Compressive phase retrieval

Matthew L. Moravec; Justin K. Romberg; Richard G. Baraniuk

doi:10.1117/12.736360

27 September 2007 Compressive phase retrieval

Matthew L. Moravec, Justin K. Romberg, Richard G. Baraniuk

Proceedings Volume 6701, Wavelets XII; 670120 (2007) https://doi.org/10.1117/12.736360
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

Matthew L. Moravec, Justin K. Romberg, and Richard G. Baraniuk "Compressive phase retrieval", Proc. SPIE 6701, Wavelets XII, 670120 (27 September 2007); https://doi.org/10.1117/12.736360

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