A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
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 for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude.
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Acknowledgment.
The authors are indebted to the two anonymous referees for their useful suggestions and for having drawn the authors’ attention to additional relevant references.
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© 2009 Society for Industrial and Applied Mathematics.
History
Submitted: 25 February 2008
Accepted: 23 October 2008
Published online: 4 March 2009
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Funding Information
Israel Science Foundation: 48906
Funding: This research was partially supported by the Israel Science Foundation, ISF grant 48906.
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