By Yasumichi Hasegawa
This monograph bargains with approximation and noise cancellation of dynamical structures which come with linear and nonlinear input/output relationships. It additionally care for approximation and noise cancellation of 2 dimensional arrays. it is going to be of distinct curiosity to researchers, engineers and graduate scholars who've really good in filtering idea and method thought and electronic pictures. This monograph consists of 2 elements. half I and half II will take care of approximation and noise cancellation of dynamical platforms or electronic photos respectively. From noiseless or noisy info, relief could be made. a mode which reduces version info or noise used to be proposed within the reference vol. 376 in LNCIS [Hasegawa, 2008]. utilizing this technique will permit version description to be taken care of as noise aid or version relief with no need to hassle, for instance, with fixing many partial differential equations. This monograph will suggest a brand new and straightforward procedure which produces an analogous effects because the technique taken care of within the reference. As facts of its beneficial influence, this monograph offers a brand new legislation within the feel of numerical experiments. the hot and simple technique is done utilizing the algebraic calculations with no fixing partial differential equations. For our goal, many real examples of version info and noise relief can be provided.
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Additional info for Algebraically Approximate and Noisy Realization of Discrete-Time Systems and Digital Images
0 ... ⎦ 0 1 αn ⎡ [proof] By 1), the noisy part in the data can be excluded in the sense of the number of dimensions. 17). 17). ˆ a (n,p) Therefore, we obtain the cleaned-up Hankel matrices H ¯ . 15) to the Ha (n+1,p) ¯ . Remark 1: A determination method of the degree n in the linear system σ = ((Rn , Fs ), g, hs ) is found in the Principal Component Method. The method is very popular. Remark 2: Let S and N be the norm of a signal and a noise. Then the selected N ratio of matrices in the algorithm may be considered as S+N .
6. 8 Fig. 8} is composed of relatively small and equally-sized numbers in the square root of HaT (6,50) Ha (6,50) , the noisy realization of a linear system obtained by the algebraic CLS method may be good for 3-dimensional space. 2) After determining the number n of dimensions which is 3, we will continue the noisy realization algorithm by the algebraic CLS method. Therefore, the modiﬁed impulse response I(0) of a linear system obtained by the algebraic CLS method is realized by a 3-dimensional linear system σc = ((R3 , Fc ), e1 , hc ).
08 0 Algebraically Noisy Realization of Linear Systems In this section, we discuss the algebraically noisy realization problem of linear systems. Firstly, we must refer to the information criterion method AIC in noisy cases of linear systems which is more commonly used. We will compare our algorithm by the algebraic CLS method with the AIC method. 5 Algebraically Noisy Realization of Linear Systems 37 In order to make our discussion simple, we assume that the set Y of outout is the set R of real numbers, namely 1-output.