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Proceedings Paper

Compressive phase retrieval
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Paper Abstract

The theory of compressive sensing enables accurate and robust signal reconstruction from a number of measurements dictated by the signal's structure rather than its Fourier bandwidth. A key element of the theory is the role played by randomization. In particular, signals that are compressible in the time or space domain can be recovered from just a few randomly chosen Fourier coefficients. However, in some scenarios we can only observe the magnitude of the Fourier coefficients and not their phase. In this paper, we study the magnitude-only compressive sensing problem and in parallel with the existing theory derive sufficient conditions for accurate recovery. We also propose a new iterative recovery algorithm and study its performance. In the process, we develop a new algorithm for the phase retrieval problem that exploits a signal's compressibility rather than its support to recover it from Fourier transform magnitude measurements.

Paper Details

Date Published: 27 September 2007
PDF: 11 pages
Proc. SPIE 6701, Wavelets XII, 670120 (27 September 2007); doi: 10.1117/12.736360
Show Author Affiliations
Matthew L. Moravec, Rice Univ. (United States)
Justin K. Romberg, Georgia Institute of Technology (United States)
Richard G. Baraniuk, Rice Univ. (United States)


Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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