Learning optimal nonlinearities for iterative thresholding algorithms

Understand

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems.

• In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA.
• The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions.
• Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.