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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