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In this paper, we concentrate on the maximal inclusion problem of locating the zeros of the sum of maximal monotone operators in the framework of proximal point method. Such problems arise widely in several applied mathematical fields such as signal and image processing. We define two new maximal monotone operators and characterize the solutions of the considered problem via the zeros of the new operators...
This paper is mainly on how to design optimal fractional orders by simulated annealing algorithm so that we can obtain fairly good correlation peak. In the first section, the definition of anamorphic fractional correlation is introduced which is more complicated and useful than ordinary correlation. Secondly, several performance measures are presented and simulated annealing algorithm is used to gain...
The main purpose of the present paper is to have a study on the maximal peak of anamorphic fractional correlation. The definition of anamorphic fractional correlation is introduced which is compared by ordinary correlation in the one dimensional case. Furthermore, we present an approach of how to choose the six fractional orders to obtain maximal peak when the input signal is a dilated or shifted...
This paper contains a discussion of the optical implementation of the anamorphic fractional Fourier transform. Firstly, the definition of fractional Fourier transform and its discrete form are given as well as their properties. Secondly, a fast algorithm is presented. Thirdly, an implementation of fractional Fourier transform is observed. Lastly, the definition is extended to two-dimensional case...
In this paper, we are concerned with two dimensional vector valued scaling functions and wavelet functions. A study on the accuracy condition is made and two numerical examples are presented. Furthermore, we conclude that these results are more complicated that in the one dimensional case and the flexibility may by used to satisfy the requirement of applications.
In this paper, we are dealing with the accuracy conditions of one dimensional vector-valued scaling functions. When the symbol functions is defined by lattice structure, we present that accuracy of order two and three implies some nonlinear equations. In the end, two examples are given which seems better than one dimensional of ordinary case.
In this paper, we are dealing with the problem of anamorphic fractional correlation and its optical and digital implementations. Firstly, the definitions of ordinary correlation operation in one and two dimensions are introduced. Secondly, an optical implementation of self correlation is presented. Thirdly, we present the definitions of fractional correlation with dimension one as well as anamorphic...
This paper concerns mainly about two approaches to implement the anamorphic fractional correlation operation. Firstly, the definition of anamorphic fractional correlation is introduced. Secondly, an optical approach of implementing the correlation operation is presented. Lastly, since the optical implementation is somewhat troublesome, we will show how to exploit the anamorphic fractional correlation...
This paper examines a class of univariate wavelet functions with a matrix factorization. Firstly, the property of an important function is surveyed. Secondly, the result is applied to demonstrate the properties of the filters as well as the scaling and wavelet functions. It is presented that two scaling functions are reflections of each other for some pair of parameters. Examples are developed to...
This paper contains a discussion of the applications of matrix theory to filter bank construction. Firstly, two matrix transformations as well as their properties are examined. Secondly, the above results are applied to construct paraunitary filter banks, and the structures of those kinds of filters are studied. In the end, examples are developed to illustrate the proposed technique.
This paper proposes a recursive approach to generate univariate orthonormal wavelet. We will first study two sequences which are crucial for the wavelet construction by matrix factorization. Secondly, we show that the filters of the wavelet (scaling) function can be obtained quite easily. Our proposed results are verified through numerical study.
This paper focuses on the properties of real orthogonal matrices and the applications to the construction of paraunitary multifilter banks. Firstly, formulas of multiple multiplications of real orthogonal matrices as well as some interesting applications are given. Secondly, the above results are applied to give an easy approach to compute a class of paraunitary multifilter banks. In the end, some...
Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. It is pointed out in this paper that we must avoid those "multi-wavelets" being just pairs of standard wavelets. The main purpose of this paper is to charaterize a class of matrices which is crucial for the construction of orthogonal...
A basic problem of this paper is the application of computer-generated holography to optics. Firstly, the definition of anamorphic fractional correlation is introduced and it is pointed out this operation is successfully used to compare the similarities of two signals. This paper describes two computational processes to obtain the correlation result by means of computer-generated holography. The advantages...
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