On Variable Density Compressive Sampling

TL;DR

This paper introduces an optimization-based method for designing variable density sampling profiles in compressed sensing, improving sampling efficiency and providing theoretical insights, especially for MRI applications.

Contribution

It formulates a convex optimization approach to optimize sampling profiles based on coherence minimization, including a refinement for prior support information.

Findings

Optimized sampling profiles improve reconstruction quality.

Method is validated through numerical experiments.

Provides theoretical support for MRI sampling techniques.

Abstract

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution provides an optimized sampling profile. This minimization problem is solved with the use of convex optimization algorithms. We also propose a refinement of our technique when prior information is available on the signal support in the sparsity basis. The effectiveness of the method is confirmed by numerical experiments. Our results also provide a theoretical underpinning to state-of-the-art variable density Fourier sampling procedures used in magnetic resonance imaging.