Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.900-916
Publication Date: 1994/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
multi-dimensional signals,  optimum approximation,  orthogonal expansions,  stochastic signals,  

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Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.