The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients

Yuichi Kida; Takuro Kida

doi:10.1117/12.795760

3 September 2008 The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 7075, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications XI; 70750E (2008) https://doi.org/10.1117/12.795760
Event: Optical Engineering + Applications, 2008, San Diego, California, United States

Abstract

In this paper, we establish the optimum interpolation approximation for a set of multi-dimensional statistical orthogonal expansions. Each signal has a bounded linear combination of higher order self-correlations and mutual-correlations with respect to coefficients of the expansion. For this set of signals, we present the optimum interpolation approximation that minimizes various worst-case measures of mean-square error among all the linear and the nonlinear approximations. Finally, as a practical application of the optimum interpolation approximation, we present a discrete numerical solution of linear partial differential equations with two independent variables.

Citation Download Citation

Yuichi Kida and Takuro Kida "The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients", Proc. SPIE 7075, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications XI, 70750E (3 September 2008); https://doi.org/10.1117/12.795760

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