Restoration of single-channel images with multi-channel filtering in the wavelet domain

The authors develop a multi-channel formulation of a single-channel filtering problem in the wavelet domain. This technique is based on an orthogonal matrix representation of the 2-D separable wavelet transform. It is shown that semiblock circulant structures resulting from a similarity transformation with this matrix operator permit a multi-channel treatment of a noisy blurred image, yielding an adaptive restoration technique in the wavelet frequency domain. A novel formulation of the 2-D separable wavelet decomposition is presented that clearly produces matrices which may be block-diagonalized with an array Fourier transform. Some experimental results based on the implementation of the wavelet-based multi-channel filtering methods discussed are presented. The method described offers much potential for improved adaptive image restoration in the wavelet domain