Average Case Recovery Analysis of Tomographic Compressive Sensing

TL;DR

This paper provides an average case analysis of tomographic compressive sensing, establishing recovery thresholds that significantly improve imaging quality in fluid dynamics applications.

Contribution

It introduces an average case recovery analysis for tomographic compressive sensing, enhancing understanding of its performance and establishing new weak recovery thresholds.

Findings

Recovery thresholds align with numerical experiments.

Improvement of tomographic imaging in fluid dynamics by a factor of three.

Establishment of tail bounds for recovery properties.

Abstract

The reconstruction of three-dimensional sparse volume functions from few tomographic projections constitutes a challenging problem in image reconstruction and turns out to be a particular instance problem of compressive sensing. The tomographic measurement matrix encodes the incidence relation of the imaging process, and therefore is not subject to design up to small perturbations of non-zero entries. We present an average case analysis of the recovery properties and a corresponding tail bound to establish weak thresholds, in excellent agreement with numerical experiments. Our result improve the state-of-the-art of tomographic imaging in experimental fluid dynamics by a factor of three.