9 September 2011 The optimum approximation of multidimensional vector signals by multi-input multi-output matrix filter banks
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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, 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 (9 September 2011); doi: 10.1117/12.893770; https://doi.org/10.1117/12.893770
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KEYWORDS
Matrices

Electronic filtering

Multidimensional signal processing

Optical filters

Filtering (signal processing)

Nonlinear filtering

Chemical elements

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