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.

An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, 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.

We solve the inverse nodal problem of reconstructing the potential function q and its derivatives, as well as the boundary conditions of a Sturm-Liouville problem using the nodal points together with the integral average of q. All the algorithms have a first-order convergence rate.

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems.

2009年12月3日 · [1] Arridge S R 1999 Optical tomography in medical imaging Inverse Problems 15 R41-93 Crossref; Google Scholar [2] Yodh A and Chance B 1995 Spectroscopy and imaging with diffusing light Phys. Today 48 38-40. Crossref; Google Scholar [3] Hebden J C, Arridge S R and Delpy D T 1997 Optical imaging in medicine: I. Experimental techniques Phys. Med. Biol. …

We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem.

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear), and certain regularization strategy is thus needed.

There are various important applications being subject of current research that belong to this class of problems. Typically inverse problems are ill-posed in the sense that already small noise in the data causes tremendous errors in the solution.