Direct deconvolution of noisy blurred images

Two new algorithms for deconvolving image blur are presented. Both are based on the computation of the zeros of an image's z-transform and the separation of the zeros into sets belonging to the image and to the point spread function (psf). The zeros lie on a sheet existing in a four-dimensional space. The first algorithm is applicable when the psf is known a priori; portions of the zero sheet are matched using a Euclidean measure, then zeros are selected from the remainder and an image is algebraically reconstructed by QR decomposition. The second algorithm is applicable when an ensemble of differently blurred images are recorded from the same object (e.g. astronomical speckle images); even though the psf is unknown for each member of the ensemble, parts of the zero sheet corresponding to the actual (unblurred) image can be matched over the ensemble and a reconstruction made. Encouraging results have been obtained with both algorithms for small positive images corrupted by small amounts of noise.<
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