A fast Iterative Shrinkage-Thresholding Algorithm with application to wavelet-based image deblurring

Authors:
Amir Beck;Marc Teboulle
Affiliations:
Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Haifa 32000, Israel;School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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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 is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a 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.