MULTICHANNEL RESTORATION OF SINGLE CHANNEL IMAGES US IN G A WAVELET D ECO M P 0 SIT ION
Mark R. Banham, Hector Gonzale, Nikolas P. Galatsanos · 1993
In this paper, multichannel linear filt.ering is applied to the restoration of single channel images t.hrough the use of a wavelet decomposition. A new matrix structure for the separable 3-D wavelet transform is present.ed which allows the transformation of block circulant operat,ors, found in 2-D linear filtering problems, into semi- block circulant operators, which are defined here. These operators are easily treated as block diagonal matrices in the wavelet-frequency domain. An adaptive Wiener filter is implemented in t,his domain, which utilizes the cross correlat,ions between subbands in the decomposition to subst antially improve the restoration of noisy-blurred images over that found with single channel filtering. This improvement is especially evident when the power spectrum of the original image is available.