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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

Authors: Amir Beck, Marc Teboulle

Published: 2009 (Journal Paper)

Source: SIAM Journal on Imaging Sciences

Algorithm: FISTA

DOI: 10.1137/080716542

Summary

Introduces FISTA (Fast Iterative Shrinkage-Thresholding Algorithm), an accelerated proximal gradient method achieving O(1/k²) convergence rate for composite convex minimization with a Lipschitz-smooth term and a proximal-friendly nonsmooth term such as L1 regularization. Extends ISTA with Nesterov-style momentum and became a foundational algorithm for sparse signal recovery and regularized optimization.

Abstract

Primary

Paper epubs.siam.org

Standard

DOI 10.1137/080716542

Tags

  • FISTA

  • Proximal gradient

  • Iterative shrinkage-thresholding

  • Convex optimization

  • Sparse recovery

  • First-order methods