ZERO TRACKS FOR BLIND DECONVOLUTION OF BLURRED ENSEMBLES

The analytically continued Fourier transform of a two-dimensional imag e vanishes to zero on a two-dimensional surface embedded in a four-dim ensional space. This surface uniquely characterizes the image and is k nown as a zero sheet. An algorithm is described that employs the zero- sheet concept to blindly deconvolve an ensemble of differently blurred images. To overcome the difficulty of operating within a four-dimensi onal space, we calculate projections of the zero sheets, known as zero tracks. The zero tracks of each member of the ensemble are superimpos ed on a plane. The zero tracks that pertain to the original image are similar for every blurred and contaminated image. By contrast those as sociated with the blurring vary widely across the ensemble. A method o f selecting the appropriate zero tracks in order to reconstruct an est imate of the original image is presented. Preliminary results for smal l positive images suggest that this deconvolution technique may be suc cessful even when the level of contamination is significant.