A Mini-batch Quasi-Newton Proximal Method for Constrained Total Variation Nonlinear Image Reconstruction

Abstract. Over the years, computational imaging with accurate nonlinear physical models has garnered considerable interest due to its ability to achieve high-quality reconstructions. However, using such nonlinear models for reconstruction is computationally demanding. A popular choice for solving the corresponding inverse problems is the accelerated stochastic proximal method (ASPM), with the caveat that each iteration is still expensive. To overcome this issue, we propose a mini-batch quasi-Newton proximal method (BQNPM) tailored to image reconstruction problems with constrained total variation regularization. Compared to ASPM, BQNPM requires fewer iterations to converge. Moreover, we propose an efficient approach to compute a weighted proximal mapping at a cost similar to that of the proximal mapping in ASPM. We also analyze the convergence of BQNPM in the nonconvex setting. We assess the performance of BQNPM on three-dimensional inverse-scattering problems with linear and nonlinear physical models. Our results on simulated and real data demonstrate the effectiveness and efficiency of BQNPM, while also validating our theoretical analysis.