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Sparsity-enforcing regularisation and ISTA revisited

Publication ,  Journal Article
Daubechies, I; Defrise, M; De Mol, C
Published in: Inverse Problems
August 5, 2016

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 It also presents the previously unpublished proof of an extension of the original framework.

Duke Scholars

Published In

Inverse Problems

DOI

EISSN

1361-6420

ISSN

0266-5611

Publication Date

August 5, 2016

Volume

32

Issue

10

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Daubechies, I., Defrise, M., & De Mol, C. (2016). Sparsity-enforcing regularisation and ISTA revisited. Inverse Problems, 32(10). https://doi.org/10.1088/0266-5611/32/10/104001
Daubechies, I., M. Defrise, and C. De Mol. “Sparsity-enforcing regularisation and ISTA revisited.” Inverse Problems 32, no. 10 (August 5, 2016). https://doi.org/10.1088/0266-5611/32/10/104001.
Daubechies I, Defrise M, De Mol C. Sparsity-enforcing regularisation and ISTA revisited. Inverse Problems. 2016 Aug 5;32(10).
Daubechies, I., et al. “Sparsity-enforcing regularisation and ISTA revisited.” Inverse Problems, vol. 32, no. 10, Aug. 2016. Scopus, doi:10.1088/0266-5611/32/10/104001.
Daubechies I, Defrise M, De Mol C. Sparsity-enforcing regularisation and ISTA revisited. Inverse Problems. 2016 Aug 5;32(10).
Journal cover image

Published In

Inverse Problems

DOI

EISSN

1361-6420

ISSN

0266-5611

Publication Date

August 5, 2016

Volume

32

Issue

10

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics