Fast Multi-dimensional Filter Networks Design, Optimization and Implementation

As the title implies a fast filter network is a structure of filters, designed for efficient computation of a set of multi-dimensional filters. The efficiency is due to decomposition of multi-dimensional filter sets into a structure of smaller sparse filters called sub-filters. The structure used, forms a directed acyclic graph which allows the sub-filters to contribute to several output nodes of the networks, i.e. several filters in the set. The use of filter networks involves non-trivial design, i.e. choosing the network structure and optimizing each sub-filter. In this thesis, the filter networks are constrained to perform linear filtering, one of the most fundamental operation in signal processing. The design problem associated with filter networks is described and solutions found has been implemented for extracting features like signal orientation, local frequency, local phase, local bandwidth and degree of anisotropy from volumetric data. Filter networks has many potential applications and the primary target in this thesis has been local structure analysis. The implemented filter networks show a computational gain of factors exceeding 50 for estimation of local 3-D structure compared to standard convolution. As a proof of concept showing use in medical applications, filter networks for enhancement of medical 3-D data is presented.