We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Instead of a vector field ∇u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with divP ∈ L. We prove existence and uniqueness for solutions of the equation P divP = 0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only ...

Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 14 September 2020Accepted: 07 2021Published online: 20 December 2021Keywordseikonal equation, high-order solver, semi-Lagrangian Hermite interpolation, direct marchingAMS Subject Headings65N99, 65Y20, 49M99Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Pub...

Integration of surface normal vectors is a vital component in many shape reconstruction algorithms that require integrating surface normals to produce their final outputs, the depth values. In this paper, we introduce a fast and efficient method for computing the depth values from surface normal vectors. The method is based on solving the Eikonal equation using Fast Marching Method. We introduc...

It is known that curvature relation plays a key role in the propagation of two-dimensional waves in an excitable model. Such a relation is believed to obey the eikonal equation for typical excitable models (e.g., the FitzHugh-Nagumo (FHN) model), which states that the relation between the normal velocity and the local curvature is approximately linear. In this paper, we show that for a simplifi...