Effective noise‐suppressed and artifact‐reduced reconstruction of SPECT data using a preconditioned alternating projection algorithm

Purpose: 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. Methods: 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. Results: 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