This document proposes a Split Augmented Lagrangian Shrinkage (SALSA) algorithm to solve optimization problems involving sparsity-promoting regularization terms. It uses variable splitting to separate the data fidelity and regularization terms, and then applies an augmented Lagrangian method with soft-thresholding updates to iteratively minimize the overall cost function. Previous related approaches like iterative soft thresholding, two-step iterative soft thresholding, and fast iterative soft thresholding are also discussed.

1. SPLIT AUGMENTED LAGRANGIAN SHRINKAGE
ALGORITHM
Mario A. T. Figueiredo, Jose’ M. Bioucas-Dias, and Manya V. Afonso

2. PROBLEM
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3. PREVIOUS RESEARCH
A number of methods are present to solve equation (1) namely
 Iterative Soft Thresholding (IST)
 Two-step IST (TwIST)
 Fast IST Algorithm (FISTA)
 Sparse Reconstruction by Separable Approximation (SpaRSA)

4. PROPOSED APPROACH
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5. VARIABLE SPLITTING
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6. AUGMENTED LAGRANGIAN
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7. AL ALGORITHM
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8. MODIFIED AL ALGORITHM
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9. AL FOR VARIABLE SPLITTING
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10. SALSA
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Soft Thresholding