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A Model Based Data Driven Dictionary Learning for Seismic Data Representation
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 79th EAGE Conference and Exhibition 2017, Jun 2017, Volume 2017, p.1 - 5
Abstract
Summary
In this work, we consider a space-time variable signal cone to model seismic data. The signal cone variability is obtained through scaling, slanting and translation of the kernel for cone-limited (C-limited) functions (functions whose Fourier transform lives within a cone) or for C-Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a nonlinear optimization problem which we address by a fixed point method that utilizes a variable projection method with $ell_{1}$ constraints on the linear parameters and other constraints on the nonlinear parameters. We observe that slow decay and oscillatory behavior of the kernel for C-limited functions constitute bottlenecks for the optimization problem which we partially overcome by the C-Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity promoting curvelet decomposition, matching pursuit Fourier interpolation and sparsity promoting plane wave decomposition methods.
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