Parallel proximal methods for total variation minimization

Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.Comment: To be presented at ICASSP 201

A Recursive Born Approach to Nonlinear Inverse Scattering

The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails