In this paper a novel method of noise reduction in color images is presented. The new technique is capable of attenuating both impulsive and Gaussian noise, while preserving and even enhancing the sharpness of the image edges. Extensive simulations reveal that the new method outperforms significantly the standard techniques widely used in multivariate signal processing. In this work we apply the new noise reduction method for the enhancement of the images of the so called gene chips. We demonstrate that the new technique is capable of reducing the impulsive noise present in microarray images and that it facilitates efficient spot location and the estimation of the gene expression levels due to the smoothing effect and preservation of the spot edges. This paper contains a comparison of the new technique of impulsive noise reduction with the standard procedures used for the processing of vector valued images, as well as examples of the efficiency of the new algorithm when applied to typical microarray images.
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This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant.
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