Year: 2009
Type: preprint
Abstract: Consider the $n$-dimensional vector $y=X\be+\e$, where $\be \in \R^p$ has only $k$ nonzero entries and $\e \in \R^n$ is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a non-asymptotic upper bound on the probability that the optimal decoder for $β$ declares a wrong sparsity pattern, given any generic perturbation matrix $X$. In the case when $X$ is randomly drawn from a Gaussian ensemble, we obtain asymptotically sharp sufficient conditions for exact recovery, which agree with the known necessary conditions previously established.
Source: arXiv (Cornell University)
Author: Rad, Kamiar Rahnama
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1666765691