Post-smoothed Maximum-likelihood Research Articles

Improved myocardial perfusion PET imaging with MRI assisted reconstruction incorporating multi-resolution joint entropy

Myocardial perfusion (MP) PET imaging plays an important role in risk assessment and stratification of patients with coronary artery disease. In this work, we developed an anatomy-assisted maximum a posteriori (MAP) reconstruction method incorporating a wavelet-based joint entropy (WJE) prior for MP PET imaging. Using the XCAT phantom, we first simulated three MP PET datasets, one with normal perfusion and the other two with non-transmural and transmural regionally reduced perfusion of the left ventricular myocardium. We then simulated MP PET datasets of the three cases with respiratory and cardiac (RC) motion to represent realistic clinical situations. Moreover, two MR image datasets of the same subjects without and with RC motion were simulated without the perfusion defect correspondence. Using the simulated data, the proposed method was evaluated quantitatively in terms of noise–contrast tradeoff, and compared with the post-smoothed maximum-likelihood and the conventional MAP methods. The detectability of perfusion defects with various myocardial coverage was also evaluated through receiver operating characteristic analysis using the channelized Hotelling observer. The results demonstrated that the WJE-MAP method improved the noise–contrast tradeoff, leading to significantly enhanced defect detectability over the other two methods in the non-transmural defects, while maintaining comparable performance in the transmural defect. In addition to the simulation study, the proposed method was further evaluated on the acquired PET/MRI data of a Jaszczak phantom with cold rods. Compared with the other two methods, the WJE-MAP method improved the tradeoff between noise and contrast in the smaller rods, thereby indicating its clinical potential for improving defect detectability in MP PET/MR imaging.

Evaluation of Parallel Level Sets and Bowsher's Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction.

In this article, we evaluate Parallel Level Sets (PLS) and Bowsher's method as segmentation-free anatomical priors for regularized brain positron emission tomography (PET) reconstruction. We derive the proximity operators for two PLS priors and use the EM-TV algorithm in combination with the first order primal-dual algorithm by Chambolle and Pock to solve the non-smooth optimization problem for PET reconstruction with PLS regularization. In addition, we compare the performance of two PLS versions against the symmetric and asymmetric Bowsher priors with quadratic and relative difference penalty function. For this aim, we first evaluate reconstructions of 30 noise realizations of simulated PET data derived from a real hybrid positron emission tomography/magnetic resonance imaging (PET/MR) acquisition in terms of regional bias and noise. Second, we evaluate reconstructions of a real brain PET/MR data set acquired on a GE Signa time-of-flight PET/MR in a similar way. The reconstructions of simulated and real 3D PET/MR data show that all priors were superior to post-smoothed maximum likelihood expectation maximization with ordered subsets (OSEM) in terms of bias-noise characteristics in different regions of interest where the PET uptake follows anatomical boundaries. Our implementation of the asymmetric Bowsher prior showed slightly superior performance compared with the two versions of PLS and the symmetric Bowsher prior. At very high regularization weights, all investigated anatomical priors suffer from the transfer of non-shared gradients.

Evaluation of Three MRI-Based Anatomical Priors for Quantitative PET Brain Imaging

In emission tomography, image reconstruction and therefore also tracer development and diagnosis may benefit from the use of anatomical side information obtained with other imaging modalities in the same subject, as it helps to correct for the partial volume effect. One way to implement this, is to use the anatomical image for defining the a priori distribution in a maximum-a-posteriori (MAP) reconstruction algorithm. In this contribution, we use the PET-SORTEO Monte Carlo simulator to evaluate the quantitative accuracy reached by three different anatomical priors when reconstructing positron emission tomography (PET) brain images, using volumetric magnetic resonance imaging (MRI) to provide the anatomical information. The priors are: 1) a prior especially developed for FDG PET brain imaging, which relies on a segmentation of the MR-image (Baete , 2004); 2) the joint entropy-prior (Nuyts, 2007); 3) a prior that encourages smoothness within a position dependent neighborhood, computed from the MR-image. The latter prior was recently proposed by our group in (Vunckx and Nuyts, 2010), and was based on the prior presented by Bowsher (2004). The two latter priors do not rely on an explicit segmentation, which makes them more generally applicable than a segmentation-based prior. All three priors produced a compromise between noise and bias that was clearly better than that obtained with postsmoothed maximum likelihood expectation maximization (MLEM) or MAP with a relative difference prior. The performance of the joint entropy prior was slightly worse than that of the other two priors. The performance of the segmentation-based prior is quite sensitive to the accuracy of the segmentation. In contrast to the joint entropy-prior, the Bowsher-prior is easily tuned and does not suffer from convergence problems.

Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT

Multipinhole single photon emission computed tomography (SPECT) imaging has several advantages over single pinhole SPECT imaging, including an increased sensitivity and an improved sampling. However, the quest for a good design is challenging, due to the large number of design parameters. The effect of one of these, the amount of overlap in the projection images, on the reconstruction image quality, is examined in this paper. The evaluation of the quality is based on efficient approximations for the linearized local impulse response and the covariance in a voxel, and on the bias of the reconstruction of the noiseless projection data. Two methods are proposed that remove the overlap in the projection image by blocking certain projection rays with the use of extra shielding between the pinhole plate and the detector. Also two measures to quantify the amount of overlap are suggested. First, the approximate method, predicting the contrast-to-noise ratio (CNR), is validated using postsmoothed maximum likelihood expectation maximization (MLEM) reconstructions with an imposed target resolution. Second, designs with different amounts of overlap are evaluated to study the effect of multiplexing. In addition, the CNR of each pinhole design is also compared with that of the same design where overlap is removed. Third, the results are interpreted with the overlap quantification measures. Fourth, the two proposed overlap removal methods are compared. From the results we can conclude that, once the complete detector area has been used, the extra sensitivity due to multiplexing is only able to compensate for the loss of information, not to improve the CNR. Removing the overlap, however, improves the CNR. The gain is most prominent in the central field of view, though often at the cost of the CNR of some voxels at the edges, since after overlap removal very little information is left for their reconstruction. The reconstruction images provide insight in the multiplexing and truncation artifacts.

Single and Multipinhole Collimator Design Evaluation Method for Small Animal SPECT

High-resolution functional imaging of small animals is often obtained by single pinhole SPECT with circular orbit acquisition. Multipinhole SPECT adds information due to its improved sampling, and can improve the trade-off between resolution and sensitivity. To evaluate different pinhole collimator designs an efficient method is needed that quantifies the reconstruction image quality. In this paper, we propose a fast, approximate method that examines the quality of individual voxels of a postsmoothed maximum likelihood expectation maximization (MLEM) reconstruction by studying their linearized local impulse response (LLIR) and (co)variance for a predefined target resolution. For validation, the contrast-to-noise ratios (CNRs) in some voxels of a homogeneous sphere and of a realistic rat brain software phantom were calculated for many single and multipinhole designs. A good agreement was observed between the CNRs obtained with the approximate method and those obtained with postsmoothed MLEM reconstructions of simulated noisy projections. This good agreement was quantified by a least squares fit through these results, which yielded a line with slope 1.02 (1.00 expected) and a y-intercept close to zero (0 expected). 95.4% of the validation points lie within three standard deviations from that line. Using the approximate method, the influence on the CNR of varying a parameter in realistic single and multipinhole designs was examined. The investigated parameters were the aperture diameter, the distance between the apertures and the axis-of-rotation, the focal distance, the acceptance angle, the position of the apertures, the focusing distance, and the number of pinholes. The results can generally be explained by the change in sensitivity, the amount of postsmoothing, and the amount of overlap in the projections. The method was applied to multipinhole designs with apertures focusing at a single point, but is also applicable to other designs.

Comparison of statistical reconstructions with isotropic and anisotropic resolution in PET

Statistical reconstruction methods based on the penalized maximum likelihood (or maximum a posteriori) principle have gained increasing attention in emission tomography. Fessler and Rogers have shown in 1996 that penalized maximum likelihood reconstruction with a conventional quadratic penalty results in anisotropic point spread functions (PSFs). Since then several approaches have been developed to design modified penalty functions to achieve isotropic PSFs. While an image with an isotropic PSF may be useful in some situations, its performance on clinical detection and quantitation tasks is unknown. In this paper we compare the task performances between reconstructions with isotropic and anisotropic PSFs using computer simulations. The performance on lesion detection is measured by a channelized Hotelling observer, and the performance on region of interest quantitation is evaluated by the bias and variance tradeoff. The results show that reconstructions with a conventional quadratic penalty function (anisotropic resolution) outperform post-smoothed maximum likelihood reconstructions (isotropic resolution) for both tasks, which indicates that isotropic resolution may not be suitable for lesion detection and quantitation.

Evaluation of anatomy based reconstruction for partial volume correction in brain FDG-PET

FDG-PET contributes to the diagnosis and management of neurological diseases. In some of these diseases, pathological gray matter (GM) areas may have a reduced FDG uptake. Detection of these regions can be difficult and some remain undiscovered using visual assessment. The main reason for this detection problem is the relatively small thickness of GM compared to the spatial resolution of PET, known as the partial volume effect. We have developed an anatomy-based maximum-a-posteriori reconstruction algorithm (A-MAP) which corrects for this effect during the reconstruction using segmented magnetic resonance (MR) data. Monte-Carlo based 3-D brain software phantom simulations were used to investigate the influence of the strength of anatomy-based smoothing in GM, the influence of misaligned MR data, and the effect of local segmentation errors. A human observer study was designed to assess the detection performance of A-MAP versus post-smoothed maximum-likelihood (ML) reconstruction. We demonstrated the applicability of A-MAP using real patient data. The results for A-MAP showed improved recovery values and robustness for local segmentation errors. Misaligned MR data reduced the recovery values towards those obtained by post-smoothed ML, for small registration errors. In the human observer study, detection accuracy of hypometabolic regions was significantly improved using A-MAP, compared to post-smoothed ML ( P < 0.004). The patient study confirmed the applicability of A-MAP in clinical practice. Conclusion: A-MAP is a promising technique for voxel-based partial volume correction of FDG-PET of the human brain.