Multichannel IIR Image Deconvolution Using Gröbner Bases

This paper aims at providing a new method based on groebner bases to generated convolution filters from any convolution filter bank. The result deconvolution filters may be FIR or IIR according to the convolution filter bank´s property. Previous work only can process few filter banks that have FIR deconvolution filters., The mothod used in this paper is extended to adapt for all kind of filter banks. Using groebner bases and algebraic geometry theory, a criterion theorem on the invertibility of filter bank was found and an efficient algorithm to computed convolution filters was proposed. The algorithm could output a deconvolution filter bank with smaller number of terms without using any prior information of the filters. Simulation results showed that this method has a good reconstruction quality in noise environments.