Year: 2013
Type: preprint
Abstract: We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the $\ell_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the $\ell_1$-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and null space properties for the recovery of partially sparse vectors and show that these new properties are implied by their original counterparts. We show also how to extend recovery under noisy measurements to the partially sparse case.
Source: arXiv (Cornell University)
Institutions: Princeton University, Lehigh University, University of Coimbra
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1829976833