Lokalt adaptiva metoder för fria diskontinuitetsproblem

In many modern applications, like medical image reconstruction, the solution of interest is described by a discontinuous function. Unfortunately, it is a priori unknown where the discontinuities are located and their location has to be determined numerically. In fact, computing discontinuities wrongly or inaccurately could be either fatal (as in obstacle and tumor detection) or scientifically costly.

In this project, we solve image reconstruction problems by constructing methods that automatically adjust to the discontinuities of the underlying (observed) data. This adjustment leads to methods, which adaptively (in an iterative manner) reduce the reconstruction error, allowing to obtain the discontinuities accurately and hence yield qualitatively sound reconstructions, while keeping the computational complexity of the underlying problem on a manageable size.