Feasibility-based fixed point networks

Abstract Inverse problems consist of recovering a signal from collection noisy measurements. These can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect data perturbations. Hand-chosen analytic yield desirable theoretical guarantees, but such approaches have limited effectiveness signals due their inability leverage large amounts available data. To this end, work fuses data-driven convex in theoretically sound manner. This accomplished using feasibility-based fixed point networks (F-FPNs). Each F-FPN defines nonexpansive operators, each which the composition projection-based operator operator. Fixed iteration used compute points these weights operators are tuned so that closely represent Numerical examples demonstrate performance increases by F-FPNs when compared standard TV-based methods for CT reconstruction comparable neural network based on algorithm unrolling. Codes Github: github.com/howardheaton/feasibility_fixed_point_networks .