TH‐C‐103‐11: Accelerated Barrier Optimization Compressed Sensing (ABOCS) for CT Reconstruction with Improved Convergence

Abstract

Purpose: Recently, we proposed an algorithm of accelerated barrier optimization compressed sensing (ABOCS) for iterative CT reconstruction. The previous implementation of ABOCS uses gradient projection (GP) with a Barzilai‐Borwein (BB) step‐size selection (GP‐BB) to search for the optimal solution. Despite the high computational efficiency of each iteration, the algorithm does not converge stably due to its non‐monotonic behavior. We further improve the convergence of ABOCS using a modified Nesterov method and investigate the ABOCS performance on patient data. Methods: To implement the Nesterov method for ABOCS, we first modify the objective function to make it continuous and differentiable. The traditional Nesterov algorithm requires Lipschitz and strong convex constants of the objective as inputs. These two parameters, however, are difficult to calculate in the ABOCS optimization framework, especially due to the large‐size and ill‐posed system matrix in the CT reconstruction as well as the singularities in the total‐variation term. We therefore apply the unknown‐parameter Nesterov (UPN) approach to adaptively estimate the parameters during the optimization. Results: Comparison studies are carried out on studies of computer simulation, physical phantom and head‐and‐neck patient. In all of these studies, the ABOCS results using UPN show more stable and faster convergence than those of the GPBB implementation. As shown in the simulation study, UPN achieves the same image quality as that of GPBB, but reduces the iteration numbers by 50%. In the Catphan600 phantom study, a high‐quality image with relative reconstruction error (RRE) less than 3% compared to the full‐view Result is obtained using UPN with 17% projections (60 views). Using 25% projections (91 views), the proposed method reduces the RRE from 21% as in the FBP results to 7.3% on the head‐and‐neck patient. Conclusion: As compared to GPBB, our new method significantly improves the convergence with higher stability and less iterations.