The Approximation of Image Blur Restoration Filters by Finite Impulse Responses

Image blur can often be modeled by a linear spatially invariant, symmetric point spread function. For this class of functions, several restoration filters are known in the literature. The approximation of their frequency transfer functions (ftf's) by the ftf's of small finite impulse response (FIR) filters has been studied. Accurate approximations will be possible by 9 × 9 FIR's with 8-bit elements if the approximation is done in a weighted MMSE sense, and if the truncation of the element values will be carried out such that the errors are small. A heuristic truncation algorithm MINIM will be described. An example of restoration by a 9 × 9 FIR will be shown.