Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation wind...

We discuss numerical interpolation schemes used in Vlasov codes. An improved conservative semi-Lagrangian scheme is compared with the latest nonconservative and conservative schemes for a long run-time nonlinear problem of the beam-plasma interaction with respect to the mass and energy conservations.

We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.

We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh optimization algorithm can reduce the W 1,∞ semi-norm of the interpolation error. For these examp...

In this paper we consider the problem of developing a variational theory for interpolation by radial basis functions on spheres. The interpolants have the property that they minimise the value of a certain semi-norm, which we construct explicitly. We then go on to investigate forms of the interpolant which are suitable for computation. Our main aim is to derive error bounds for interpolation fr...

Abstract. Inspired by the graph Laplacian and the point integral method, we introduce a novel weighted graph Laplacian method to compute a smooth interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted graph Laplacian is a reliable and efficient interpolation method. In addition, it is easy ...

We propose a novel semi-supervised learning scheme using adaptive interpolation on multiple one-dimensional (1-D) embedded data. For a give high dimensional data set, we smoothly map it onto several different one-dimensional (1-D) sequences, so that the labeled subset is converted to a 1-D subset for each of these sequences. Applying the cubic interpolation of the labeled subset, we obtain a su...

An active-contour-interpolation approach is proposed for semi-automatic video object generation. In this approach, user can de ne the contour of the same video object on multiple frames and the computer interpolates the missing contours automatically. Typical active contour model is adapted and the contour interpolation problem is decomposed into two directional contour tracking problems and a ...

This invited contribution first reviews basic features of multivariate interpolation by radial basis functions, before selected of its advanced topics are addressed, including recent results concerning local polyharmonic spline interpolation. The latter is one main ingredient of a novel class of adaptive meshfree semi-Lagrangian methods for transport problems. The construction of these particle...