Deep learning (DL) based methods have become increasingly attractive in image motion estimation applications. In this study we investigate the use of a noise-to-noise (N2N) training strategy for improving the robustness of a DL motion-estimation network in the presence of high imaging noise in the image data. This strategy is based on the rationale that the image motion estimated from one noisy measurement of a given image pair should be equally applicable for registering the image pair when it is obtained from a different noisy measurement. In the experiments we demonstrated the proposed approach for motion-compensated noise suppression in cardiac-gated SPECT imaging, where we utilized the image data acquired from 237 clinical cases at 50% reduced dose. The proposed N2N approach yielded an average reduction of 18.5% in the mean-squared-error (MSE) of the gate frames compared to a traditional training approach. It also achieved a more uniform performance among the different cardiac phases in spite of their statistical image variability.

Motion compensation is an effective approach for reducing motion blur and suppressing noise in cardiac gated imaging. In this work, we propose to introduce a temporal regularization measure in optimization of a deep learning (DL) network for motion compensation in cardiac-gated SPECT images. This introduced measure is used to exploit the temporal consistency in the physical motion of the myocardium among consecutive phases of the cardiac cycle. In the experiment we demonstrated this approach on a set of 197 clinical acquisitions with imaging dose reduced by $50 \%$. The results demonstrate that the proposed approach can lead to improved motion compensation accuracy among all individual gates by the DL network, with an average reduction by $6 \%$ in the mean-squared-error of the motioncompensated myocardium, indicating that the proposed approach can be more robust in combating the excessive noise level in reduced dose imaging.

Motion compensation is effective for reducing motion blur in cardiac gated imaging. In this work, we investigate the potential benefit of incorporating an anatomical similarity measure in training a deep learning (DL) network for motion compensation on cardiac gated SPECT images, which are known to suffer from limited data counts and exhibit image intensity distortion (due to partial-volume effect) associated with cardiac motion. In this similarity measure we utilize the spatial image gradient to characterize the correspondence of boundary points on the left-ventricular wall between two gate frames. In the experiment we demonstrated this approach on a set of 197 clinical acquisitions, and the results show that with the proposed approach the DL network can improve the anatomical similarity among the gate frames upon motion compensation.

Deep learning denoising methods have been found to be effective for noise suppression in reduced-dose studies in medical imaging applications. In this work, we investigate the feasibility of improving the generalizability of a denoising network by using a dose-blind training approach, in which the network is trained with a loss function defined to accommodate the varying data statistics associated with multiple reduced-dose levels. In the experiments, we demonstrated this approach on quarter- and eighth-dose data from a set of 895 clinical cardiac SPECT perfusion imaging acquisitions. The quantitative results show that a dose-blind denoising network could generalize well over both dose levels, and outperformed dose-specific training in detection of perfusion defects at both quarter- and eighth-dose data (p-values-4; paired t-test).

Motion compensation is an effective approach for noise suppression and motion blur reduction in cardiac gated SPECT imaging. In this work, we investigate the potential benefit of using a deep learning network for motion compensation in a sequence of gated images throughout the cardiac cycle in the presence of large inter-subject variability and imaging degrading factors. We make use a set of clinical acquisitions from 130 subjects and quantify the motion compensation accuracy by variants of two known cascaded learning networks (namely VTN and VoxelMorph). The results in the experiments show that both networks can yield accurate compensation results in both standard dose and half dose studies. Specifically, VTN achieved a relative MSE of 0.0312 (full dose) and 0.0561 (half dose), compared to 0.0340 (full dose) and 0.0356 (half dose) for VoxelMorph. Both networks also outperformed the classical optical flow equation (OFE) method.

Cardiac SPECT perfusion imaging is important for diagnosis and evaluation of coronary artery diseases. However, the acquired image data can suffer from motion blur due to patient respiratory motion. We propose a maximum-likelihood estimation (MLE) approach to determine a surrogate respiratory signal from short-time acquisition frames for motion correction. To compensate for the low data counts in the short-time frames, we employ a regularization term to exploit the similarity in acquired data among neighboring acquisition angles. In the experiments we validated this approach first on a set of simulated phantom data with known respiratory motion, and then on clinical acquisitions from 17 subjects. The results demonstrate that the proposed MLE approach could yield a reliable respiratory motion signal even with the acquisition frame duration being as short as 100ms, and outperformed both center-of-mass and Laplacian eigen-maps methods.

