We review the current state-of-the-art of diffuse optical imaging, which is an emerging
technique for functional imaging of biological tissue. It involves generating images using …

We survey mathematical developments in the inverse method of electrical impedance
tomography which consists in determining the electrical properties of a medium by making …

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-
posed inverse problem requiring carefully designed reconstruction procedures to ensure …

With contributions from leading international researchers, this second edition of Electrical
Impedance Tomography: Methods, History and Applications has been fully updated …

Objective: Deep learning has recently been applied to electrical impedance tomography
(EIT) imaging. Nevertheless, there are still many challenges that this approach has to face …

Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

In this monograph, the main subject of the author's considerations is coefficient inverse
problems. Arising in many areas of natural sciences and technology, such problems consist …

A large class of inverse problems for PDEs are only well-defined as mappings from
operators to functions. Existing operator learning frameworks map functions to functions and …

Even from casual observation it is apparent that most physical phenomena vary both in
space and time. For example, the temperature of the atmosphere changes continuously at …

This survey article deals mainly with two inverse problems and the relation between them.
The first inverse problem we consider is whether one can determine the electrical …