Recovery of signals from unordered partial frame coefficients |
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Authors: | Deguang Han Fusheng Lv Wenchang Sun |
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Affiliation: | 1. Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA;2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
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Abstract: | In this paper, we study the feasibility and stability of recovering signals in finite-dimensional spaces from unordered partial frame coefficients. We prove that with an almost self-located robust frame, any signal except from a Lebesgue measure zero subset can be recovered from its unordered partial frame coefficients. However, the recovery is not necessarily stable with almost self-located robust frames. We propose a new class of frames, namely self-located robust frames, that ensures stable recovery for any input signal with unordered partial frame coefficients. In particular, the recovery is exact whenever the received unordered partial frame coefficients are noise-free. We also present some characterizations and constructions for (almost) self-located robust frames. Based on these characterizations and construction algorithms, we prove that any randomly generated frame is almost surely self-located robust. Moreover, frames generated with cube roots of different prime numbers are also self-located robust. |
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Keywords: | 42C15 46C05 Self-located robust frames Robust frames Erasure recovery |
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