Based on the compressive sensing,a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions.Instead of estimating the reconstructed data through minimizing the objective function,the auth...Based on the compressive sensing,a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions.Instead of estimating the reconstructed data through minimizing the objective function,the authors parameterize the problem as a linear combination of few elementary thresholding functions,which can be solved by calculating the linear weighting coefficients.It is to update the thresholding functions during the process of iteration.The advantage of this method is that the optimization problem only needs to be solved by calculating linear coefficients for each time.With the elementary thresholding functions satisfying certain constraints,a global convergence of the iterative algorithm is guaranteed.The synthetic and the field data results prove the effectiveness of the proposed algorithm.展开更多
Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. ...Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions axe usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi- interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function.展开更多
文摘Based on the compressive sensing,a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions.Instead of estimating the reconstructed data through minimizing the objective function,the authors parameterize the problem as a linear combination of few elementary thresholding functions,which can be solved by calculating the linear weighting coefficients.It is to update the thresholding functions during the process of iteration.The advantage of this method is that the optimization problem only needs to be solved by calculating linear coefficients for each time.With the elementary thresholding functions satisfying certain constraints,a global convergence of the iterative algorithm is guaranteed.The synthetic and the field data results prove the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Nos.61272023,61179041)
文摘Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions axe usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi- interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function.
