TY - JOUR

T1 - A fast iterative shrinkage-thresholding algorithm for linear inverse problems

AU - Beck, Amir

AU - Teboulle, Marc

N1 - Publisher Copyright:
© 2009 Society for Industrial and Applied Mathematics.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Deconvolution

KW - Global rate of convergence

KW - Image deblurring

KW - Iterative shrinkage-thresholding algorithm

KW - Least squares and l regularization problems

KW - Linear inverse problem

KW - Optimal gradient method

KW - Two-step iterative algorithms

UR - http://www.scopus.com/inward/record.url?scp=85014561619&partnerID=8YFLogxK

U2 - 10.1137/080716542

DO - 10.1137/080716542

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AN - SCOPUS:85014561619

SN - 1936-4954

VL - 2

SP - 183

EP - 202

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 1

ER -