Ruikang Yang

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 filters 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. >

Optimal weighted median filters under structural constraints

An algorithm is developed for finding optimal weighted median (WM) filters which minimize noise subject to a predetermined set of structural constraints on the filters behavior. Based on the derivation of the output moments of weighted medians, it is shown that optimal weighted medians with structural constraints may be found by solving a group of linear inequalities. One-dimensional applications are discussed.<<ETX>>

Order statistics learning vector quantizer

We propose a novel class of learning vector quantizers (LVQs) based on multivariate data ordering principles. A special case of the novel LVQ class is the median LVQ, which uses either the marginal median or the vector median as a multivariate estimator of location. The performance of the proposed marginal median LVQ in color image quantization is demonstrated by experiments.

Fast algorithms for analyzing and designing weighted median filters

Abstract In this paper, two fast algorithms are developed to compute a set of parameters, called Mis, of weighted median filters for integer weights and real weights, respectively. The Mis, which characterize the statistical properties of weighted median filters and are the critical parameters in designing optimal weighted median filters, are defined as the cardinality of the positive subsets of weighted median filters. The first algorithm, which is for integer weights, is about four times faster than the existing algorithm. The second algorithm, which applies for real weights, reduces the computational complexity significantly for many applications where the symmetric weight structures are assumed. Applications of these new algorithms include design of optimal weighted filters, computations of the output distributions, the output moments, and the rank selection probabilities, and evaluation of noise attenuation for weighted median filters.

An efficient design method for optimal weighted median filtering

Earlier research has shown that the problem of optimal weighted median filtering with structural constraints can be formulated as a nonconvex nonlinear programming problem in general. However, its high computational complexity and poor performance due to its nonconvex nature prohibit it from practical applications. In this paper, we shall show that the design problem can be formulated as a convex quadratic programming problem. The new algorithm is very efficient in the sense of computational complexity. The algorithm is also efficient in the sense of its capability to approach the global minimum. Using the algorithm optimal 1-D weighted median filters preserving pulses of length 3, 4 and 5 are tabulated.<<ETX>>

On root structures and convergence properties of weighted median filters

AbstractA weighted median filter is a nonlinear digital filter consisting of a window of length 2N + 1 and a weight vector W=(W−N,..., W0,..., WN). A root signal of a median type filter is a signal that is invariant to the filter. However, not all weighted median filters possess the convergence property. In this paper, we shall study the root structures and the convergence behavior of a subclass of weighted median filters, calledclass- 1 filters, which is symmetric in its weight vector. We shall introduce an important parameter, calledfeature value, and show that any one-dimensional unappended signal of lengthL will converge to a root signal in at most

A class of order statistics learning vector quantizers

3\left\lceil {\frac{{L - 2}}{{2(2N + 2 - p)}}} \right\rceil

Parametric analysis of weighted order statistic filters

passes of aclass −1 filter with window width 2N + 1 and thefeature value p.