Constructing test instances for Basis Pursuit Denoising

Abstract

The number of available algorithms for the so-called Basis Pursuit Denoising problem (or the related LASSO-problem) is large and keeps growing. Similarly, the number of experiments to evaluate and compare these algorithms on different instances is growing. In this note, we present a method to produce instances with exact solutions which is based on a simple observation which is related to the so called source condition from sparse regularization.

References in corpus (6)

• Alternating Direction Algorithms for ${\ell }_1$-Problems in Compressive Sensing
• Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
• Joint-sparse recovery from multiple measurements
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• On the performance of algorithms for the minimization of ${\ell }_1$-penalized functionals
• L1Packv2: A Mathematica package for minimizing an ${\ell }_1$-penalized functional

Cited by in corpus (2)

• Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
• Coercive functions from a topological viewpoint and properties of minimizing sets of convex functions appearing in image restoration