Bregman Regularized Statistical Image Reconstruction Method and Application to Prior Image Constrained Compressed Sensing (PICCS)

摘要

Recently, the Statistical Image Reconstruction (SIR) and compressed sensing (CS) framework has shown promise in the x-ray computed tomography (CT) community. In this paper, we propose to establish an equivalence between the unconstrained optimization problem and a constrained optimization with explicit data consistency term. The immediate consequence of the equivalence is to enable one to use the well-developed optimization method to solve the constrained optimization problem to refine the solution of the corresponding unconstrained optimization problem. As an application of this equivalence, the method was used to develop a convergent and numerically efficient implementation for the prior image constrained compressed sensing (PICCS).