Nonlinear smoothing filters based on rank estimates of location

Abstract

Abstracf-A class of nonlinear filters is introduced, which is based on the rank estimates (R-estimate\) of location parameters in statistical theory. We show first how moving-window rank filters (R-filters) can be defined starting from rank estimates of location. These filters utilize the relative ranks of the observations in each window to produce a n output value. A special class of rank filters produces outputs which a r e medians of selected pairwise averages of observations inside each ~i n d o w .The Wilcoxon filter is one simple example of such a n R-filter. The concept of rank \Vinsorization allows a limiting of the influence of larger rank ohservations. W e extend the idea of r a n k Winsorization to that of averaging only observations which lie within small temporal neighhorhoods. This leads to a definition of the class of generalized Wilcoxon (GW) filters, w hich a r e paranietrized b j three parameters, namelj, the degrees of temporal a n d rank Winsorization and the degree of averaging. The GW filters can be defined to have desirable characteristics of edge preservation, detail retention. and impulse re-,jection, in addition to the property of Gaussian noise smoothing. Performance characteristics of these filters a r e considered through anal-?\is and %iniulations with one-dimensional signals. The filters considered here together with recent results on L-and M-filters show that all three well-known classes of rohust location estimates, the L-, M-, and R-estimates, can be applied to nonlinear smoothing of signals. I. IN"WDUCIX)NINEAR filters have been widely used for successfully L suppressing additive Gaussian noise in noisy sequences composed of desired signals and noise in many digital signal processing schemes. One of the advantages of linear filters is that efficient FFT algorithms may be exploited to reduce the computation time required for the processing; a wide variety of other efficient and practical hardware implementations are also available for linear filters. It is, however, well known that linear filters, which are best for reducing additive Gaussian noise in a noisy data sequence, give poor performance characteristics in certain situations of practical interest. For example, they smear out any edges in an image. and they are also very poor in suppressing impulsive noise with heavy-tailed probability density function. In these circumstances, nonlinear and/or adaptive techniques need to be employed to Manuscript received Deccniber 5 . 1987: rcviwd November 30. 1988 obtain a reasonable recovered version of the desired signal.In order to overcome these disadvantages of linear filters and to get better performance in such cases, nonlinear techniques have been proposed and shown to be very effective in such situations [11][12][13][14][15][16][17][18][19]. Median filters, whose outputs are defined as medians of the input values in neighborhoods around each point of the discrete-time noisy signal, for example, have strongly nonlinear characteristics. being able to reject quite effectively impu...

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