In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted esti...In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ (1,∞), p_2,…,p_m ∈(1,∞], p ∈ (0,∞) with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1(R n,M_l(logL) σw)× p2(Rn,M~w)×...×Lpm(Rn,Mw) to Lp(Rn,w)with σ to be a constant depending only on p_1 and the order of commutator展开更多
The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral...The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.展开更多
In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,...In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,∞(Rn), and the associated kernel K(x; yl,.. , Ym) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.展开更多
In this paper, we obtain certain Lpw(Rn)-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provide...In this paper, we obtain certain Lpw(Rn)-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ (n-1)/2, b ∈ BMO(Rn), 1 p ∞ and w ∈ A1 . Moreover, if δ (n-1)/2, then we prove that the above maximal operator admits weak type (H1w(Rn), L1w(Rn))-mapping properties for b ∈ BMO(Rn) and w ∈ A1 under the surface condition on Σed .展开更多
In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions dependin...In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.展开更多
As synthetic aperture radar(SAR) has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nucl...As synthetic aperture radar(SAR) has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization(WNNM) is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis(PCA) and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures(BLS-GSM) method, non-local means(NLM) filtering in terms of both quantitative measure and visual perception quality.展开更多
Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image ...Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minim...In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.展开更多
This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subsp...This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subspace.Based on Lagrangian relaxation and secant approximation method,we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of iterations.Furthermore,we design efficient implementations for our algorithm and compare it with a semismooth Newton(SSN)algorithm and a root-finding(Root-F)algorithm.Numerical results on a diversity of test problems show that our algorithm is superior than SSN and Root-F.展开更多
In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed f...In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.展开更多
Based on Bernstein's Theorem, Kalandia's Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial app...Based on Bernstein's Theorem, Kalandia's Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia's Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.展开更多
A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1(R...A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1(Rn)×···×L^pm(Rn) with weight MBw for certain maximal operator MB and general weight w, and a two-weight weighted norm estimate for this operator, are obtained.展开更多
Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is b...Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).展开更多
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
In this paper we prove the existence of global attractor for the generalized dissipative KdVequation on R, and give an upper bound for its Hausdorff and fractal dimensions.
In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using w...In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.展开更多
In recent years,accurate Gaussian noise removal has attracted considerable attention for mobile applications,as in smart phones.Accurate conventional denoising methods have the potential ability to improve denoising p...In recent years,accurate Gaussian noise removal has attracted considerable attention for mobile applications,as in smart phones.Accurate conventional denoising methods have the potential ability to improve denoising performance with no additional time.Therefore,we propose a rapid post-processing method for Gaussian noise removal in this paper.Block matching and 3D filtering and weighted nuclear norm minimization are utilized to suppress noise.Although these nonlocal image denoising methods have quantitatively high performance,some fine image details are lacking due to the loss of high frequency information.To tackle this problem,an improvement to the pioneering RAISR approach(rapid and accurate image super-resolution),is applied to rapidly post-process the denoised image.It gives performance comparable to state-of-the-art super-resolution techniques at low computational cost,preserving important image structures well.Our modification is to reduce the hash classes for the patches extracted from the denoised image and the pixels from the ground truth to 18 filters by two improvements:geometric conversion and reduction of the strength classes.In addition,following RAISR,the census transform is exploited by blending the image processed by noise removal methods with the filtered one to achieve artifact-free results.Experimental results demonstrate that higher quality and more pleasant visual results can be achieved than by other methods,efficiently and with low memory requirements.展开更多
基金This research was supported by the NSFC (10971228).
文摘In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ (1,∞), p_2,…,p_m ∈(1,∞], p ∈ (0,∞) with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1(R n,M_l(logL) σw)× p2(Rn,M~w)×...×Lpm(Rn,Mw) to Lp(Rn,w)with σ to be a constant depending only on p_1 and the order of commutator
基金Foundation item:the Education Commission of Shandong Province(J98P51)
文摘The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.
基金Supported by National Natural Science Foundation of China (Grant No. 10971228)
文摘In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,∞(Rn), and the associated kernel K(x; yl,.. , Ym) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.
基金Supported by School of Education, Korea University Grant in 2011
文摘In this paper, we obtain certain Lpw(Rn)-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ (n-1)/2, b ∈ BMO(Rn), 1 p ∞ and w ∈ A1 . Moreover, if δ (n-1)/2, then we prove that the above maximal operator admits weak type (H1w(Rn), L1w(Rn))-mapping properties for b ∈ BMO(Rn) and w ∈ A1 under the surface condition on Σed .
