New results on sparse representations in unions of orthonormal bases
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913213154590720 |
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| author | Zhang, Tao Ge, Gennian |
| author_facet | Zhang, Tao Ge, Gennian |
| contents | 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]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New results on sparse representations in unions of orthonormal bases Zhang, Tao Ge, Gennian Combinatorics Information Theory 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]. |
| title | New results on sparse representations in unions of orthonormal bases |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2401.15571 |