Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 59, Issue 11, Pages 5289-5301Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2011.2162324
Keywords
1-Bit compressive sensing; consistent reconstruction; quantization; trust-region algorithms
Categories
Funding
- NSF through UCLA IPAM [DMS-0439872]
- NSF [DMS-07-48839, CCF-0431150, CCF-0728867, CCF-0926127, CNS-0435425, CNS-0520280]
- ONR [N00014-08-1-1101, N00014-07-1-0936, N00014-08-1-1067, N00014-08-1-1112, N00014-08-1-1066]
- U. S. Army Research Laboratory
- U. S. Army Research Office [W911NF-09-1-0383]
- Alfred P. Sloan Research Fellowship
- DARPA/ONR [N66001-08-1-2065]
- AFOSR [FA9550-07-1-0301, FA9550-09-1-0432]
- ARO MURI [W911NF-09-1-0383, W911NF-07-1-0185]
- Texas Instruments Leadership University Program
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1028790] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0748839] Funding Source: National Science Foundation
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The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross nonlinearities applied to the measurements. In this paper we introduce a new algorithm-restricted-step shrinkage (RSS)-to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for nonconvex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest.
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