Interpolation using Hankel tensor completion

3d Interpolation Using Hankel Tensor Completion by Orthogonal Matching Pursuit

Introduction. Seismic data are often sparsely or irregularly sampled along one or more spatial axes. Irregular sampling can produce artifacts in seismic imaging results, thus multidimensional interpolation of seismic data is often a key processing step in exploration seismology. Many solution methods have appeared in the literature: for instance in Spitz (1991), Sacchi (2000) it was proposed to...

Quasi-Hankel low-rank matrix completion: a convex relaxation

The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this relaxation, an important question is whether the two optimization problems lead to the same solution. This question was addressed in the literature mostly in the ca...

Improved Temporal Resolution TWIST Reconstruction using Annihilating Filter-based Low-rank Hankel Matrix

In dynamic contrast enhanced (DCE) MRI, temporal and spatial resolution can be improved by timeresolved angiography with interleaved stochastic trajectories (TWIST). However, due to view sharing, the temporal resolution of TWIST is not a true one. To overcome this limitation, we employ recently proposed annihilating filter-based low rank Hankel matrix approach (ALOHA) that interpolates the miss...

Off the grid tensor completion for seismic data interpolation

Fast Hankel tensor-vector product and its application to exponential data fitting

This paper is contributed to a fast algorithm for Hankel tensor–vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor–vector products by sketching the algorithm for both one-dimensional and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonal...