Optimisation technique for the implementation of two-dimensional recursive digital filters by sectioning

Abstract

The problem of two-dimensional recursive digital filtering of large images by the sectioning (or block-mode) technique has been considered. It has been stated that, if the impulse-response sequence of the recursive digital filter dies down relatively sharply, by a suitable truncation, the available sectioning techniques can be used to perform the filtering operation, as with nonrecursive filters. An analytical approach is presented which formulates the upper bound on the norm of error resulting from the application of truncation. This bound is found to be independent of the size of blocks. In addition, an expression for the computation time is obtained, when a mixed radix two-dimensional FFT is used. Using these expressions, a simple procedure for minimising the truncation error and computation time is suggested which determines suitable values of the parameters involved. The effectiveness of the optimisation procedure developed here has been examined for smoothing operation of an X-ray image on a CDC 6500 computer.