On the performance of algorithms for the minimization of ${\ell }_1$-penalized functionals

Abstract

The problem of assessing the performance of algorithms used for the minimization of an ${\ell }_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation isochrones' is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.

18 pages, 10 figures; v3: expanded version with an additional synthetic test problems

References in corpus (3)

• Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
• Tomographic inversion using ${\ell }_1$-norm regularization of wavelet coefficients
• L1Packv2: A Mathematica package for minimizing an ${\ell }_1$-penalized functional

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