L1-norm penalized least squares with SALSA

This lecture note describes an iterative optimization algorithm, ‘SALSA’, for solving L1-norm penalized least squares problems. We describe the use of SALSA for sparse signal representation and approximation, especially with overcomplete Parseval transforms. We also illustrate the use of SALSA to perform basis pursuit (BP), basis pursuit denoising (BPD), and morphological component analysis (MCA). The algorithm, ‘SALSA’, was developed by Afonso, Bioucas-Dias, and Figueiredo.

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