Super-resolution of points and curves
A talk in the BI.discrete series by
Stefan Kunis from (Universität Osnabrück)
| Abstract: | The term super-resolution is used in many different contexts but in general asks for resolving fine details from low-frequency
measurements. Algebraic techniques have proven useful in this context with different imaging tasks such as spike
reconstruction (single molecule microscopy), phase retrieval (X-ray crystallography), and contour reconstruction (natural
images). The available data typically consists of a blurred version of the specimen or equivalently trigonometric moments of
low to moderate order and one asks for the reconstruction of fine details modeled by zero- or positive-dimensional algebraic
varieties. Often, such reconstruction problems have a generically unique solution when the number of data is larger
than the degrees of freedom in the model. Beyond that, we concentrate on simple a-priori conditions to guarantee that the
reconstruction problem is well or only mildly ill conditioned. For the reconstruction of points on the complex torus, popular
results ask the order of the moments to be larger than the inverse minimal distance of the points. Moreover, simple and
efficient eigenvalue based methods achieve this stability numerically in specific settings. Recently, the situations
involving clustered points, points with multiplicities, and positive-dimensional algebraic varieties are starting to gain
interest, and these shall be discussed within this talk. Zugangsdaten: ID 926 5310 0938 Password: 1928 |