This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
We propose and study an iterative sparse reconstruction for Fourier domain optical coherence tomography （FD OCT） image by solving a constrained optimization problem that minimizes L-1 norm. Our method takes the spec...We propose and study an iterative sparse reconstruction for Fourier domain optical coherence tomography （FD OCT） image by solving a constrained optimization problem that minimizes L-1 norm. Our method takes the spectral shape of the OCT light source into consideration in the iterative image reconstruction procedure that allows deconvolution of the axial point spread function from the blurred image during reconstruction rather than after reconstruction. By minimizing the L-1 norm, the axial resolution and the signal to noise ratio of image can both be enhanced. The effectiveness of our method is validated using numerical simulation and experiment.展开更多
The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sw...The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.展开更多
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
基金supported in part by the government of United States,NIH BRP grants 1R01 EB 007969NIH/NIE R011R01EY021540-01A1,and by internal start-up research funding from Michigan Technological University
文摘We propose and study an iterative sparse reconstruction for Fourier domain optical coherence tomography （FD OCT） image by solving a constrained optimization problem that minimizes L-1 norm. Our method takes the spectral shape of the OCT light source into consideration in the iterative image reconstruction procedure that allows deconvolution of the axial point spread function from the blurred image during reconstruction rather than after reconstruction. By minimizing the L-1 norm, the axial resolution and the signal to noise ratio of image can both be enhanced. The effectiveness of our method is validated using numerical simulation and experiment.
基金This work is partially supported by Sloan FoundationNSF DMS0513073+1 种基金ONR grant N00014-02-1-0090DARPA grant N00014-02-1-0603
文摘The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.