Deep learning (DL) denoising has recently found applications in a wide range of important problems in medical imaging. A practical challenge encountered in clinical applications is that the acquired image data can exhibit great variability in terms of noise level among different subjects. In this study, we investigate whether it can be beneficial to exploit the varying data statistics among different subjects in a DL denoising network. We propose a modified loss function in the form of a weighted sum of mean-squared-errors for DL training in which the contribution from individual subjects is adjusted according to their noise levels. In the experiments we demonstrated this approach with a set of 895 clinical acquisitions in cardiac SPECT studies with 50% of standard dose. The quantitative results show that the proposed approach can further improve both the regional accuracy of the reconstructed left ventricle and the detection accuracy of perfusion defects.

Lowering the administered dose in SPECT myocardial perfusion imaging (MPI) has become an important clinical problem. In this study we investigate the potential benefit of applying a deep learning (DL) approach for suppressing the elevated imaging noise in low-dose SPECT-MPI studies. We adopt a supervised learning approach to train a neural network by using image pairs obtained from full-dose (target) and low-dose (input) acquisitions of the same patients. In the experiments, we made use of acquisitions from 1,052 subjects and demonstrated the approach for two commonly used reconstruction methods in clinical SPECT-MPI: 1) filtered backprojection (FBP), and 2) ordered-subsets expectation-maximization (OSEM) with corrections for attenuation, scatter and resolution. We evaluated the DL output for the clinical task of perfusion-defect detection at a number of successively reduced dose levels (1/2, 1/4, 1/8, 1/16 of full dose). The results indicate that the proposed DL approach can achieve substantial noise reduction and lead to improvement in the diagnostic accuracy of low-dose data. In particular, at 1/2 dose, DL yielded an area-under-the-ROC-curve (AUC) of 0.799, which is nearly identical to the AUC = 0.801 obtained by OSEM at full-dose ( p -value = 0.73); similar results were also obtained for FBP reconstruction. Moreover, even at 1/8 dose, DL achieved AUC = 0.770 for OSEM, which is above the AUC = 0.755 obtained at full-dose by FBP. These results indicate that, compared to conventional reconstruction filtering, DL denoising can allow for additional dose reduction without sacrificing the diagnostic accuracy in SPECT-MPI.

We designed a dedicated multi-detector multi-pinhole brain SPECT scanner to generate images of higher quality compared to general-purpose systems. The system, AdaptiSPECT-C, is intended to adapt its sensitivity-resolution trade-off by varying its aperture configurations allowing both high-sensitivity dynamic and high-spatial-resolution static imaging. The current system design consists of 23 detector heads arranged in a truncated spherical geometry. In this work, we investigated the axial and angular sampling capability of the current stationary system design. Two data acquisition schemes using limited rotation of the gantry and two others using axial translation of the imaging bed were also evaluated concerning their impact on image quality through improved sampling. Increasing both angular and axial sampling in the current prototype system resulted in quantitative improvements in image quality metrics and qualitative appearance of the images as determined in studies with specifically selected phantoms. Visual improvements for the brain phantoms with clinical distributions were less pronounced but presented quantitative improvements in the fidelity (normalized root-mean-square error (NRMSE)) and striatal specific binding ratio (SBR) for a dopamine transporter (DAT) distribution, and in NRMSE and activity recovery for a brain perfusion distribution. More pronounced improvements with increased sampling were seen in contrast recovery coefficient, bias, and coefficient of variation for a lesion in the brain perfusion distribution. The negligible impact of the most cranial ring of detectors on axial sampling, but its significant impact on sensitivity and angular sampling in the cranial portion of the imaging volume-of-interest were also determined.

4D image reconstruction can significantly improve the image quality in cardiac-gated imaging using single-photon emission computed tomography (SPECT). However, it is also associated with increased computation complexity which prevents it from being widely used in the clinic. In this study, we investigate a post-processing approach for cardiac-gated SPECT images by using a 3D residual convolutional neural network (CNN). In our formulation, the network is trained to produce images that are comparable to 4D reconstruction. In the experiments, we demonstrated this approach on a set of 197 clinical acquisitions. The results show that the proposed CNN approach can effectively suppress the noise level in the reconstructed myocardium. It also outperforms two alternative post-processing methods, including a non-local means (NLM) filter previously developed for gated SPECT images.

