Inverse spectral decomposition with the SPGL1 algorithm

Inverse spectral decomposition (ISD) is a technique that decomposes a seismic trace to a time-frequency map by inverse strategy. In this case, spectral decomposition is treated as an inversion problem of Ax = b. Sparse time-frequency maps can be obtained at an acceptable cost with the help of robust sparse inversion algorithms. In this paper, we apply the spectral projected gradient for L1 minimization (SPGL1) algorithm to ISD to seek a sparse spectrum. We treat A as a Ricker wavelet based continuous wavelet transform operator instead of a matrix. A synthetic example shows the sparse performance of SPGL1 inversion. We apply the proposed method to seismic data de-noising and hydrocarbon detection. Synthetic and field data examples demonstrate the two applications, respectively.