Abstract
Orthogonal matching pursuit (OMP) is an efficient method for decomposing a seismic trace with regard to an atom dictionary. The original OMP optimizes one unique single objective in terms of successively maximizing the inner product between an atom and its corresponding residual at different approximating levels. Though the inner product effectively measures signal similarity at a global time scale, it tends to neglect localizing an atom whose peak position plays a key role in seismic reconstruction. To address this limitation, we propose a peak colocalized orthogonal matching pursuit (PCOMP) strategy that optimizes two objectives, i.e., signal correlation and peak colocalization, both of which are defined based on signal residuals and atoms. Compared with the original OMP, the PCOMP extends a much larger search space in favor of more accurate seismic reconstruction. In this scenario, the genetic algorithm (GA) used for solving the original OMP is not suitable for the PCOMP. Therefore, we propose to solve the two objective optimization problem by exploiting an improved nondominated sorting genetic algorithm (NSGA-II) algorithm, which not only increases the diversity of searching for optimization and but also reduces the reconstruction error over the GA. Furthermore, the constrained atom positions obtained from the peak colocalization objective enable efficient convergence. Experiments for seismic data validate the advantages of the proposed PCOMP.
Highlights
Sparse decomposition, which assumes that signals can be sparsely represented in one certain domain, plays an important role in seismic signal processing, including timefrequency analysis [1]–[3], noise attenuation [4]–[8], seismic inversion [9], deconvolution [10], data compression [11], etc
We propose a peak colocalized orthogonal matching pursuit (PCOMP) method that is based on two objectives, i.e., signal correlation and peak colocalization
In order to solve the optimization problem existing in the larger search space established by the two objective function (12), we exploit an improved nondominated sorting genetic algorithm (NSGA-II) for computing the optimization
Summary
Sparse decomposition, which assumes that signals can be sparsely represented in one certain domain, plays an important role in seismic signal processing, including timefrequency analysis [1]–[3], noise attenuation [4]–[8], seismic inversion [9], deconvolution [10], data compression [11], etc. The inner product just measures signal similarity between the atom and residual at a global time scale and does not guarantee the peak of the atom and that of the residual have the same location To address this limitation, we propose a peak colocalized orthogonal matching pursuit (PCOMP) method that is based on two objectives, i.e., signal correlation and peak colocalization. Instead of acquiring one optimal solution in each iteration of GA, NSGA-II provides multiple ways for choices and mutations, which incorporate the potential information of signal correlation and peak position. This greatly increases the diversity of local search. We take the peak position into account to obtain effective decomposition results
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