Sparsity regularization in inverse problems Preface

The aim of this special issue of Inverse Problems is to provide a forum for ongoing works on the topic of sparsity regularization as a paradigm for solving inverse problems. The special issue consists of one perspective paper and twelve research papers, with topics covering theoretical developments, computational techniques, and novel applications. In the perspective paper researchers present an overview of early developments of sparsity regularization, including motivations from sparse representation and denoising by thresholding. The perspective centers around the celebrated iterative soft thresholding algorithm, and discusses its derivation, convergence analysis and acceleration techniques.