This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/...This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/,the only solution of triangle open_H f+f^p=O.展开更多
The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involut...The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.展开更多
A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR-...A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).展开更多
In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and ...In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg’s measurement-disturbation relationship and mass generation in systems like graphene devices.展开更多
In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concep...In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express and study. These concepts can perfect the theory of [J.L. Wu, A new representation theory and some methods on quaternion division algebra, JP Journal of Algebra, 2009, 14(2): 121-140] and unify the complex algebra and quaternion division algebra.展开更多
This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, s...This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.展开更多
This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quater...This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.展开更多
In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion alg...In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion algebras) and we provide the hyperquaternionic approach to the inner product null space (IPNS) representation of conic sections.展开更多
This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds.Moreover,it is shown that after normalization,the...This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds.Moreover,it is shown that after normalization,the solution converges smoothly to the unique solution of the Monge-Ampère equation for(n−1)-quaternionic psh functions.展开更多
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on ...In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.展开更多
Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J...Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(?) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(?)RPn(?) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (?) RPn(?) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.展开更多
In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-sphere...In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".展开更多
Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric ...Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric to HPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4（M） = 1 is greater than or equal to m/2 ＋ 1 for m ≥ 10, then M is isometric to HPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.展开更多
For a harmonic map between two hyperkäher manifolds,we prove a Weitzenböck type formula for the defining quantity of quaternionic maps,and apply it to harmonic morphisms.We also provide a sufficient and nece...For a harmonic map between two hyperkäher manifolds,we prove a Weitzenböck type formula for the defining quantity of quaternionic maps,and apply it to harmonic morphisms.We also provide a sufficient and necessary condition for a smooth map being quaternionic.展开更多
The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quatern...The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.展开更多
In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a fu...In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).展开更多
In this paper,an algorithm on measurement noise with adaptive strong tracking unscented Kalman filter(ASTUKF)is advanced to improve the precision of pose estimation and the stability for data computation.To suppress h...In this paper,an algorithm on measurement noise with adaptive strong tracking unscented Kalman filter(ASTUKF)is advanced to improve the precision of pose estimation and the stability for data computation.To suppress high-frequency noise,an infinite impulse response filter(IIRF)is introduced at the front end of ASTUKF to preprocess the original data.Then the covariance matrix of the error is corrected and the measurement noise is estimated in the process of filtering.After that,the data from the experiment were tested on the hardware experiment platform.The experimental results show that compared to the traditional extended Kalman filter(EKF)and unscented Kalman filter(UKF)algorithms,the root mean square error(RMSE)of the roll axis results from the algorithm proposed in this paper is respectively reduced by approximately 57.5%and 36.1%;the RMSE of the pitch axis results decreases by nearly 58.4%and 51.5%,respectively;and the RMSE of the yaw axis results decreases almost 62.8%and 50.9%,correspondingly.The above results indicate that the algorithm enhances the ability of resisting high-frequency vibration interference and improves the accuracy of attitude solution.展开更多
The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improv...The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improved algorithmal expressions for strap down attitude ut ilizing the angular increment output by the laser gyro from the last two and cur rent updating periods according to the number of gyro samples, and analyses the algorithm error in the classical coning motion. Compared with the conventional algorithms, simulational results show that this improved algorithm has higher precision. A new way to improve the rotation vector algorithms is provided.展开更多
In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color im...In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.展开更多
文摘This paper deals with the problem of the type triangle open_H f+f^p=O inquaternionic Heisenberg group,where triangle open_H is the quaternionic Heisenberg Laplacian.Itis proved that,under suitable conditions on p and/,the only solution of triangle open_H f+f^p=O.
基金supported by NSFC(12071422)Zhejiang Province Science Foundation of China(LY14A010018)。
文摘The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.
文摘A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).
文摘In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg’s measurement-disturbation relationship and mass generation in systems like graphene devices.
文摘In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express and study. These concepts can perfect the theory of [J.L. Wu, A new representation theory and some methods on quaternion division algebra, JP Journal of Algebra, 2009, 14(2): 121-140] and unify the complex algebra and quaternion division algebra.
