An interdisciplinary journal combining mathematical and experimental papers on inverse problems with numerical and practical approaches to their solution.

An interdisciplinary journal combining mathematical and experimental papers on inverse problems with numerical and practical approaches to their solution.

Abstract. Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps.

Numerically, we transform the inverse source problem into an optimization framework, incorporating Tikhonov regularization to mitigate the ill-posedness of the inverse problem. We then propose an iterative thresholding algorithm to solve this optimization problem efficiently.

Inverse Problems 36 (2020) 060301 Preface References [1] Tr¨oltzschF2010 Optimal Control of Partial Differential Equations ((GraduateStudiesinMathe- maticsvol112))(Providence,RI:AmericanMathematicalSociety) [2] HinzeM,PinnauR,UlbrichMandUlbrichS2009 Optimization with PDE Constraints (Berlin: Springer)

An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution.

The inverse problem is formulated as a topology optimization problem, and solved by means of a heuristic algorithm based on the topological derivative and a level set representation of the scatterers.

2020年5月25日 · The papers collected in this special issue present topics at the current forefront of research in optimal control of differential equations and illustrate their relation to inverse problems. In the following, we put these contributions into context.

3D geophysical inversions the inverse problems are large scale and routine tasks such as computing the trace of a matrix or extracting its diagonal entries become computationally demanding.

Three areas are briefly reviewed: how the journal was born, how inverse problems are not ordinary mathematical problems, and how their study either remains connected with the original ‘natural inverse problem’ or extends to mathematical developments which are sometimes not justified by any ‘natural inverse problem’! Examples are given.