On the paper Optimal dual frames of probabilistic erasures

2025/07/15 by Mondal, Shankhadeep, R. N. Mohapatra, Mohapatra, Ram Narayan
Computer Science · Engineering · #42C15 #47B02 #94A12 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2507.11452

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Optimal dual pairs of frames for erasures
• Optimal dual frames and dual pairs for probability modelled erasures using weighted average of operator norm and spectral radius
• Frames, Graphs and Erasures

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