基金This work is supported by Universidad Nacional de Rio Cuarto.
文摘In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.
基金supported by the National Natural Science Foundation of China(6140130861572063)+7 种基金the Natural Science Foundation of Hebei Province(F2016201142F2016201187)the Natural Social Foundation of Hebei Province(HB15TQ015)the Science Research Project of Hebei Province(QN2016085ZC2016040)the Science and Technology Support Project of Hebei Province(15210409)the Natural Science Foundation of Hebei University(2014-303)the National Comprehensive Ability Promotion Project of Western and Central China
文摘As synthetic aperture radar(SAR) has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization(WNNM) is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis(PCA) and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures(BLS-GSM) method, non-local means(NLM) filtering in terms of both quantitative measure and visual perception quality.
基金This work is supported by the National Natural Science Foundation of China nos.11971215 and 11571156,MOE-LCSMSchool of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China.
文摘Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
基金supported by the National Natural Science Foundation of China under grants U21A20455,61972265,11871348 and 11701388by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007.
文摘In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.
基金supported by the National Natural Science Foundation of China(No.11871153)the Natural Science Foundation of Fujian Province of China(No.2019J01644).
文摘This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subspace.Based on Lagrangian relaxation and secant approximation method,we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of iterations.Furthermore,we design efficient implementations for our algorithm and compare it with a semismooth Newton(SSN)algorithm and a root-finding(Root-F)algorithm.Numerical results on a diversity of test problems show that our algorithm is superior than SSN and Root-F.
基金supported by National Natural Science Foundation of China(Grant No.11901107)the Young Elite Scientists Sponsorship Program by CAST(Grant No.2019QNRC001)+1 种基金the Shanghai Sailing Program(Grant No.19YF1402600)the Science and Technology Commission of Shanghai Municipality Project(Grant No.19511120700).
文摘In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.
基金Supported by National Natural Science Foundation of China(No. 10471107) SF of Wuhan University(No. 20127004).
文摘Based on Bernstein's Theorem, Kalandia's Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia's Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871024 and 10931001)the Key Laboratory of Mathematics and Complex System (at Beijing Normal University), Ministry of Education, China
文摘The author establishes weighted strong type estimates for iterated commutators of multi- linear fractional operators.
基金Supported by the National Natural Science Foundation of China (Grant No.10671210)
文摘A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1(Rn)×···×L^pm(Rn) with weight MBw for certain maximal operator MB and general weight w, and a two-weight weighted norm estimate for this operator, are obtained.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971228)
文摘Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
文摘In this paper we prove the existence of global attractor for the generalized dissipative KdVequation on R, and give an upper bound for its Hausdorff and fractal dimensions.
基金The authors would like to thank the anonymous referees for their valuable suggestions and comments, which improved the paper greatly. The work was supported by Natural Science Foundation of Guangdong Province,China (Grant No.S2012040007993) and Educational Commission of Guangdong Province, China (Grant No. 2012LYM_0122), NNSF of China (Grand No.11126147), NNSF of China (Grand No.11201197) and NNSF of China (Grand No.11271069).
文摘In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.
基金This research was funded by the National Natural Science Foundation of China under Grant Nos.61873117,62007017,61773244,61772253,and 61771231。
文摘In recent years,accurate Gaussian noise removal has attracted considerable attention for mobile applications,as in smart phones.Accurate conventional denoising methods have the potential ability to improve denoising performance with no additional time.Therefore,we propose a rapid post-processing method for Gaussian noise removal in this paper.Block matching and 3D filtering and weighted nuclear norm minimization are utilized to suppress noise.Although these nonlocal image denoising methods have quantitatively high performance,some fine image details are lacking due to the loss of high frequency information.To tackle this problem,an improvement to the pioneering RAISR approach(rapid and accurate image super-resolution),is applied to rapidly post-process the denoised image.It gives performance comparable to state-of-the-art super-resolution techniques at low computational cost,preserving important image structures well.Our modification is to reduce the hash classes for the patches extracted from the denoised image and the pixels from the ground truth to 18 filters by two improvements:geometric conversion and reduction of the strength classes.In addition,following RAISR,the census transform is exploited by blending the image processed by noise removal methods with the filtered one to achieve artifact-free results.Experimental results demonstrate that higher quality and more pleasant visual results can be achieved than by other methods,efficiently and with low memory requirements.