Published as Journal of Applied Geophysics, 130, 194-208, (2016)

Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform

Shuwei Gan% latex2html id marker 7754
\setcounter{footnote}{1}\fnsymbol{footnote}, Shoudong Wang% latex2html id marker 7755
\setcounter{footnote}{1}\fnsymbol{footnote}, Yangkang Chen% latex2html id marker 7756
\setcounter{footnote}{2}\fnsymbol{footnote}, Xiaohong Chen% latex2html id marker 7757
\setcounter{footnote}{1}\fnsymbol{footnote}, Weiling Huang% latex2html id marker 7758
\setcounter{footnote}{1}\fnsymbol{footnote}and Hanming Chen% latex2html id marker 7759
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\setcounter{footnote}{1}\fnsymbol{footnote}State Key Laboratory of Petroleum Resources and Prospecting
China University of Petroleum
Fuxue Road 18th
Beijing, China, 102200
Email: &
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\setcounter{footnote}{2}\fnsymbol{footnote}Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924, USA


According to the compressive sensing (CS) theory in the signal-processing field, we proposed a new CS approach based on a fast projection onto convex sets (POCS) algorithm with sparsity constraint in the seislet transform domain. The seislet transform appears to be the sparest among the state-of-the-art sparse transforms. The FPOCS can obtain much faster convergence than conventional POCS (about two thirds of conventional iterations can be saved), while maintaining the same recovery performance. The FPOCS can obtain faster and better performance than FISTA for relatively cleaner data but will get slower and worse performance than FISTA, which becomes a reference to decide which algorithm to use in practice according the noise level in the seismic data. The seislet transform based CS approach can achieve obviously better data recovery results than $f-k$ transform based scenarios, considering signal-to-noise ratio (SNR), local similarity comparison, and visual observation, because of a much sparser structure in the seislet transform domain. We have used both synthetic and field data examples to demonstrate the superior performance the proposed seislet-based FPOCS approach.