In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogon...In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks.展开更多
This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector par...This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
In this paper Haar wavelet integral operational matrices are introduced and then applied to analyse linear time varying systems. The method converts the original problem to solving linear algebraic equations. Hence, ...In this paper Haar wavelet integral operational matrices are introduced and then applied to analyse linear time varying systems. The method converts the original problem to solving linear algebraic equations. Hence, computational difficulties are considerably reduced. Based on the property of time frequency localization of Haar wavelet bases, the solution of a system includes both the frequency information and the time information. Other orthogonal functions do not have this property. An example is given, and the results are shown to be very accurate.展开更多
The main result of this paper is a bi-parameter Tb theorem for Littlewood-Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure...The main result of this paper is a bi-parameter Tb theorem for Littlewood-Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure μ = μn × μm, where the measures μn and μm are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter b-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again.展开更多
文摘In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks.
基金Supported by the National Natural Science Foundation of China(61573378)the Fundamental Research Funds for the Central Universities(15CX06064A)
文摘This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
基金国家重点基础研究发展规划( 973)( the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000)国家自然科学基金( the National Natural Science Foundation of China under Grant No.60133020, No.10671002, No.10771002)+1 种基金 浙江大学CAD&CG国家重点实验室开放课题( No.A0503) 澳门科技发展基金( No.045/2006/A)
文摘In this paper Haar wavelet integral operational matrices are introduced and then applied to analyse linear time varying systems. The method converts the original problem to solving linear algebraic equations. Hence, computational difficulties are considerably reduced. Based on the property of time frequency localization of Haar wavelet bases, the solution of a system includes both the frequency information and the time information. Other orthogonal functions do not have this property. An example is given, and the results are shown to be very accurate.
文摘The main result of this paper is a bi-parameter Tb theorem for Littlewood-Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure μ = μn × μm, where the measures μn and μm are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter b-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again.