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arXiv · 2401.15571

New results on sparse representations in unions of orthonormal bases

Tao Zhang·Gennian Ge
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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].

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Tao Zhang, Gennian Ge. 2024-01-28. New results on sparse representations in unions of orthonormal bases. https://arxiv.org/abs/2401.15571

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