Inverse Problems. Basics, theory and applied examples

DOI10.1007/978-3-662-45811-2zbMath1331.65083OpenAlexW4235154321MaRDI QIDQ2346865

Mathias Richter

Publication date: 4 June 2015

Published in: Mathematik im Fokus (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-45811-2

zbMATH Keywords

ARTFourier transformcollocation methodGalerkin methodinverse problemRadon transformtextbookdiscrete Fourier transformcomputerized tomographyprojection methodconvolution equationsnonlinear ill-posed problemTikhonov regularizationdiscrepancy principleleast squares problemregularization methodleast squares methodlinear ill-posed problemLandweber iterationintegral equation of the first kindGauss-Newton methodsource conditiongravimetryparameter estimation problemFredholm integral equation of the first kindsignal analysisVolterra integral equation of the first kind

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Radon transform (44A12) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for integral transforms (65R10) Nonlinear ill-posed problems (47J06) General applied mathematics (00A69) Mathematics for nonmathematicians (engineering, social sciences, etc.) (00A06) Numerical methods for ill-posed problems for integral equations (65R30) Applications to the sciences (65Z05) Fredholm integral equations (45B05) Volterra integral equations (45D05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for integral equations (65R32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22) Numerical solution of inverse problems involving ordinary differential equations (65L09) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01) Numerical solution of ill-posed problems involving ordinary differential equations (65L08)

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