In this paper,based on the previous published work by Ke et al.(2019)and Li et al.(2022),by using the matrix splitting technique,generalized fixed point iteration method(GFPI)is established to solve the absolute value...In this paper,based on the previous published work by Ke et al.(2019)and Li et al.(2022),by using the matrix splitting technique,generalized fixed point iteration method(GFPI)is established to solve the absolute value equation(AVE).The proposed method not only includes SOR-like method,FPI method,MFPI method and so on,but also generates some special versions.Some convergence conditions of the proposed method with different iteration error norms are presented.Furthermore,methods corresponding to other splitting methods are studied in detail.The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments.展开更多
This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimato...This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimator satisfies a fixed point equation.The convergence property of the proposed algorithm is established.Numerical studies are conducted to evaluate the finite sample performance of the proposed algorithm.展开更多
Abstract This paper aims at the multichannel synthetic aperture radar （SAR） image speckle reduc- tion. This paper proposes a novel energy minimized regularization model for multichannel image denoising, which is an ...Abstract This paper aims at the multichannel synthetic aperture radar （SAR） image speckle reduc- tion. This paper proposes a novel energy minimized regularization model for multichannel image denoising, which is an extension of the non-local total variational model for gray-scale image. It contains two terms, namely the vectorial data fidelity term and the non-local vectorial total variation term. The latter is constructed by high-dimensional non-local gradient that contains the structure information of the multichannel image. The existence and the uniqueness of the solution of the model are proved. A fixed point iterative algorithm is designed to acquire the solution of this model. The convergence property of this algorithm is proved as well. This model is applied to the multipolarimetric and multi-temporal RAI）ARSAT-2 images despeckling. The result shows that this model performs better than the original vectorial total variational model on texture preserving.展开更多
A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algori...A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.展开更多
Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix spl...Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix splitting based iterative methods.In this paper,by using Anderson acceleration on general splitting iterative methods for linear systems,three classes of methods are given.The first one is obtained by directly applying Anderson acceleration on splitting iterative methods.For the second class of methods,Anderson acceleration is used periodically in the splitting iteration process.The third one is constructed by combining the Anderson acceleration and split iteration method in each iteration process.The key of this class of method is to determine a combination coefficient for Anderson acceleration and split iteration method.One optimal combination coefficient is given.Some theoretical results about the convergence of the considered three methods are established.Numerical experiments show that the proposed methods are effective.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12371378)the Natural Science Foundation of Fujian Province(Grant No.2024J01980)。
文摘In this paper,based on the previous published work by Ke et al.(2019)and Li et al.(2022),by using the matrix splitting technique,generalized fixed point iteration method(GFPI)is established to solve the absolute value equation(AVE).The proposed method not only includes SOR-like method,FPI method,MFPI method and so on,but also generates some special versions.Some convergence conditions of the proposed method with different iteration error norms are presented.Furthermore,methods corresponding to other splitting methods are studied in detail.The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments.
基金Supported by the National Natural Science Foundation of China(11701571)
文摘This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimator satisfies a fixed point equation.The convergence property of the proposed algorithm is established.Numerical studies are conducted to evaluate the finite sample performance of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Nos.61072142,61271437,61201337)the Science Research Project of National University of Defense Technology of China(Nos.JC12-02-05,JC13-02-03)
文摘Abstract This paper aims at the multichannel synthetic aperture radar （SAR） image speckle reduc- tion. This paper proposes a novel energy minimized regularization model for multichannel image denoising, which is an extension of the non-local total variational model for gray-scale image. It contains two terms, namely the vectorial data fidelity term and the non-local vectorial total variation term. The latter is constructed by high-dimensional non-local gradient that contains the structure information of the multichannel image. The existence and the uniqueness of the solution of the model are proved. A fixed point iterative algorithm is designed to acquire the solution of this model. The convergence property of this algorithm is proved as well. This model is applied to the multipolarimetric and multi-temporal RAI）ARSAT-2 images despeckling. The result shows that this model performs better than the original vectorial total variational model on texture preserving.
基金supported by the National Natural Science Foundation of China(No.61271014)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301110003)the Graduated Students Innovation Fund of Hunan Province(No.CX2012B238)
文摘A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.
基金funded by the National Natural Science Foun China(Grant Nos.12171045,11671051).
文摘Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix splitting based iterative methods.In this paper,by using Anderson acceleration on general splitting iterative methods for linear systems,three classes of methods are given.The first one is obtained by directly applying Anderson acceleration on splitting iterative methods.For the second class of methods,Anderson acceleration is used periodically in the splitting iteration process.The third one is constructed by combining the Anderson acceleration and split iteration method in each iteration process.The key of this class of method is to determine a combination coefficient for Anderson acceleration and split iteration method.One optimal combination coefficient is given.Some theoretical results about the convergence of the considered three methods are established.Numerical experiments show that the proposed methods are effective.
