Optimum Constrained Image Restoration Filters

An optimum image restoration filter is described which minimizes the radius of gyration of the corrected or composite system point-spread function subject to constraints on the radius of gyration of the restoration fitter point-spread function, the total noise power in the restored image, and the shape of the composite system frequency spectrum. The filter function is obtained as the solution to a set of simultaneous differential equations subject to nonlinear integral constraints. Except for an assumption regarding the general shape of noise spectral density, the filter design is data independent. By constraining the radius of gyration of the restoration filter point-spread function, truncation errors resulting from edge effects are controlled. An iterative technique is introduced which virtually eliminates the sidelobes of the composite system point-spread function. The resulting suboptimal restoration filter effectively suppresses undesirable secondary oscillations which may otherwise appear in the composite system point-spread function and introduce "ghosts" in the restored data. A detailed study of the restoration filter performance as a function of its parameter variations is described and a number of examples are provided to demonstrate the fundamental properties of the restoration filter.