We propose a patient-specific ("personalized") approach for tailoring the injected activities to individual patients in order to achieve dose reduction in SPECT-myocardial perfusion imaging (MPI). First, we develop a strategy to determine the minimum dose levels required for each patient in a large set of clinical acquisitions (857 subjects) such that the reconstructed images are sufficiently similar to that obtained at conventional clinical dose. We then apply machine learning models to predict the required dose levels on an individual basis based on a set of patient attributes which include body measurements and various clinical variables. We demonstrate the personalized dose models for two commonly used reconstruction methods in clinical SPECT-MPI: 1) conventional filtered backprojection (FBP) with post-filtering and 2) ordered-subsets expectation-maximization (OS-EM) with corrections for attenuation, scatter and resolution, and evaluate their performance in perfusion-defect detection by using the clinical Quantitative Perfusion SPECT software package. The results indicate that the achieved dose reduction can vary greatly among individuals from their conventional clinical dose and that the personalized dose models can achieve further reduction on average compared with a global (non-patient specific) dose reduction approach. In particular, the average personalized dose level can be reduced to 58% and 54% of the full clinical dose, respectively, for FBP and OS-EM reconstruction, while without deteriorating the accuracy in perfusion-defect detection. Furthermore, with the average personalized dose further reduced to only 16% of full dose, OS-EM can still achieve a detection accuracy level comparable to that of FBP with full dose.

Respiratory motion is known to cause non-uniform blur in the reconstructed myocardium in cardiac perfusion imaging with single photon emission computed tomography (SPECT), which can adversely degrade the detectability of perfusion defects. To deal with this issue, we recently proposed a motion-compensated reconstruction scheme by using acquisitions with amplitude-binning. In this study, we evaluate the potential benefit of respiratory motion correction by quantifying the contrast-to-noise ratio (CNR) of the perfusion defects in the reconstructed images using clinical acquisitions. The results demonstrate that with motion correction the CNR is improved to 1.77 from 1.57 (without correction). In addition, there is also an improvement in the spatial resolution of the left ventricular wall. We also investigate the robustness of this reconstruction scheme for reduced dose imaging.

Cardiac images in single photon emission computed tomography (SPECT) are known to suffer from loss of resolution associated with respiratory motion. In this work, we investigate the use of a spatially adaptive smoothing prior in a motion-compensated reconstruction framework for SPECT, wherein respiratory binned data are incorporated into the reconstruction of the myocardium with respect to a reference respiratory bin. In the experiments, we evaluated this approach with both simulated imaging data and two sets of clinical acquisitions. The results show that the proposed approach can be effective for improving the heart wall in terms of both the noise level and spatial resolution. The proposed approach was also demonstrated to be robust when the imaging dose was reduced.

Cardiac single photon emission computed tomography (SPECT) images are known to suffer from both cardiac and respiratory motion blur. In this paper, we investigate a 4-D reconstruction approach to suppress the effect of respiratory motion in gated cardiac SPECT imaging. In this approach, the sequence of cardiac gated images is reconstructed with respect to a reference respiratory amplitude bin in the respiratory cycle. To combat the challenge of inherent high-imaging noise, we utilize the data counts acquired during the entire respiratory cycle by making use of a motion-compensated scheme, in which both cardiac motion and respiratory motion are taken into account. In the experiments, we first use Monte Carlo simulated imaging data, wherein the ground truth is known for quantitative comparison. We then demonstrate the proposed approach on eight sets of clinical acquisitions, in which the subjects exhibit different degrees of respiratory motion blur. The quantitative evaluation results show that the 4-D reconstruction with respiratory correction could effectively reduce the effect of motion blur and lead to a more accurate reconstruction of the myocardium. The mean-squared error of the myocardium is reduced by 22%, and the left ventricle (LV) resolution is improved by 21%. Such improvement is also demonstrated with the clinical acquisitions, where the motion blur is markedly improved in the reconstructed LV wall and blood pool. The proposed approach is also noted to be effective on correcting the spill-over effect in the myocardium from nearby bowel or liver activities.

Due to the irregularity in respiratory patterns observed clinically, the acquired data in cardiac SPECT with respiratory-gating can exhibit high variability among both gate intervals and acquisition angles. Such variability can lead to differing noise characteristics among respiratory gates, which would adversely affect the accuracy of motion estimation. To address this difficulty, we develop a joint motion-estimation and image-reconstruction approach, in which the respiratory motion is estimated simultaneously along with the source distribution. In the experiments, we demonstrated this joint estimation-reconstruction approach with both quantitative simulated NCAT data and a set of clinical acquisition. We also explored its robustness with reduced imaging dose. The results show that the proposed approach can further improve the reconstructed myocardium over a pre-reconstruction motion-estimation approach.

