodiments of the present systems and methods may also allow identification of extra-patient components such as beds and MR coils in the PET attenuation map, which are also difficult to identify in MR images. Although the present description is drawn to PET imaging, embodiments of the present systems and methods may also apply to SPECT imaging where SPECT emission activity and SPECT attenuation maps may be reconstructed using SPECT projection data and MR images. 
     Although specific features of various embodiments of the present systems and methods may be shown in and/or described with respect to only certain drawings and not in others, this is for convenience only. It is to be understood that the described features, structures, and/or characteristics may be combined and/or used interchangeably in any suitable manner in the various embodiments, for example, to construct additional assemblies and techniques. Furthermore, the foregoing examples, demonstrations, and process steps, for example, those that may be performed by the system controller  104 , the processing subsystem  132 , the DAS  160  and the image reconstruction unit  138  may be implemented by a single device or a plurality of devices using suitable code on a processor-based system. 
     It should also be noted that different implementations of the present disclosure may perform some or all of the steps described herein in different orders or substantially concurrently, that is, in parallel. In addition, the functions may be implemented in a variety of programming languages, including but not limited to Python, C++ or Java. Such code may be stored or adapted for storage on one or more tangible, machine-readable media, such as on data repository chips, local or remote hard disks, optical disks (that is, CDs or DVDs), solid-state drives or other media, which may be accessed by a processor-based system to execute the stored code. 
     While only certain features of the present invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.