A DeCezaro et al 2009 Inverse Problems 25 035004 doi:10.1088/0266-5611/25/3/035004
On multiple level-set regularization methods for inverse problems
A DeCezaro1, A Leitão2 and X-C Tai3,4
Show affiliationsWe analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional 
based on TV–H1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional 
, similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels.
- PACS
- MSC
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35R30 Inverse problems (undetermined coefficients, etc.) for PDE
- Subjects
- Dates
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Issue 3 (March 2009)
Received 18 August 2008, in final form 12 December 2008
Published 13 January 2009
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On multiple level-set regularization methods for inverse problems
A DeCezaro et al 2009 Inverse Problems 25 035004
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