Stable Recovery Of Signals From Frame Coefficients With Erasures At Unknown Locations

Keywords

almost robust frames; erasures; frames; signal recovery; totally robust frames

Abstract

In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.

Publication Date

1-1-2018

Publication Title

Science China Mathematics

Volume

61

Issue

1

Number of Pages

151-172

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11425-016-9143-2

Socpus ID

85037132749 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85037132749

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