Signal deconvolution by projection onto convex sets

The method of projection onto convex sets is extended to the problem of deconvolution in the presence of noise. A collection of convex sets is defined by using properties of the noise and of the ideal signal. The ideal signal is then a member of the intersection of these convex sets. A solution to the deconvolution problem is to choose a member of this intersection. Such a member is obtained by successive projections onto convex sets. If the intersection is small, then any member of the intersection should be a good estimate. One and two dimensional results have shown that this method is effective in producing estimates that are superior to conventional methods when sufficient a priori knowledge is available to define the convex sets.