1. Positron Emission Tomography (PET) scans allow for functional imaging of the body’s metabolism, making it an effective tool for locating cancerous tumors (Fig. 1). A limited-angle PET system (Fig. 2) is being developed at the Molecular Imaging Instrumentation Laboratory at Stanford, for dedicated loco-regional imaging. Tomography-based systems generally require full angular sampling (180 degrees) for faithful image reconstruction. Image degradation occurs with limited-angle tomography, due to loss of data in the Fourier domain. Clinical studies have shown decreased sensitivity and specificity due to reconstruction artifacts from limited-angle image reconstruction (see Fig. 4 for examples). Improved reconstruction of limited-angle tomography can better aid in diagnostics and treatment planning. David Fan-Chung Hsu Stanford University, Departments of Electrical Engineering and Radiology Molecular Imaging Program at Stanford School of Medicine Dept of Radiology MOTIVATION & OBJECTIVES Fig. 1: Photons (arrows) being emitted from tumor (red) References: [1] Chen, Zhiqiang, et al. "A limited-angle CT reconstruction method based on anisotropic TV minimization." Physics in medicine and biology 58.7 (2013): 2119. [2] Isernhagen, C. F., et al. "Three-dimensional anisotropic regularization for limited angle tomography." Current Directions in Biomedical Engineering 1.1 (2015): 283-285. [3] Jonsson, Elias, Sung-cheng Huang, and Tony Chan. "Total variation regularization in positron emission tomography." CAM report (1998): 98-48. [4] Lauer, Tod. "Deconvolution with a spatially-variant PSF." Astronomical Telescopes and Instrumentation. International Society for Optics and Photonics, 2002. Improving Reconstructed Image Quality in a Limited- Angle Positron Emission Tomography System Fig. 2: Limited-angle tomography, showing limited angular sampling range (shaded) METHODS It has been shown that total variation minimization (TV-M) can be incorporated into limited-angle tomography reconstruction to improve image quality [1] [2] [3]. However, a literature search did not find published literature on combining TV-minimization and Maximum-Likelihood Expectation Maximization (MLEM) algorithm for limited-angle sampling. A Zubal phantom and circular disk phantom were simulated with projection data from a 30 degree angular range (Fig. 3). Standard filtered backprojection (FBP) and MLEM reconstruction were performed on this limited-angle tomography dataset (Fig. 4). TV-M was incorporated into MLEM using alternating-direction method of multipliers (Fig. 5) and Richardson-Lucy (Fig. 6). Point-spread function (PSF) models were found using difference images reconstructed with and without point perturbations (Fig. 4). PSF models were incorporated into ADMM/RL TV-minimization in 3 different ways: 1)Averaging all PSFs from across the image to create one PSF that is used in the TV-M algorithms. 2)Averaging only the highest power eigen-PSFs in the image using the Karhunen-Loève decomposition [4]. 3)Split image into “blocks”, reconstruction each block with its respective PSF, and re-form image through interpolation. 20 iterations of MLEM were used for all cases to ensure comparable results, and parameters were optimized manually. Fig. 3: Ground truth emission images of Zubal phantom (left) and circular disk phantom (right) Fig. 4: Standard reconstruction using filtered backprojection (left) and MLEM with 20 iterations (middle). PSFs are shown on the right. Fig. 5: ADMM-based TV-M algorithms, using averaged PSF (left), eigen-PSFs (middle), and block-based PSF modeling (right). Fig. 6: RL-based TV-M algorithms, using averaged PSF (left), and block- based PSF modeling (right). RESULTS PSNR = 2.30 MSE = 0.59 PSNR = 4.17 MSE = 0.38 PSNR = 9.68 MSE = 0.11 PSNR = 9.63 MSE = 0.11 PSNR = 13.05 MSE = 0.05 PSNR = 9.67 MSE = 0.11 PSNR = 9.11 MSE = 0.12 PSNR = 10.61 MSE = 0.09 PSNR = 10.39 MSE = 0.09 PSNR = 9.23 MSE = 0.12 PSNR = 10.01 MSE = 0.10 PSNR = 7.60 MSE = 0.17 PSNR = 8.77 MSE = 0.13 PSNR = 8.31 MSE = 0.15 CONCLUSION ADMM-based TV-minimization (highlighted in green) using averaged PSF gives the best results, with PSNR improving by 35% and MSE reducing by 54%.