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2010 | OriginalPaper | Chapter

25. Sparsity in Inverse Geophysical Problems

Authors : Markus Grasmair, Markus Haltmeier, Otmar Scherzer

Published in: Handbook of Geomathematics

Publisher: Springer Berlin Heidelberg

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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.

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Title: Sparsity in Inverse Geophysical Problems
Authors: Markus Grasmair
Markus Haltmeier
Otmar Scherzer
Publisher: Springer Berlin Heidelberg
Book: Handbook of Geomathematics
Print ISBN: 978-3-642-01545-8

Electronic ISBN: 978-3-642-01546-5

Copyright Year: 2010
DOI: https://doi.org/10.1007/978-3-642-01546-5_25

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