articleSIAM Journal on Imaging SciencesJan 1, 2009Closed access

A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

ABAmir BeckMTMarc Teboulle

Technion – Israel Institute of Technology · Tel Aviv University

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Abstract

We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also known to converge quite slowly. In this paper we present a new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising numerical results…

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Topics & keywords

Topics
Keywords
  • Deblurring
  • Thresholding
  • Algorithm
  • Rate of convergence
  • Shrinkage
  • Inverse problem
  • Mathematics
  • Wavelet
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