Recursive Regularization Filters: Design, Properties, and Applications
M. Unser, A. Aldroubi, M. Eden
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 3, pp. 272-277, March 1991.
Least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed. For each problem, there is a family of discrete regularization filters (R-filters) which allow an efficient determination of the solutions. These operators are stable symmetric lowpass filters with an adjustable scale factor. Two decomposition theorems for the z-transform of such systems are presented. One facilitates the determination of their impulse response, while the other allows an efficient implementation through successive causal and anticausal recursive filtering. A case of special interest is the design of R-filters for the first- and second-order difference operators. These results are extended for two-dimensional signals and, for illustration purposes, are applied to the problem of edge detection. This leads to a very efficient implementation (8 multiplies + 10 adds per pixel) of the optimal Canny edge detector based on the use of a separable second-order R-filter.
@ARTICLE(http://bigwww.epfl.ch/publications/unser9103.html, AUTHOR="Unser, M. and Aldroubi, A. and Eden, M.", TITLE="Recursive Regularization Filters: {D}esign, Properties, and Applications", JOURNAL="{IEEE} Transactions on Pattern Analysis and Machine Intelligence", YEAR="1991", volume="13", number="3", pages="272--277", month="March", note="")