Cardiac gated images in single photon emission computed tomography (SPECT) are known to suffer from increased noise due to low data counts. In this work, we investigate a post-filtering approach for SPECT images based on nonlocal means (NLM) filtering. In order to exploit the inherent correlation of the signal components among the different cardiac gates, we employ a spatiotemporal NLM filter, in which both space and temporal neighborhoods are taken into account in the similarity processing. In the experiments, we demonstrated this approach with both simulated NCAT imaging data and a set of clinical acquisition. The results show that the use of temporal smoothing in NLM could be much more effective for improving the quality of gated images than spatial smoothing.

In respiratory-gated cardiac SPECT with amplitude binning, the acquisition time can vary greatly both among respiratory gates and among acquisition angles within each gate. If not properly accounted for, this uneven distribution in acquired data statistics will lead to limited-angle artifacts in reconstruction, which in turn can impact on the accuracy of respiratory motion correction. We investigate a compensation scheme for this uneven distribution by directly taking into account in the imaging model the actual acquisition time at different projection angles. In the experiment, we demonstrated this approach with simulated NCAT imaging data, for which quantitative results were obtained on both the reconstructed myocardium and estimated motion; we also tested the proposed approach on a set of clinical acquisition. The results show that the proposed approach could effectively suppress the limited-angle artifacts and improve the reconstruction in terms of both image accuracy and lesion detectability.

Cardiac gated SPECT is an important clinical tool for assessment of both myocardial perfusion and ventricular function. Spatiotemporal (aka 4D) reconstruction has been demonstrated to be effective for suppressing the increased noise in cardiac gated SPECT. In this work, we propose a joint 4D reconstruction approach to accommodate the different respiratory phases in a dual cardiac-respiratory gating scheme in order to combat the artifacts of respiratory motion in cardiac SPECT. The proposed approach is to exploit the correlation in the signal component among both the cardiac and respiratory phases in the acquired data. In our experiments we evaluated the approach using simulated SPECT imaging with the 4D NCAT phantom and Tc-99m labeled Sestamibi as the imaging agent. Our results demonstrate that the proposed approach could effectively suppress the artifacts caused by respiratory motion in the reconstruction.

With increasing availability of multimodality imaging systems, high-resolution anatomical images can be used to guide the reconstruction of emission tomography studies. By measuring reader performance on a lesion detection task, this study investigates the improvement in image-quality due to use of prior anatomical knowledge, for example organ or lesion boundaries, during SPECT reconstruction. Simulated (67)Ga -citrate source and attenuation distributions were created from the mathematical cardiac-torso (MCAT) anthropomorphic digital phantom. The SIMIND Monte Carlo software was then used to generate SPECT projection data. The data were reconstructed using the De Pierro maximum a posteriori (MAP) algorithm and the rescaled-block-iterative (RBI) algorithm for comparison. We compared several degrees of prior knowledge about the anatomy: no knowledge about the anatomy; knowledge of organ boundaries; knowledge of organ and lesion boundaries; and knowledge of organ, lesion, and pseudo-lesion (non-emission uptake altering) boundaries. The MAP reconstructions used quadratic smoothing within anatomical regions, but not across any provided region boundaries. The reconstructed images were read by human observers searching for lesions in a localization receiver operating characteristic (LROC) study of the relative detection/localization accuracies of the reconstruction algorithms. Area under the LROC curve was computed for each algorithm as the comparison metric. We also had humans read images reconstructed using different prior strengths to determine the optimal trade-off between data consistency and the anatomical prior. Finally by mixing together images reconstructed with and without the prior, we tested to see if having an anatomical prior only some of the time changes the observer's detection/localization accuracy on lesions where no boundary prior is available. We found that anatomical priors including organ and lesion boundaries improve observer performance on the lesion detection/localization task. Use of just organ boundaries did not provide a statistically significant improvement in performance however. We also found that optimal prior strength depends on the level of anatomical knowledge, with a broad plateau in which observer performance is near optimal. We found no evidence that having anatomical priors use lesion boundaries only when available changes the observer's performance when they are not available. We conclude that use of anatomical priors with organ and lesion boundaries improves reader performance on a lesion-detection/localization task, and that pseudo-lesion boundaries do not hurt reader performance. However, we did not find evidence that a prior using only organ boundaries helps observer performance. Therefore we suggest prior strength should be tuned to the organ-only case, since a prior will likely not be available for all lesions.

