Optimal weighted median filtering under structural constraints

A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter's behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters. >

[1]  Sung-Jea Ko,et al.  Center weighted median filters and their applications to image enhancement , 1991 .

[2]  Moncef Gabbouj,et al.  2-D Optimal Weighted Median Filters , 1992 .

[3]  Pao-Ta Yu,et al.  On the existence and design of the best stack filter based associative memory , 1992 .

[4]  R. Lippmann,et al.  An introduction to computing with neural nets , 1987, IEEE ASSP Magazine.

[5]  Edward J. Coyle,et al.  Adaptive stack filtering under the mean absolute error criterion , 1990, Other Conferences.

[6]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .

[7]  Moncef Gabbouj,et al.  Minimum Mean Absolute Error Stack Filtering with Structural Constraints and Goals , 1990 .

[8]  Edward J. Coyle,et al.  Stack filters and the mean absolute error criterion , 1988, IEEE Trans. Acoust. Speech Signal Process..

[9]  M. Gabbouj,et al.  Optimal weighted median filters under structural constraints , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[10]  Peter D. Wendt.  Nonrecursive and recursive stack filters and their filtering behavior , 1990, IEEE Trans. Acoust. Speech Signal Process..

[11]  T. Loupas,et al.  An adaptive weighted median filter for speckle suppression in medical ultrasonic images , 1989 .

[12]  Yrjö Neuvo,et al.  Adaptive DPCM With Median Type Predictors , 1991 .

[13]  Bing Zeng.  On the root structures of weighted median filters , 1991 .

[14]  Yrjö Neuvo,et al.  Motion adaptive scan rate up-conversion , 1992, Multidimens. Syst. Signal Process..

[15]  Pao-Ta Yu,et al.  On the existence and design of the best stack filter based associative memory , 1990, IEEE International Symposium on Circuits and Systems.

[16]  Pao-Ta Yu,et al.  Convergence behavior and N-roots of stack filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[17]  Moncef Gabbouj,et al.  Weighted medians - positive Boolean functions conversion algorithms , 1993, Signal Process..

[18]  M. K. Prasad,et al.  Analysis of weighted median filters based on inequalities relating the weights , 1992 .

[19]  Moncef Gabbouj,et al.  Optimal weighted order statistic filters under structural constraints , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[20]  Jaakko Astola,et al.  Adaptive Stack Filtering with Application to Image Processin , 1993, IEEE Trans. Signal Process..

[21]  Moncef Gabbouj,et al.  Optimal stack filtering and the estimation and structural approaches to image processing , 1989, Sixth Multidimensional Signal Processing Workshop,.

[22]  D. Brownrigg.  Generation of representative members of an RrSst weighted median filer class , 1986 .

[23]  D. R. K. Brownrigg,et al.  The weighted median filter , 1984, CACM.

[24]  Moncef Gabbouj,et al.  Median Based Idempotent filters , 1991, J. Circuits Syst. Comput..

[25]  Jaakko Astola,et al.  A new class of nonlinear filters-neural filters , 1993, IEEE Trans. Signal Process..

[26]  Jaakko Astola,et al.  Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation , 1991, IEEE Trans. Signal Process..

[27]  Yrjö Neuvo,et al.  Improving TV picture quality with linear-median type operations , 1988 .

[28]  M. K. Prasad,et al.  Weighted median filters: generation and properties , 1989, IEEE International Symposium on Circuits and Systems,.

[29]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[30]  Moncef Gabbouj,et al.  Real Domain Adaptive WOS Filtering using Neural Network Approximations , 1993, IEEE Winter Workshop on Nonlinear Digital Signal Processing.

[31]  B I Justusson,et al.  Median Filtering: Statistical Properties , 1981 .