Zero tracks for blind deconvolution of blurred ensembles

The analytically continued Fourier transform of a two-dimensional image vanishes to zero on a two-dimensional surface embedded in a four-dimensional space. This surface uniquely characterizes the image and is known 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-dimensional space, we calculate projections of the zero sheets, known as zero tracks. The zero tracks of each member of the ensemble are superimposed on a plane. The zero tracks that pertain to the original image are similar for every blurred and contaminated image. By contrast those associated with the blurring vary widely across the ensemble. A method of selecting the appropriate zero tracks in order to reconstruct an estimate of the original image is presented. Preliminary results for small positive images suggest that this deconvolution technique may be successful even when the level of contamination is significant.