Learning MMSE Optimal Thresholds for FISTA

Fast iterative shrinkage/thresholding algorithm (FISTA) is one of the most commonly used methods for solving linear inverse problems. In this work, we present a scheme that enables learning of optimal thresholding functions for FISTA from a set of training data. In particular, by relating iterations of FISTA to a deep neural network (DNN), we use the error backpropagation algorithm to find thresholding functions that minimize mean squared error (MSE) of the reconstruction for a given statistical distribution of data. Accordingly, the scheme can be used to computationally obtain MSE optimal variant of FISTA for performing statistical estimation.