Implementation of Two-Dimensional Nonlinear Filters Using Linear Convolutions

The object of the research is multidimensional nonlinear Volterra filters (polynomial filters), determined by truncated functional series. The subject of the research is the methods of Volterra filters effective realization, based on representation thereof in matrix form and decomposition procedure. The article is aimed at development of ways of effective realization of two-dimensional (2-D) discrete Volterra filters due to paralleling and unification of computing operations. To describe the process of multidimensional discrete filtering the matrix representation of the Volterra filters is used. The concept of block convolution is introduced, which makes it possible to reduce the calculation of nonlinear convolutions to a sequence of calculations of linear 2-D convolutions, and then to estimate the volume of necessary calculations. An approach to realization of 2-D discrete Volterra filters is proposed, based on decomposition of matrix representation on non-linear 2-D convolutions. The given approach allows reducing the problem of nonlinear Volterra filters realization to series-parallel execution of linear 2-D convolutions and may serve as a foundation for development of parallel computational structures intended for realization of high-speed algorithms of non-linear filtering. The method of realization of 2-D discrete Volterra filters, based on execution of decomposition of the matrix representation of non-linear convolutions, allows to use the known methods and algorithms of multidimensional filtration for realization of Volterra filters and to give clear interpretation thereof. The suggested method of Volterra filters realization through using series-parallel execution of calculations provides an opportunity of realization thereof based on systolic processors.