Level-set approaches of L2-type for recovering shape and contrast in ill-posed problems

DOI10.1080/17415977.2011.639452zbMath1257.65029OpenAlexW2070695193MaRDI QIDQ5894981

Adriano De Cezaro, Antonio Leitão

Publication date: 29 October 2012

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2011.639452

zbMATH Keywords

regularizationHilbert spacenumerical experimentsPoisson equationill-posed problemslevel set methodspiecewise constant level setTikhonov functionals

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (6)

On a level-set method for ill-posed problems with piecewise nonconstant coefficients ⋮ A regularization method based on level sets and augmented Lagrangian for parameter identification problems with piecewise constant solutions ⋮ On the identification of piecewise constant coefficients in optical diffusion tomography by level set ⋮ Geometric reconstruction in bioluminescence tomography ⋮ Level-set approaches of L₂-type for recovering shape and contrast in ill-posed problems ⋮ Regularization approaches for quantitative photoacoustic tomography using the radiative transfer equation

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