Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable ...Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.展开更多
This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of po...In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.展开更多
In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we prese...In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.展开更多
Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedur...Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly- nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11（6） （2013）, 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.展开更多
A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimens...A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a （a 〉 1） dilation to higher dimension with an arbitrary expansive matrix dilation.展开更多
A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coef...A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.展开更多
Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l...Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.展开更多
The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the ...The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.展开更多
A necessary condition is given for general nonuniform Gabor frames, which generalizes Benedetto and Walnut＇s theorem. A sufficient and necessary condition for a class of nonuniform Gabor frames is proved.
The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding fra...The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.展开更多
A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to...A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.展开更多
A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions...A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions. Then different fusion rules are employed in different regions so that the target information is preserved as much as possible. In addition, steerable non-separable wavelet frame transform is used in the process of multi-resolution analysis, so the system achieves favorable characters of orientation and invariant shift. Compared with other image fusion methods, experimental results showed that the proposed method has better capabilities of target recognition and preserves clear background information.展开更多
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra...In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.展开更多
A novel technique for the video watermarking based on the discrete wavelet transform (DWT) is present. The intra frames of video are transformed to three gray image firstly, and then the 2th-level discrete wavelet dec...A novel technique for the video watermarking based on the discrete wavelet transform (DWT) is present. The intra frames of video are transformed to three gray image firstly, and then the 2th-level discrete wavelet decomposition of the gray images is computed, with which the watermark W is embedded simultaneously into and invert wavelet transform is done to obtain the gray images which contain the secret information. Change the intra frames of video based on the three gray images to make the intra frame contain the secret information. While extracting the secret information, the intra frames are transformed to three gray image, 2th-level discrete wavelet transform is done to the gray images, and the watermark W’ is distilled from the wavelet coefficients of the three gray images. The test results show the superior performance of the technique and potential for the watermarking of video.展开更多
基金supported by NBHM, Department of Atomic Energy, Government of India (Grant No. 2/48(8)/2016/NBHM(R.P)/R&D II/13924)
文摘Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.
文摘This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
文摘In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.
基金This work was supported by CONICET and Universidad Nacional de San Luis
文摘In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.
文摘Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly- nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11（6） （2013）, 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.
基金Supported by the National Natural Science Foundation of China (No.10671062)Innovation Scientists and Technicians Troop Construction Projects of Henan Province of China (No.084100510012)the Natural Science Foundation for the Education Department of Henan Province of China (No.2008B510001)
文摘A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a （a 〉 1） dilation to higher dimension with an arbitrary expansive matrix dilation.
文摘A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.
基金Supported by the National Natural Science Foundation of China(11071065,11101142,11171306,10671062)the China Postdoctoral Science Foundation(20100480942)+1 种基金the Ph.D.Programs Foundation of the Ministry of Education of China(20094306110004)the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province
文摘Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.
基金supported by Hunan Education Office Foundation under Grant 06C260
文摘The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.
基金The project is partially supported by a grant from Beijing Educational Committee (KM200410005013)
文摘A necessary condition is given for general nonuniform Gabor frames, which generalizes Benedetto and Walnut＇s theorem. A sufficient and necessary condition for a class of nonuniform Gabor frames is proved.
文摘The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.
基金This project was supported by the National Nature Science Foundation of China (60473119)
文摘A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.
基金Project (No. 2004CB719401) supported by the National Basic Research Program (973) of China
文摘A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions. Then different fusion rules are employed in different regions so that the target information is preserved as much as possible. In addition, steerable non-separable wavelet frame transform is used in the process of multi-resolution analysis, so the system achieves favorable characters of orientation and invariant shift. Compared with other image fusion methods, experimental results showed that the proposed method has better capabilities of target recognition and preserves clear background information.
文摘In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.
基金Supported by the Science and Technology Plan Foundation of GuangDong (No. 2004B16001006) and the Science and Technology Plan Foundation of Dongguan (No. 2004D1015)
文摘A novel technique for the video watermarking based on the discrete wavelet transform (DWT) is present. The intra frames of video are transformed to three gray image firstly, and then the 2th-level discrete wavelet decomposition of the gray images is computed, with which the watermark W is embedded simultaneously into and invert wavelet transform is done to obtain the gray images which contain the secret information. Change the intra frames of video based on the three gray images to make the intra frame contain the secret information. While extracting the secret information, the intra frames are transformed to three gray image, 2th-level discrete wavelet transform is done to the gray images, and the watermark W’ is distilled from the wavelet coefficients of the three gray images. The test results show the superior performance of the technique and potential for the watermarking of video.
