The optimum approximation of a multidimensional filter bank having analysis filters with small nonlinear characteristics
Yuichi Kida, Takuro Kida · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
Firstly, we present the optimum interpolation approximation for multi-dimensional vector signals. The presented approximation shows high performance such that it minimizes various worst-case measures of error of approximation simultaneously. Secondly, we consider a set of restricted multi-dimensional vector signals that all elements of the corresponding generalized spectrum vector are separable-variable functions. For this set of restricted multi-dimensional vector signals, we present the optimum interpolation approximation. Moreover, based on this property, putting the variables to be identical with each other in the approximation, we present a certain optimum interpolation approximation for generalized filter bank with generalized non-linear analysis filters. This approximation also shows the high performance similar to the above-mentioned approximations. Finally, as a practical application of the optimum interpolation approximation for multi-dimensional vector signals, we present a discrete numerical solution of linear partial differential equations with many independent variables.