Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435–1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems concerning the determination of defects of various types by different kinds of boundary measurements and we show that these problems are exponentially ill-posed.

in this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. then a common general forward modeling for them is given and the corresponding inversion problem is presented. then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a baye...

Inverse elastic-wave scattering problems are shown to be ill-posed in general. Standard simplifying assumptions--the first Born approximation, the physical optics approximation, and the stopping power approximation of tomography--are shown to reduce to the same ill-posed mathematical problem, that of inverting a Fourier transform. Practical implications of this fact are illustrated with examples.

‎in the present paper we consider a time-fractional inverse diffusion problem‎, ‎where data is given at $x=1$ and the solution is required in the interval $0

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The object...

Many theoretical and practical problems in science involve acquisition of data via indirect observations of a model or phenomena. Naturally, the observed data are determined by the physical properties of the model sought, as well as by the physical laws that govern the problem, however, they also depend on the experimental configuration. Unlike the model and the physical laws, the latter can be...