Statistical Image Reconstruction via Denoised Ordered-Subset Statistically Penalized Algebraic Reconstruction Technique (DOS-SPART)

摘要

Statistical Image Reconstruction (SIR) often involves a balance of two requirements: the first requirement is enforcing a minimal difference between the forward projection of the reconstructed image with the measured projection data and the second requirement enforcing some kind of image smoothness, which depends on the specific selection of regularizer, to reduce the noise in the reconstructed image. The needed delicate balance between these two requirements in the numerical implementations often slow down the reconstruction speed due to either a degradation in convergence rate of the algorithm or a degradation of parallellizability of the numerical implementation algorithms. In this work, a general numerical implementation strategy has been proposed to allow the SIR algorithms to be implemented in two decoupled and alternating steps. The first step using SIR without any regularizer which allows for the use of the well-known ordered subset (OS) strategy to accelerate the image reconstruction. The second step solves a denoising problem without involving the data fidelity term. The alternation of these two decoupled steps enable one to perform SIR with both high convergence rate and high parallellizability. The total variation norm of the image has been used as an example of regularizers to illustrate the proposed numerical implementation strategy. Numerical simulations have been performed to validate the proposed algorithm. The noise-spatial resolution tradeoff curve and convergence speed of the algorithm have been investigated and compared against the conventional gradient descent based implementation strategy.