Application of a convex phase retrieval method to blind seismic deconvolution
Title  Application of a convex phase retrieval method to blind seismic deconvolution 
Publication Type  Conference 
Year of Publication  2014 
Authors  Ernie Esser, Felix J. Herrmann 
Conference Name  EAGE Annual Conference Proceedings 
Month  06 
Keywords  blind deconvolution, convex phase retrieval, EAGE, source wavelet estimation 
Abstract  A classical strategy for blind seismic deconvolution is to first estimate the autocorrelation of the unknown source wavelet from the data and then recover the wavelet by assuming it has minimum phase. However, computing the minimum phase wavelet directly from the amplitude spectrum can be sensitive to even extremely small errors, especially in the coefficients close to zero. Since the minimum phase requirement follows from an assumption that the wavelet should be as impulsive as possible, we propose to directly estimate an impulsive wavelet by minimizing a weighted l2 penalty subject to a constraint on its amplitude spectrum. This nonconvex model has the form of a phase retrieval problem, in this case recovering a signal given only estimates of the magnitudes of its Fourier coefficients. Following recent work on convex relaxations of phase retrieval problems, we propose a convex semidefinite program for computing an impulsive minimum phase wavelet whose amplitude spectrum is close to a given estimate, and we show that this can be robustly solved by a Douglas Rachford splitting method for convex optimization. 
URL  https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/esser2014EAGEacp/esser2014EAGEacp.pdf 
DOI  10.3997/22144609.20141590 
Presentation  https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/esser2... 
Citation Key  esser2014EAGEacp 
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