Learned Interpretable Residual Extragradient ISTA for Sparse Coding

TL;DR

This paper introduces ELISTA, a novel residual extragradient-based LISTA method that improves sparse coding efficiency, offers interpretability, and guarantees linear convergence through theoretical analysis and empirical validation.

Contribution

The paper proposes ELISTA, a residual extragradient LISTA with theoretical convergence guarantees and enhanced interpretability over existing serial LISTA models.

Findings

ELISTA achieves linear convergence.

Extensive experiments verify its advantages.

Provides interpretability for Res-Net.

Abstract

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our method attains linear convergence. In practice, extensive empirical results verify the advantages of our method.