Travelling salesman-based variable density sampling

TL;DR

This paper introduces a novel method for generating continuous sampling trajectories using a traveling salesman problem solver, enabling practical implementation of compressed sensing in systems like MRI and radio-interferometry.

Contribution

It provides a theoretical framework for the probability density of initial measurements and demonstrates the method's efficiency through preliminary simulations.

Findings

Strategy matches the efficiency of independent random sampling

Trajectories are feasible for real acquisition systems

Theoretical derivation supports practical implementation

Abstract

Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire sam- ples along continuous trajectories. Examples include magnetic resonance imaging (MRI), radio-interferometry, mobile-robot sampling, ... In this paper, we propose to generate continuous sampling trajectories by drawing a small set of measurements independently and joining them using a travelling salesman problem solver. Our contribution lies in the theoretical derivation of the appropriate probability density of the initial drawings. Preliminary simulation results show that this strategy is as efficient as independent drawings while being implementable on real acquisition systems.