Year: 2013
Type: preprint
Abstract: Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult. Several conditions were introduced which guarantee that, for small $k$ and for certain matrices, simply placing entries with desired characteristics on a randomly chosen support will produce vectors which can be recovered by $\ell_1$ minimization. In this work, we consider the case of large $k$ and propose both a methodology to quickly check whether a given vector is recoverable, and to construct vectors with the largest possible support. Moreover, we gain new insights in the recoverability in a non-asymptotic regime. The theoretical results are illustrated with computational experiments.
Source: arXiv (Cornell University)
Authors: Kruschel, Christian, Lorenz, Dirk A.
Institutions: University of Göttingen, Technische Universität Braunschweig
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2951034132