  In this article, two closed and convex sets for blind deconvolution problem
are proposed. Most blurring functions in microscopy are symmetric with respect
to the origin. Therefore, they do not modify the phase of the Fourier transform
(FT) of the original image. As a result blurred image and the original image
have the same FT phase. Therefore, the set of images with a prescribed FT phase
can be used as a constraint set in blind deconvolution problems. Another convex
set that can be used during the image reconstruction process is the epigraph
set of Total Variation (TV) function. This set does not need a prescribed upper
bound on the total variation of the image. The upper bound is automatically
adjusted according to the current image of the restoration process. Both of
these two closed and convex sets can be used as a part of any blind
deconvolution algorithm. Simulation examples are presented.
