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.