Optimal linear filters for pyramidal decomposition

Abstract

A method for determining the optimal linear filters for use in pyramidal decompositions under the minimum mean square error criterion is presented. The pyramidal structure has analysis and interpolation filters. The equations describing the optimal filters are nonlinear in the filter coefficients, making direct solution intractable. However, the optimal filters can be determined by iteratively solving for the optimal analysis and interpolation filters. This leads to a linear system of equations that can be solved using least squares or QR factorization. The optimization is valid in a data dependent or stochastic setting. Convergence and computational complexity of the algorithm are discussed. Some results of optimal linear filters applied to images are presented.