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Published May 2011 | public
Book Section - Chapter

The value of redundant measurement in compressed sensing

Abstract

The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected.

Additional Information

© 2011 IEEE. This work was supported in part by NSF under grant DMS-0914892, by ONR under grant N00014-08-1-1110, and by AFOSR under grants FA9550-09-1-0643 and FA9550-09-1-0551. V. Kostina was supported in part by the Natural Sciences and Engineering Research Council of Canada. M. F. Duarte was supported in part by NSF Supplemental Funding DMS-0439872 to UCLA-IPAM,P.I.

Additional details

Created:
August 19, 2023
Modified:
January 13, 2024