Compressive sensing

Abstract

Computer-implemented method for determining optimal sampling grid during seismic data reconstruction includes: a) constructing an optimization model, via a computing processor, given by minu∥Su∥1s.t. ∥Ru−b∥2≦σ wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator; b) defining mutual coherence as μ ≤ C S ⁢ m ( log ⁢ ⁢ n ) 6 , wherein C is a constant, S is a cardinality of Su, m is proportional to number of seismic traces on the observed grid, and n is proportional to number of seismic traces on the reconstruction grid; c) deriving a mutual coherence proxy, wherein the mutual coherence proxy is a proxy for mutual coherence when S is over-complete and wherein the mutual coherence proxy is exactly the mutual coherence when S is a Fourier transform; and d) determining a sample grid r*=arg minr μ(r).

Dependencies are inferred from the claim text.