Sparsity-enforcing regularisation and ISTA revisited

Journal Article (Journal Article)

About two decades ago, the concept of sparsity emerged in different disciplines such as statistics, imaging, signal processing and inverse problems, and proved to be useful for several applications. Sparsity-enforcing constraints or penalties were then shown to provide a viable alternative to the usual quadratic ones for the regularisation of ill-posed problems. To compute the corresponding regularised solutions, a simple, iterative and provably convergent algorithm was proposed and later on referred to as the iterative soft-thresholding algorithm. This paper provides a brief review of these early results as well as that of the subsequent literature, albeit from the authors' limited perspective. It also presents the previously unpublished proof of an extension of the original framework.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Defrise, M; De Mol, C

Published Date

  • August 5, 2016

Published In

Volume / Issue

  • 32 / 10

Electronic International Standard Serial Number (EISSN)

  • 1361-6420

International Standard Serial Number (ISSN)

  • 0266-5611

Digital Object Identifier (DOI)

  • 10.1088/0266-5611/32/10/104001

Citation Source

  • Scopus