Recovery Of Signals From Unordered Partial Frame Coefficients

Keywords

Erasure recovery; Robust frames; Self-located robust frames

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.

Publication Date

1-1-2018

Publication Title

Applied and Computational Harmonic Analysis

Volume

44

Issue

1

Number of Pages

38-58

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.acha.2016.04.002

Socpus ID

84963734966 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84963734966

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