In order to reconstruct attenuation maps with improved spatial resolution and quantitative accuracy, we developed an approximate method of incorporating system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission reconstruction. Our method approximately models the blur caused by the finite intrinsic detector resolution, the nonideal source collimation and detector collimation. We derived the formulation using the optimization transfer principle as in the derivation of the OSTR algorithm. The formulation includes one forward-blur step and one back-blur step, which do not severely slow down reconstruction. The formulation could be applicable to various transmission geometries, such as point-source, line-source, and sheet-source systems. Through computer simulations of the MCAT phantom and transmission measurements of the air-filled Data Spectrum Deluxe single photo emission computed tomography (SPECT) Phantom on a system which employed a cone-beam geometry and a system which employed a scanning-line-source geometry, we showed that incorporation of RC increased spatial resolution and improved the quantitative accuracy of reconstruction. In simulation studies, attenuation maps reconstructed with RC correction improved the quantitative accuracy of emission reconstruction.

Due to the extended imaging times employed in single photon emission computed tomography (SPECT) and positron emission tomography (PET), patient motion during imaging is a common clinical occurrence. The fast and accurate correction of the three-dimensional (3-D) translational and rotational patient motion in iterative reconstruction is thus necessary to address this important cause of artifacts. We propose a method of incorporating 3-D Gaussian interpolation in the projector/backprojector pair to facilitate compensation for rigid-body motion in addition to attenuation and distance-dependent blurring. The method works as the interpolation step for moving the current emission voxel estimates and attenuation maps in the global coordinate system to the new patient location in the rotating coordinate system when calculating the expected projection. It also is employed for moving back the backprojection of the ratio of the measured projection to the expected projection and backprojection of the unit value (sensitivity factor) to the original location. MCAT simulations with known six-degree-of-freedom (6DOF) motion were employed to evaluate the accuracy of our method of motion compensation. We also tested the method with acquisitions of the data spectrum anthropomorphic phantom where motion during SPECT acquisition was measured using the Polaris IR motion tracking system. No motion artifacts were seen on the reconstructions with the motion compensation.

Model and human observers have been compared in a series of localization receiver operating characteristic (LROC) studies involving single-slice and multislice image displays. The task was detection of Ga-avid lymphomas within single photon emission computed tomography (SPECT)-reconstructed transverse slices of a mathematical phantom, and the studies involved four reconstruction strategies: the filtered-backprojection (FBP) and ordered-subset expectation-maximization (OSEM) algorithms with two- and three-dimensional postreconstruction filtering. The human-observer data was drawn from studies performed by Wells et al. (2000), while multiclass versions of the nonprewhitening (NPW), channelized nonprewhitening (CNPW), and channelized Hotelling (CH) model observers, each capable of performing the tumor search task, were applied. The channelized observers were evaluated with multiple square-channel models and both with and without internal noise. For the multislice studies, two different capacities for integrating the slice information were also tested. The CH observer gave good quantitative agreement with the human data from both image-display studies when the internal-noise model was used. The CNPW observer performed similarly with the iterative strategies. Wells et al. had shown that human observers are imperfect integrators of multislice information, and this is characterized as increased internal noise with the model observers.

The algorithm we consider here is a block-iterative (or ordered subset) version of the interior point algorithm for transmission reconstruction. Our algorithm is an interior point method because each vector of the iterative sequence [x(k)], k = 0, 1, 2, ... satisfies the constraints a(j) < x(j)k < b(j), j = 1, ..., J. Because it is a block-iterative algorithm that reconstructs the transmission attenuation map and places constraints above and below the pixel values of the reconstructed image, we call it the BITAB method. Computer simulations using the three-dimensional mathematical cardiac and torso phantom, reveal that the BITAB algorithm in conjunction with reasonably selected prior upper and lower bounds has the potential to improve the accuracy of the reconstructed attenuation coefficients from truncated fan beam transmission projections. By suitably selecting the bounds, it is possible to restrict the over estimation of coefficients outside the fully sampled region, that results from reconstructing truncated fan beam projections with iterative transmission algorithms such as the maximum-likelihood gradient type algorithm.

