Dynamic Spike Super-resolution and Applications to Ultrafast Ultrasound Imaging

TL;DR

This paper introduces a novel fully dynamical super-resolution method that simultaneously reconstructs positions and velocities of moving particles from low-frequency measurements, with applications to ultrafast ultrasound imaging.

Contribution

It proposes a phase-space lifting approach for joint super-resolution of positions and velocities, providing rigorous analysis and demonstrating advantages over existing methods.

Findings

Method successfully reconstructs particle positions and velocities in simulations.

The approach outperforms traditional two-step methods in accuracy.

Application to ultrasound imaging improves blood vessel and flow velocity recovery.

Abstract

We consider the dynamical super-resolution problem consisting in the recovery of positions and velocities of moving particles from low-frequency static measurements taken over multiple time steps. The standard approach to this issue is a two-step process: first, at each time step some static reconstruction method is applied to locate the positions of the particles with super-resolution and, second, some tracking technique is applied to obtain the velocities. In this paper we propose a fully dynamical method based on a phase-space lifting of the positions and the velocities of the particles, which are simultaneously reconstructed with super-resolution. We provide a rigorous mathematical analysis of the recovery problem, both for the noiseless case and in presence of noise (in the discrete setting). Several numerical simulations illustrate and validate our method, which shows some advantage over existing techniques. We then discuss the application of this approach to the dynamical super-resolution problem in ultrafast ultrasound imaging: blood vessels' locations and blood flow velocities are recovered with super-resolution.