A fast iterative shrinkage-thresholding algorithm for linear inverse problems

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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 for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude.

Original languageEnglish
Pages (from-to)183-202
Number of pages20
JournalSIAM Journal on Imaging Sciences
Issue number1
StatePublished - 2009


  • Deconvolution
  • Global rate of convergence
  • Image deblurring
  • Iterative shrinkage-thresholding algorithm
  • Least squares and l regularization problems
  • Linear inverse problem
  • Optimal gradient method
  • Two-step iterative algorithms


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