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Oleg Burdakov

Co-authors: Hans Knutsson and Björn Svensson

A novel approach in multilinear least-squares with application to optimal design of filter networks

Filter networks is a rapidly developing area due to the ability to significantly lower the computation time in multidimensional signal processing, especially in medical imaging. The design is based on solving a multilinear least-squares (MLLS) problem where the use of conventional methods is often practically impossible, because it is a non-convex large-scale optimization problem with a lot of local minimizers. So far, successful network designs have been restricted to special types of filters, e.g. those used for analyzing local signal structures where Linköping University is one of the world leading centers. The lack of efficient methods for solving MLLS is however a bottleneck for further progress in filter network design. Our cooperation is aimed on development of efficient MLLS methods. This will allow us to produce more generic and flexible network solutions. In this talk we will present our approach, in which we introduce convex programming sub-problems that capture the nature of each local minimizer. The sub-problems can be effectively solved by the interior point methods. Important is that our binary characteristics of each sub-problem are well-understood. This allows a systematic search among the local minimizers by checking a reasonably small number of them. To ease this search we plan to apply some strategies like the branch and bound. The results of this basic research will produce a core for the next stage project aimed to design filter networks for a wider range of applications.

Sidansvarig: karin.johansson@liu.se
Senast uppdaterad: 2019-12-03