On the paper Optimal dual frames of probabilistic erasures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912484294656000 |
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| author | Mondal, Shankhadeep Mohapatra, Ram Narayan |
| author_facet | Mondal, Shankhadeep Mohapatra, Ram Narayan |
| contents | In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate via counterexamples that the conditions provided are not sufficient to guarantee uniqueness. We also noticed a mistake in the proof of the theorem and proved the correct version of the theorem with a stronger but valid condition. Furthermore, we show that the corollary asserting uniqueness for a tight frame assumption is also incorrect. Our results refine the understanding of probability optimal dual frame constructions and offer a more complete characterization of the 1-erasure probability optimal duals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the paper Optimal dual frames of probabilistic erasures Mondal, Shankhadeep Mohapatra, Ram Narayan Functional Analysis 42C15, 47B02, 94A12 In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate via counterexamples that the conditions provided are not sufficient to guarantee uniqueness. We also noticed a mistake in the proof of the theorem and proved the correct version of the theorem with a stronger but valid condition. Furthermore, we show that the corollary asserting uniqueness for a tight frame assumption is also incorrect. Our results refine the understanding of probability optimal dual frame constructions and offer a more complete characterization of the 1-erasure probability optimal duals. |
| title | On the paper Optimal dual frames of probabilistic erasures |
| topic | Functional Analysis 42C15, 47B02, 94A12 |
| url | https://arxiv.org/abs/2507.11452 |