New results on sparse representations in unions of orthonormal bases
Combinatorics
2024-01-30 v1 Information Theory
math.IT
Abstract
The problem of sparse representation has significant applications in signal processing. The spark of a dictionary plays a crucial role in the study of sparse representation. Donoho and Elad initially explored the spark, and they provided a general lower bound. When the dictionary is a union of several orthonormal bases, Gribonval and Nielsen presented an improved lower bound for spark. In this paper, we introduce a new construction of dictionary, achieving the spark bound given by Gribonval and Nielsen. Our result extends Shen et al.' s findings [IEEE Trans. Inform. Theory, vol. 68, pp. 4230--4243, 2022].
Cite
@article{arxiv.2401.15571,
title = {New results on sparse representations in unions of orthonormal bases},
author = {Tao Zhang and Gennian Ge},
journal= {arXiv preprint arXiv:2401.15571},
year = {2024}
}