Sparse seismic imaging using variable projection

TL;DR

This paper introduces a novel method combining variable projection with sparsity optimization to efficiently recover sparse signals and auxiliary parameters simultaneously, demonstrated on seismic imaging data.

Contribution

It presents a new approach that integrates variable projection with sparsity-promoting optimization for large-scale sparse deconvolution problems.

Findings

Efficient algorithm for large-scale sparse deconvolution.

Successful application to seismic imaging data.

Improved recovery of sparse signals with unknown auxiliary parameters.

Abstract

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simultaneously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with sparsity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demonstrate the algorithm on a seismic imaging example.