Stolt's f-k migration for plane wave ultrasound imaging.

Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wave-fronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals.

A PROOF OF CONVERGENCE OF THE HORN AND SCHUNCK OPTICAL FLOW ALGORITHM IN ARBITRARY DIMENSION.

The Horn and Schunck (HS) method, which amounts to the Jacobi iterative scheme in the interior of the image, was one of the first optical flow algorithms. In this article, we prove the convergence of the HS method, whenever the problem is well-posed. Our result is shown in the framework of a generalization of the HS method in dimension ≥ 1, with a broad definition of the discrete Laplacian.