Interpolatory estimation of multi-dimensional orthogonal expansions with stochastic coefficients

The interpolation of multidimensional signals is widely considered in connection with the problem of suppressing the immanent redundancy contained in an image without vitiating the quality of the resultant approximation. The minimization of the approximation error is one of the important problems in this field. In the field of information processing, one sometimes considers the orthonormal development of an image each coefficient of which represents the principal feature of the image. The selection of the orthonormal bases becomes important in this problem. Fisher´s criterion is a powerful tool for declustering. The combination of these two analyses is an interesting problem in image processing. In the present work, the optimum interpolatory approximation of multidimensional orthogonal expansions is established, and some remarks are made on the above problem