A Two-Level Iterative Method for Image Reconstruction with Radial Basis Functions

Abstract

Radial basis functions are popular basis for interpolating scattered data during the image reconstruction process in graphic analysis. In this context, the solution of a linear system of equations is required for each color (blue, red, green) and represents the most time-consuming operation. In this paper a two-level iterative algorithm is proposed to solve efficiently these linear systems of equations. This two-level algorithm consists of a preconditioned iterative method which enforces at each iteration a projection of the residual onto a suitable coarse space. This constraint is ensured by solving an auxiliary second-level problem at each iteration. Numerical results illustrate the convergence properties of the proposed method on a wide range of interpolation problems for image reconstruction.

Fast Iterative Solvers for Large Compressed-Sparse Row Linear Systems on Graphics Processing Unit

“…CPU and GPU algorithms are compared in simple and double precision for two test cases: 2D and 3D. The first test case arises from the discretization of Laplacian problems [24] [25], [26] applied to image reconstruction (for 2D and 3D image rendering). The second test case arises from the finite element discretization acoustics problems, similar to those presented in [27] for an open roof-car compartment (in 2D and 3D), but with a discretization with stabilized finite element [28] within the domain and with infinite element on the artificial boundary conditions defined on the truncation boundary of the domain [29] [30] [31].…”

RBF-vortex methods for the barotropic vorticity equation on a sphere

“…Preconditioned iterations are also strongly accelerative [1,53,54,64,82]. Barba and Yokota argue that these improvements are very well-suited to emerging computer architectures [2].…”

Coarse Space Correction for Graphic Analysis

“…This approach consists of a coarse space correction [26,41] applied to the solution of the interface problem arising from the domain decomposition method. In references [17,18] for graphic analysis this approach is applied directly to the solution of the linear system (2). Each iteration of the algorithm involves a projection of the residual on a coarse space basis.…”

“…The first tentative of coarse space correction to solve CSRBF interpolation problem has been presented in [17]. Choosing as a coarse space basis the eigenvectors of the CSRBF interpolation problem definitely improves the convergence of the iterative method.…”