Localization ROC (LROC) observer studies examined whether detector response compensation (DRC) in ordered-subset, expectation-maximization (OSEM) reconstructions helps in the detection and localization of hot tumors. Simulated gallium (Ga-67) images of the thoracic region were used in the study. The projection data modeled the acquisition of attenuated 93- and 185-keV photons with a medium-energy parallel-hole collimator, but scatter was not modeled. Images were reconstructed with five strategies: 1) OSEM with no DRC; 2) OSEM preceded by restoration filtering; 3) OSEM with iterative DRC; 4) OSEM with an ideal DRC; and 5) filtered backprojection (FBP) with no DRC. All strategies included attenuation correction. There were four LROC studies conducted. In a study using a single tumor activity, the ideal DRC offered the best performance, followed by iterative DRC, restoration filtering, OSEM with no DRC, and FBP. Statistical significance at the 5% level was found between all pairs of strategies except for restoration filtering and OSEM with no DRC. A similar ranking was found for a more realistic study using multiple tumor activities. Additional studies considered the effects of OSEM iteration number and tumor activity on the detection improvement that iterative DRC offered with respect to OSEM with no DRC.

Spatiotemporal reconstruction of cardiac-gated SPECT images permits us to obtain valuable information related to cardiac function. However, the task of reconstructing this four-dimensional (4-D) data set is computation intensive. Typically, these studies are reconstructed frame-by-frame: a nonoptimal approach because temporal correlations in the signal are not accounted for. In this work, we show that the compression and signal decorrelation properties of the Karhunen-Loève (KL) transform may be used to greatly simplify the spatiotemporal reconstruction problem. The gated projections are first KL transformed in the temporal direction. This results in a sequence of KL-transformed projection images for which the signal components are uncorrelated along the time axis. As a result, the 4-D reconstruction task is simplified to a series of three-dimensional (3-D) reconstructions in the KL domain. The reconstructed KL components are subsequently inverse KL transformed to obtain the entire spatiotemporal reconstruction set. Our simulation and clinical results indicate that KL processing provides image sequences that are less noisy than are conventional frame-by-frame reconstructions. Additionally, by discarding high-order KL components that are dominated by noise, we can achieve savings in computation time because fewer reconstructions are needed in comparison to conventional frame-by-frame reconstructions.

In SPECT imaging of the chest, nonuniform attenuation correction requires use of a patient specific attenuation (mu) map. Such a map can be obtained by estimating the regions of (1) the lungs and (2) the soft tissues and bones, and then assigning an appropriate value of attenuation coefficient (mu) to each region. The authors proposed a method to segment such regions from the Compton scatter and photopeak window SPECT slices of Tc-99m Sestamibi studies. The Compton scatter slices are used to segment the body outline and to estimate the regions of the lungs. Locations of the back bone and sternum are estimated from the photopeak window slices to assist in the segmentation. To investigate the accuracy of using Compton scatter slices in estimating the regions of the body and the lungs, a Monte-Carlo SPECT simulation of an anthropomorphic phantom with an activity distribution and noise characteristics similar to patient data was conducted. Energy windows of various widths were simulated for use in locating a suitable Compton scatter window for imaging, The effects of attenuation correction using a mu map based on segmentation were also studied. The results demonstrated for the activity and mu maps studied herein that: (1) reasonable contrast could be obtained from Compton scatter data for the segmentation of the lung regions, (2) true positive rates of 99% and 89% for determining the body and lung regions, respectively, with total error rates of 4% and 29%, could be achieved, (3) usage of a mu map based on segmentation for attenuation correction improved relative quantification over filtered backprojection, (4) variations in the assigned mu value of 40% smaller or 40% larger in the lung regions had an insignificant impact on the results of relative quantification, (5) a wide energy window away from the photopeak window for recording scattered events could benefit both the segmentation of the lung regions and the attenuation correction of the activity in the myocardium region, and (6) usage of a smaller than true mu value in the lung regions of an assigned mu map might benefit attenuation correction for absolute quantification.

A filtering approach is described, which accurately compensates for the 2D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the frequency distance principle (FDP) which states that points in the object at a specific source-to-detector distance provide the most significant contribution to specified frequency regions in the discrete Fourier transform (DFT) of the sinogram. By modeling the detector point spread function as a 2D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3D DFT of the set of all sinogram slices. To minimize noise amplification the inverse filter is rolled off at high frequencies by using a previously published Wiener filter strategy. Attenuation compensation is performed with Bellini's method. It was observed that the tomographic point response, after distance-dependent filtering with the FDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods. Furthermore, it was shown that processing with this filtering technique provides reconstructions with minimal degradation in image fidelity.