A New Enhancement to the Iterative Method

We propose a new method for deconvolution that extends the BID algorithm by recursively invoking itself on the residual at each iteration.

The residual image, , used to correct in the BID algorithm is the difference between blurred images, therefore it is a blurred image itself. The correction to that is needed is a deblurred version of . An estimate of this deblurred residual can be obtained by recursively invoking this deblurring procedure on the residual image along with the same estimate of the PSF. The residual image of the previous recurrence serves as both the observed image and the initial estimate, , in the new recurrence. The new recurrence blurs its observed image and computes the residual as before. The procedure recurs again to deblur this residual image. The recursion continues for as many levels as desired. Finally, at the deepest recursion level, the BID algorithm is applied for some small number of iterations. The resulting is passed up to the next higher recurrence and used to correct .

This algorithm has several advantages over the previous approaches. First, there are no nonlinear steps in the algorithm, so its results are free of artifacts; in particular, flux is conserved. Second, by applying only a few iterations at each level (except perhaps the top level) the algorithm converges rapidly because no recurrence of the procedure is allowed to proceed far enough to enter the range of minimal returns. Third, the method is stable because during each iteration the restoration is stopped, a simpler, related problem is defined, and the restoration continues. The Discussion section will elaborate on the stability of the algorithm.