Title

Reconstruction of Signals From Frame Coefficients With Erasures at Unknown Locations

Authors

Authors

D. G. Han;W. C. Sun

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

IEEE Trans. Inf. Theory

Keywords

Erasures; almost robust frames; almost self-located frames; OPTIMAL DUAL FRAMES; EQUIANGULAR TIGHT FRAMES; SEIDEL MATRICES; COMMUNICATION; ADVENT; BASES; LIFE; Computer Science, Information Systems; Engineering, Electrical &; Electronic

Abstract

We propose new approaches to the problems of recovering signals from the rearranged frame coefficients or frame coefficients with erasures at either known or unknown locations. These problems naturally arise from applications, where the encoded information needs to be transmitted, for example, in signal/image processing, information and coding theory, and communications. We show that with the appropriate choices of the frames that are used for encoding, the signal with erasures occurring at known locations can be easily recovered without inverting the (sub) frame operators each time. Our new easy to implement and cost-efficient algorithm provides perfect reconstruction of the original signal. To address the problem of recovering erased coefficients from unknown locations, we propose to use a class of frames that are almost robust with respect to m-erasures. We prove that every frame with uniform excess can be rescaled to an almost robust frame and the locations of erased data can be perfectly recovered for almost all the signals. Similar results are obtained for recovering the original order of a disordered (rearranged) set of frame coefficients. Numerical examples are presented to test the main results. Whenever the received data are noise free, we can recover the original signal exactly from frame coefficients with erasures at unknown locations or from a disordered set of frame coefficients.

Journal Title

Ieee Transactions on Information Theory

Volume

60

Issue/Number

7

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

4013

Last Page

4025

WOS Identifier

WOS:000341982200024

ISSN

0018-9448

Share

COinS