The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient ...The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.展开更多
The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were c...The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.展开更多
That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on le...That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on length-4 symmetric/anti-symmetric （SA4） orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements. Associated with the local singularity detection principle, cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform. Firstly, studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust （GHM）, Chui-Lian （CL） and SA4. Moreover, the mathematical characterization of singularities with Lipschitz exponents is explained, the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation. Finally, field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm. Because SA4 possesses the specific nature of good multi-filter properties （GMPs）, it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly, and for the half-cycle slip, it also remains better detection, location ability and the equal complexity of wavelet transform.展开更多
Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel seq...Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.展开更多
This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the ...This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.展开更多
In order to solve complex algorithm that is difficult to achieve real-time processing of Multiband image fusion within large amount of data, a real-time image fusion system based on FPGA and multi-DSP is designed. Fiv...In order to solve complex algorithm that is difficult to achieve real-time processing of Multiband image fusion within large amount of data, a real-time image fusion system based on FPGA and multi-DSP is designed. Five-band image acquisition, image registration, image fusion and display output can be done within the system which uses FPGA as the main processor and the other three DSP as an algorithm processor. Making full use of Flexible and high-speed characteristics of FPGA, while an image fusion algorithm based on multi-wavelet transform is optimized and applied to the system. The final experimental results show that the frame rate of 15 Hz, with a resolution of 1392 × 1040 of the five-band image can be used by the system to complete processing within 41ms.展开更多
The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite n...The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.展开更多
基金Supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars from the State Education Ministry (No. [2002]247) and the Young Key Teachers Foundation of Chongqing University.
文摘The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.
基金partially supported by the National Natural Science Foundation of China (Grant No. 11101142 and No. 11571107)
文摘The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.
基金National Natural Science Foundation of China (61153002)
文摘That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on length-4 symmetric/anti-symmetric （SA4） orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements. Associated with the local singularity detection principle, cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform. Firstly, studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust （GHM）, Chui-Lian （CL） and SA4. Moreover, the mathematical characterization of singularities with Lipschitz exponents is explained, the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation. Finally, field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm. Because SA4 possesses the specific nature of good multi-filter properties （GMPs）, it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly, and for the half-cycle slip, it also remains better detection, location ability and the equal complexity of wavelet transform.
基金Supported by the Doctoral Research Project of Yan’an University(Grant No.YDBK2017-21)the Foundation of Yan’an University(Grant No.YDQ2018-09)
文摘Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.
基金This work was motivated by discussions with Dr.Venke Sankaran(Edwards Air Force Research Lab,USA)and was performed while visiting the Applied Mathematics group at HeinrichHeine University,Düsseldorf,Germany.Research supported by the Air Force Ofce of Scientifc Research(AFOSR)Computational Mathematics Program(Program Manager:Dr.Fariba Fahroo)under Grant numbers FA9550-18-1-0486 and FA9550-19-S-0003.
文摘This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.
文摘In order to solve complex algorithm that is difficult to achieve real-time processing of Multiband image fusion within large amount of data, a real-time image fusion system based on FPGA and multi-DSP is designed. Five-band image acquisition, image registration, image fusion and display output can be done within the system which uses FPGA as the main processor and the other three DSP as an algorithm processor. Making full use of Flexible and high-speed characteristics of FPGA, while an image fusion algorithm based on multi-wavelet transform is optimized and applied to the system. The final experimental results show that the frame rate of 15 Hz, with a resolution of 1392 × 1040 of the five-band image can be used by the system to complete processing within 41ms.
基金Supported by National Natural Science Foundation of China (Grant Nos.11071261,60873088 and 10911120394)
文摘The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.
