On the Design of a Class of Odd-Length Biorthogonal Wavelet Filter Banks for Signal and Image Processing

In this paper, we introduce an approach to the design of odd-length biorthogonal wavelet filter banks based on semidefinite programming employing Bernstein polynomials. The method is systematic and renders a simple optimization problem, yet it offers wavelet filters ranging from maximally flat to maximal passband/stopband width. The odd-length biorthogonal filter pairs are then used in multi-focus imaging to obtain a fully-focused image from a set of registered semi-focused input images at varying focus employing the distance transform and exponentially decaying function on the subbands in wavelet domain. Various images are tested and experimental results compare favorably to recent results in literature.