Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o...Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.展开更多
Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach ofte...Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.展开更多
If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, so...In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.展开更多
文摘Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.
基金supported by the National Science Foundation for Distinguished Young Scholars(Grant No.62125104)the National Natural Science Foundation of China(Grant No.52071111).
文摘Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
文摘In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.
