Sparsity in Inverse Geophysical Problems

Markus Grasmair (), Markus Haltmeier () and Otmar Scherzer ()
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Markus Grasmair: Norwegian University of Science and Technology, Department of Mathematics
Markus Haltmeier: University of Innsbruck, Institute of Mathematics
Otmar Scherzer: University of Vienna, Computational Science Center

A chapter in Handbook of Geomathematics, 2015, pp 1659-1687 from Springer

Abstract: Abstract Many geophysical imaging problems are ill-posed in the sense that the solution does not depend continuously on the measured data. Therefore, their solutions cannot be computed directly but instead require the application of regularization. Standard regularization methods find approximate solutions with small L 2 norm. In contrast, sparsity regularization yields approximate solutions that have only a small number of nonvanishing coefficients with respect to a prescribed set of basis elements. Recent results demonstrate that these sparse solutions often much better represent real objects than solutions with small L 2 norm. In this survey, recent mathematical results for sparsity regularization are reviewed. As an application of the theoretical results, synthetic focusing in Ground Penetrating Radar is considered, which is a paradigm of inverse geophysical problem.

Keywords: Ground Penetrate Radar; Tikhonov Regularization; Constrain Minimization Problem; Ricker Wavelet; Bregman Distance (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-642-54551-1_25

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