文摘This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.
文摘This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.
文摘In this paper, by means of an isomorphism, we express the Clifford algebra Cl<sub>5,3</sub> as hyperquaternion algebra H ⊗H ⊗H ⊗H (a four-fold tensor product of quaternion algebras) and we provide the hyperquaternionic approach to the inner product null space (IPNS) representation of conic sections.
基金supported by the National Natural Science Foundation of China(Nos.12141104,11901102).
文摘This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds.Moreover,it is shown that after normalization,the solution converges smoothly to the unique solution of the Monge-Ampère equation for(n−1)-quaternionic psh functions.
基金the National Natural Science Foundation of China Grant 10261002
文摘In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.
基金Acknowledgements We would like to thank Mr.Ma Xiang for his helpful discussion.This work was supported by RFDP,Qiushi Award,973 ProjectJiechu Grant of NSFC.
文摘Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(?) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(?)RPn(?) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (?) RPn(?) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.
基金supported by National Natural Science Foundation of China(Grant Nos.11471299,11401481 and 11331002)。
文摘In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".
基金Supported by Grant No. R01-2006-000-10152-0 from the Basic Research Program of the Korea Science Engineering Foundationthe SRC Program of KOSEF and the BK21 Program of KAIST
文摘Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric to HPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4（M） = 1 is greater than or equal to m/2 ＋ 1 for m ≥ 10, then M is isometric to HPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.
文摘For a harmonic map between two hyperkäher manifolds,we prove a Weitzenböck type formula for the defining quantity of quaternionic maps,and apply it to harmonic morphisms.We also provide a sufficient and necessary condition for a smooth map being quaternionic.
基金the Research Development Foundation of Wenzhou Medical UniversityChina(No.QTJ18012)+6 种基金the Wenzhou Science and Technology Bureau of China(No.G2020031)the Guangdong Basic and Applied Basic Research Foundation of China(No.2019A1515111185)the Science and Technology Development FundMacao Special Administrative RegionChina(No.FDCT/085/2018/A2)the University of MacaoChina(No.MYRG2019-00039-FST)。
文摘The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.
文摘In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).
基金supported by the Key Research and Development Program of Shaanxi Province(No.2024NC-YBXM-246)the Shaanxi Provincial Science and Technology Department(No.2024JC-YBQN-0725)+1 种基金the Education Department of Shaanxi Province(No.23JK0371)the Shaanxi University of Technology(No.SLGRCQD2318).
文摘In this paper,an algorithm on measurement noise with adaptive strong tracking unscented Kalman filter(ASTUKF)is advanced to improve the precision of pose estimation and the stability for data computation.To suppress high-frequency noise,an infinite impulse response filter(IIRF)is introduced at the front end of ASTUKF to preprocess the original data.Then the covariance matrix of the error is corrected and the measurement noise is estimated in the process of filtering.After that,the data from the experiment were tested on the hardware experiment platform.The experimental results show that compared to the traditional extended Kalman filter(EKF)and unscented Kalman filter(UKF)algorithms,the root mean square error(RMSE)of the roll axis results from the algorithm proposed in this paper is respectively reduced by approximately 57.5%and 36.1%;the RMSE of the pitch axis results decreases by nearly 58.4%and 51.5%,respectively;and the RMSE of the yaw axis results decreases almost 62.8%and 50.9%,correspondingly.The above results indicate that the algorithm enhances the ability of resisting high-frequency vibration interference and improves the accuracy of attitude solution.
文摘The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improved algorithmal expressions for strap down attitude ut ilizing the angular increment output by the laser gyro from the last two and cur rent updating periods according to the number of gyro samples, and analyses the algorithm error in the classical coning motion. Compared with the conventional algorithms, simulational results show that this improved algorithm has higher precision. A new way to improve the rotation vector algorithms is provided.
基金The National Natural Science Foundation of China(No.61572258,61173141,61271312,61232016,61272421)the Natural Science Foundation of Jiangsu Province(No.BK2012858,BK20151530)+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.13KJB520015)Open Fund of Jiangsu Engineering Center of Network Monitoring(No.KJR1404)
文摘In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.
