Advanced Filter Design

This paper presents a general approach for obtaining optimal filters as well as filter sequences. A filter is termed optimal when it minimizes a chosen distance measure with respect to an ideal filter. The method allows specification of the metric via simultaneous weighting functions in multiple domains, e.g. the spatiotemporal space and the Fourier space. Metric classes suitable for optimization of localized filters for multidimensional signal processing are suggested and discussed. It is shown how convolution kernels for efficient spatio-temporal filtering can be implemented in practical situations. The method is based on applying a set of jointly optimized filter kernels in sequence. The optimization of sequential filters is performed using a novel recursive optimization technique. A number of optimization examples are given that demonstrate the role of key parameters such as: number of kernel coefficients, number of filters in sequence, spatio-temporal and Fourier space metrics. The sequential filtering method enables filtering using only a small fraction of the number of filter coefficients required using conventional filtering. In multidimensional filtering applications the method potentially outperforms both standard convolution and FFT based approaches by two-digit numbers.