The optimum approximation of multidimensional vector signals by multi-input multi-output matrix filter banks

Yuichi Kida; Takuro Kida

doi:10.1117/12.893770

8 September 2011 The optimum approximation of multidimensional vector signals by multi-input multi-output matrix filter banks

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 8136, Mathematics of Data/Image Pattern Coding, Compression, and Encryption with Applications XIII; 81360A (2011) https://doi.org/10.1117/12.893770
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

In this paper, we define a multi-input multi-output system composed of given analysis-filter matrices, given sampler matrices and interpolation-filter matrices to be optimized, respectively. It is assumed that input-signal vectors of this system have a finite number of variables and these input-signal vectors are contained in a certain given set of input-signal vectors. Firstly, we define new notations which expresses a kind of product between two matrices or between a vector and a matrix. Using these new notations, we show that the presented approximation satisfies a certain two conditions and prove that the presented approximation minimizes any upper-limit measure of error compared to any other linear or nonlinear approximation with same sample values, simultaneously.

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Yuichi Kida and Takuro Kida "The optimum approximation of multidimensional vector signals by multi-input multi-output matrix filter banks", Proc. SPIE 8136, Mathematics of Data/Image Pattern Coding, Compression, and Encryption with Applications XIII, 81360A (8 September 2011); https://doi.org/10.1117/12.893770

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