Average performance of Orthogonal Matching Pursuit (OMP) for sparse approximation

Karin Schnass

doi:10.1109/lsp.2018.2878061

Home/Archive/arXiv

arXiv · 1809.06684

Average performance of Orthogonal Matching Pursuit (OMP) for sparse approximation

Karin Schnass

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a theoretical analysis of the average performance of OMP for sparse approximation. For signals that are generated from a dictionary with $K$ atoms and coherence $μ$ and coefficients corresponding to a geometric sequence with parameter $α<1$, we show that OMP is successful with high probability as long as the sparsity level $S$ scales as $Sμ^2 \log K \lesssim 1-α$. This improves by an order of magnitude over worst case results and shows that OMP and its famous competitor Basis Pursuit outperform each other depending on the setting.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Karin Schnass. 2019-07-15. Average performance of Orthogonal Matching Pursuit (OMP) for sparse approximation. https://doi.org/10.1109/lsp.2018.2878061

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

cs.IT↗

arXiv2026

Sequence Reconstruction over the Deletion Channel

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $ n \geq t+\ell-1$ and $t \geq 1$.

cs.IT↗

arXiv2026

A generalization of the map $χ$

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

cs.IT↗