PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

Deep Learning-Based Fast TOF-PET Image Reconstruction Using Direction Information

Deep learning has attracted attention for positron emission tomography (PET) image reconstruction task, however, it remains necessary to further improve the image quality. In this study, we propose a novel CNN-based fast time-of-flight PET (TOF-PET) image reconstruction method to fully utilize the direction information of coincidence events. The proposed method inputs view-grouped histo-images into a 3D CNN as a multi-channel image to use the direction information of coincidence events. We evaluated the proposed method using Monte Carlo simulation data obtained from a digital brain phantom. Compared to the case without it, when using direction information, the peak signal-to-noise ratio and structural similarity were improved by 1.2 dB and 0.02, at a coincidence time resolution of 300 ps. The calculation times of the proposed method were significantly faster than the conventional iterative reconstruction. These results indicate that the proposed method improves both the speed and image quality of TOF-PET image reconstruction.

Kernel graph filtering—A new method for dynamic sinogram denoising

Low count PET (positron emission tomography) imaging is often desirable in clinical diagnosis and biomedical research, but its images are generally very noisy, due to the very weak signals in the sinograms used in image reconstruction. To address this issue, this paper presents a novel kernel graph filtering method for dynamic PET sinogram denoising. This method is derived from treating the dynamic sinograms as the signals on a graph, and learning the graph adaptively from the kernel principal components of the sinograms to construct a lowpass kernel graph spectrum filter. The kernel graph filter thus obtained is then used to filter the original sinogram time frames to obtain the denoised sinograms for PET image reconstruction. Extensive tests and comparisons on the simulated and real life in-vivo dynamic PET datasets show that the proposed method outperforms the existing methods in sinogram denoising and image enhancement of dynamic PET at all count levels, especially at low count, with a great potential in real life applications of dynamic PET imaging.

Harmonization of PET image reconstruction parameters in simultaneous PET/MRI

Objective Simultaneous PET/MRIs vary in their quantitative PET performance due to inherent differences in the physical systems and differences in the image reconstruction implementation. This variability in quantitative accuracy confounds the ability to meaningfully combine and compare data across scanners. In this work, we define image reconstruction parameters that lead to comparable contrast recovery curves across simultaneous PET/MRI systems. Method The NEMA NU-2 image quality phantom was imaged on one GE Signa and on one Siemens mMR PET/MRI scanner. The phantom was imaged at 9.7:1 contrast with standard spheres (diameter 10, 13, 17, 22, 28, 37 mm) and with custom spheres (diameter: 8.5, 11.5, 15, 25, 32.5, 44 mm) using a standardized methodology. Analysis was performed on a 30 min listmode data acquisition and on 6 realizations of 5 min from the listmode data. Images were reconstructed with the manufacturer provided iterative image reconstruction algorithms with and without point spread function (PSF) modeling. For both scanners, a post-reconstruction Gaussian filter of 3–7 mm in steps of 1 mm was applied. Attenuation correction was provided from a scaled computed tomography (CT) image of the phantom registered to the MR-based attenuation images and verified to align on the non-attenuation corrected PET images. For each of these image reconstruction parameter sets, contrast recovery coefficients (CRCs) were determined for the SUVmean, SUVmax and SUVpeak for each sphere. A hybrid metric combining the root-mean-squared discrepancy (RMSD) and the absolute CRC values was used to simultaneously optimize for best match in CRC between the two scanners while simultaneously weighting toward higher resolution reconstructions. The image reconstruction parameter set was identified as the best candidate reconstruction for each vendor for harmonized PET image reconstruction. Results The range of clinically relevant image reconstruction parameters demonstrated widely different quantitative performance across cameras. The best match of CRC curves was obtained at the lowest RMSD values with: for CRCmean, 2 iterations-7 mm filter on the GE Signa and 4 iterations-6 mm filter on the Siemens mMR, for CRCmax, 4 iterations-6 mm filter on the GE Signa, 4 iterations-5 mm filter on the Siemens mMR and for CRCpeak, 4 iterations-7 mm filter with PSF on the GE Signa and 4 iterations-7 mm filter on the Siemens mMR. Over all reconstructions, the RMSD between CRCs was 1.8%, 3.6% and 2.9% for CRC mean, max and peak, respectively. The solution of 2 iterations-3 mm on the GE Signa and 4 iterations-3 mm on Siemens mMR, both with PSF, led to simultaneous harmonization and with high CRC and low RMSD for CRC mean, max and peak with RMSD values of 2.8%, 5.8% and 3.2%, respectively. Conclusions For two commercially available PET/MRI scanners, user-selectable parameters that control iterative updates, image smoothing and PSF modeling provide a range of contrast recovery curves that allow harmonization in harmonization strategies of optimal match in CRC or high CRC values. This work demonstrates that nearly identical CRC curves can be obtained on different commercially available scanners by selecting appropriate image reconstruction parameters.