TY - JOUR

T1 - GESPAR

T2 - Efficient phase retrieval of sparse signals

AU - Shechtman, Yoav

AU - Beck, Amir

AU - Eldar, Yonina C.

PY - 2014/2/15

Y1 - 2014/2/15

N2 - We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.

AB - We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.

KW - Non-convex optimization

KW - phase retrieval

KW - sparse signal processing

UR - http://www.scopus.com/inward/record.url?scp=84893515284&partnerID=8YFLogxK

U2 - 10.1109/TSP.2013.2297687

DO - 10.1109/TSP.2013.2297687

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AN - SCOPUS:84893515284

SN - 1053-587X

VL - 62

SP - 928

EP - 938

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 4

M1 - 6701369

ER -