The authors have recently developed a preconditioned alternating projection algorithm (PAPA) with total variation (TV) regularizer for solving the penalized-likelihood optimization model for single-photon emission computed tomography (SPECT) reconstruction. This algorithm belongs to a novel class of fixed-point proximity methods. The goal of this work is to investigate how PAPA performs while dealing with realistic noisy SPECT data, to compare its performance with more conventional methods, and to address issues with TV artifacts by proposing a novel form of the algorithm invoking high-order TV regularization, denoted as HOTV-PAPA, which has been explored and studied extensively in the present work.
Using Monte Carlo methods, the authors simulate noisy SPECT data from two water cylinders; one contains lumpy “warm” background and “hot” lesions of various sizes with Gaussian activity distribution, and the other is a reference cylinder without hot lesions. The authors study the performance of HOTV-PAPA and compare it with PAPA using first-order TV regularization (TV-PAPA), the Panin–Zeng–Gullberg one-step-late method with TV regularization (TV-OSL), and an expectation–maximization algorithm with Gaussian postfilter (GPF-EM). The authors select penalty-weights (hyperparameters) by qualitatively balancing the trade-off between resolution and image noise separately for TV-PAPA and TV-OSL. However, the authors arrived at the same penalty-weight value for both of them. The authors set the first penalty-weight in HOTV-PAPA equal to the optimal penalty-weight found for TV-PAPA. The second penalty-weight needed for HOTV-PAPA is tuned by balancing resolution and the severity of staircase artifacts. The authors adjust the Gaussian postfilter to approximately match the local point spread function of GPF-EM and HOTV-PAPA. The authors examine hot lesion detectability, study local spatial resolution, analyze background noise properties, estimate mean square errors (MSEs), and report the convergence speed and computation time.
HOTV-PAPA yields the best signal-to-noise ratio, followed by TV-PAPA and TV-OSL/GPF-EM. The local spatial resolution of HOTV-PAPA is somewhat worse than that of TV-PAPA and TV-OSL. Images reconstructed using HOTV-PAPA have the lowest local noise power spectrum (LNPS) amplitudes, followed by TV-PAPA, TV-OSL, and GPF-EM. The LNPS peak of GPF-EM is shifted toward higher spatial frequencies than those for the three other methods. The PAPA-type methods exhibit much lower ensemble noise, ensemble voxel variance, and image roughness. HOTV-PAPA performs best in these categories. Whereas images reconstructed using both TV-PAPA and TV-OSL are degraded by severe staircase artifacts; HOTV-PAPA substantially reduces such artifacts. It also converges faster than the other three methods and exhibits the lowest overall reconstruction error level, as measured by MSE.
For high-noise simulated SPECT data, HOTV-PAPA outperforms TV-PAPA, GPF-EM, and TV-OSL in terms of hot lesion detectability, noise suppression, MSE, and computational efficiency. Unlike TV-PAPA and TV-OSL, HOTV-PAPA does not create sizable staircase artifacts. Moreover, HOTV-PAPA effectively suppresses noise, with only limited loss of local spatial resolution. Of the four methods, HOTV-PAPA shows the best lesion detectability, thanks to its superior noise suppression. HOTV-PAPA shows promise for clinically useful reconstructions of low-dose SPECT data.
This research has been supported in part by the United States National Science Foundation under Grant No. DMS-1115523, by the Guangdong Provincial Government of China through the “Computational Science Innovative Research Team” program, by the Natural Science Foundation of China under Grant Nos. 11071286, 91130009, and 11471013, and by the Promotive Research Fund for Excellent Young Scientists of Shandong Province under Grant No. BS2014DX003. This work has also been supported in part by Award No. 5-28527 from the National Center for Research Resources (NCRR), a component of the National Institutes of Health (NIH) and the NIH Roadmap for Medical Research, and by the Center of Emerging and Innovative Sciences (CEIS), a NYSTAR designated Center for Advanced Technology. In addition, the authors wish to thank Dr. Arman Rahmim for his advice on the design of the study. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Center for Research Resources or the National Institutes of Health. This work has been supported in part by an award from the Carol M. Baldwin Breast Cancer Research Fund.
1. INTRODUCTION 2. MATERIALS AND METHODS 2.A. Penalized maximum likelihood estimation for SPECT reconstruction 2.B. The TV and high-order TV regularization terms 2.C. Numerical algorithm 2.D. Simulations 2.D.1. Numerical phantom 2.D.2. Simulated SPECT data 2.E. Reconstruction methods 2.E.1. ML GPF-EM 2.E.2. TV-OSL 2.E.3. PAPA with total variation regularizer (TV-PAPA) 2.E.4. HOTV-PAPA 2.F. Image degradation compensation 2.G. Parameters 2.H. Quantification of reconstruction 2.H.1. Local point spread function 2.H.2. Ensemble noise and image roughness 2.H.3. Ensemble voxel variance 2.H.4. LNPS 2.H.5. Detectability of hot Gaussian spheres 2.H.6. Mean square error 3. RESULTS 3.A. Reconstructed images 3.B. Numerical analysis 3.B.1. Local spatial resolution 3.B.2. Mean square error 3.B.3. Image noise performance 3.B.4. Ensemble noise 3.B.5. Image roughness 3.B.6. Ensemble voxel variance 3.B.7. CHO lesion detectability 3.B.8. Convergence speed and computation time 3.B.9. Comparison of objective function values for TV-OSL and TV-PAPA 4. DISCUSSION 5. CONCLUSIONS
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