Title: Bregman Operator Splitting with Variable Step Size for TGV based Multi-Channel MRI Reconstruction
Speaker: Benjamin Cowen (Case Western Reserve University)
Advisor: Weihong Guo (Assistant Professor, Case Western Reserve University)
Abstract: We present fast algorithm for total generalized variation (TGV) based image reconstruction of magnetic resonance images collected by a technique known as partial parallel imaging (PPI). TGV is a generalization of the commonly employed total variation (TV) regularizer. TV reconstructs piecewise constant images and is known to produce oil-painting artifacts, while TGV reconstructs images with piecewise polynomial intensities and largely avoids this issue. The proposed algorithm combines the Bregman Operator Splitting with Variable Stepsize (BOSVS) approach derived by Chen, Hager, et al. with the closed-form expressions for the TGV subproblem that arises in the alternating directional method of multipliers, derived by Guo, Qin and Yin. The ill-conditioned inversion matrix that comes from PPI is approximated according to a stepsize rule similar to that in BOSVS. The stepsize rule starts with a Barzilai-Borwein step, then uses a line search to ensure convergence and efficiency. The proposed regularizer is shown to achieve better results than TV, especially for reconstructing smooth details, in sampling conditions as low as 7.87%.