In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling an...In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.展开更多
A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ ...A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.展开更多
Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the c...Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L 1(R) are given in terms of such generators and the local basis of shift-invariant subspaces.展开更多
In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉x...In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.展开更多
The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the te...The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich (1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz (1991).展开更多
In existing methods for segmented images,either edge point extraction or preservation of edges,compromising contrast images is so sensitive to noise.The Degeneration Threshold Image Detection(DTID)framework has been p...In existing methods for segmented images,either edge point extraction or preservation of edges,compromising contrast images is so sensitive to noise.The Degeneration Threshold Image Detection(DTID)framework has been proposed to improve the contrast of edge filtered images.Initially,DTID uses a Rapid Bilateral Filtering process for filtering edges of contrast images.This filter decomposes input images into base layers in the DTID framework.With minimal filtering time,Rapid Bilateral Filtering handles high dynamic contrast images for smoothening edge preservation.In the DTID framework,Rapid Bilateral Filtering with Shift-Invariant Base Pass Domain Filter is insensitive to noise.This Shift-Invariant Filtering estimates value across edges for removing outliers(i.e.,noise preserving base layers of the contrast image).The intensity values are calculated in the base layer of the contrast image for accurately detecting nearby spatial locations using Shift-Invariant base Pass Domain Filter(SIDF).At last,Affine Planar Transformation is applied to detect edge filtered contrast images in the DTID framework for attaining a high quality of the image.It normalizes the translation and rotation of images.With this,Degeneration Threshold Image Detection maximizes average contrast enhancement quality and performs an experimental evaluation of factors such as detection accuracy,rate,and filtering time on contrast images.Experimental analysis shows that the DTID framework reduces the filtering time taken on contrast images by 54%and improves average contrast enhancement quality by 27%compared to GUMA,HMRF,SWT,and EHS.It provides better performance on the enhancement of average contrast enhancement quality by 28%,detection accuracy rate by 26%,and reduction in filtering time taken on contrast images by 30%compared to state-of-art methods.展开更多
A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better conv...A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.展开更多
The main purpose of this paper is to establish some new sufficient conditions under which shift-invariant systems become frames in L2(Rn). As applications, we obtain new results for Gabor frames.
In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^...In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^2(0, α), two sampling theorems for αZ-shift invariant spaces with a single generator are obtained.展开更多
基金supported by National Natural Science Foundation of China(Grant No.61501493)。
文摘In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.
文摘A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.
基金the National Natural Science Foundation of China(1 0 0 71 0 71 )
文摘Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L 1(R) are given in terms of such generators and the local basis of shift-invariant subspaces.
文摘In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.
文摘The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich (1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz (1991).
文摘In existing methods for segmented images,either edge point extraction or preservation of edges,compromising contrast images is so sensitive to noise.The Degeneration Threshold Image Detection(DTID)framework has been proposed to improve the contrast of edge filtered images.Initially,DTID uses a Rapid Bilateral Filtering process for filtering edges of contrast images.This filter decomposes input images into base layers in the DTID framework.With minimal filtering time,Rapid Bilateral Filtering handles high dynamic contrast images for smoothening edge preservation.In the DTID framework,Rapid Bilateral Filtering with Shift-Invariant Base Pass Domain Filter is insensitive to noise.This Shift-Invariant Filtering estimates value across edges for removing outliers(i.e.,noise preserving base layers of the contrast image).The intensity values are calculated in the base layer of the contrast image for accurately detecting nearby spatial locations using Shift-Invariant base Pass Domain Filter(SIDF).At last,Affine Planar Transformation is applied to detect edge filtered contrast images in the DTID framework for attaining a high quality of the image.It normalizes the translation and rotation of images.With this,Degeneration Threshold Image Detection maximizes average contrast enhancement quality and performs an experimental evaluation of factors such as detection accuracy,rate,and filtering time on contrast images.Experimental analysis shows that the DTID framework reduces the filtering time taken on contrast images by 54%and improves average contrast enhancement quality by 27%compared to GUMA,HMRF,SWT,and EHS.It provides better performance on the enhancement of average contrast enhancement quality by 28%,detection accuracy rate by 26%,and reduction in filtering time taken on contrast images by 30%compared to state-of-art methods.
基金This work is supported in part by the National Natural Science Foundation of China (10771190, 10801136), the Mathematical Tianyuan Foundation of China NSF (10526036), China Postdoctoral Science Foundation (20060391063), Natural Science Foundation of Guangdong Province (07300434)
文摘A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.
基金Supported by National Natural Science Foundation of China (Grant No.61071189)the support of the Science and Technology Development Fund of Macao Special Administrative Region (Grant No.056/2010/A3)
文摘The main purpose of this paper is to establish some new sufficient conditions under which shift-invariant systems become frames in L2(Rn). As applications, we obtain new results for Gabor frames.
基金Supported by the National Natural Science Foundation of China (Grant No.10871012)the Natural Science Foundation of Beijing (Grant No.1082003)
文摘In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^2(0, α), two sampling theorems for αZ-shift invariant spaces with a single generator are obtained.