Learning optimal nonlinearities for iterative thresholding algorithms

TL;DR

This paper introduces a data-driven approach to optimize thresholding functions in ISTA by leveraging deep neural networks and backpropagation, leading to improved sparse signal estimation.

Contribution

It presents a novel method for learning optimal nonlinearities in ISTA using deep learning techniques, enhancing its performance on sparse inverse problems.

Findings

Improved estimation quality with data-adaptive ISTA.

Effective learning of thresholding functions via neural network backpropagation.

Potential for better sparse signal recovery in practical applications.

Abstract

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.