How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray CT

TL;DR

This paper adapts phase-diagram analysis from compressed sensing to X-ray CT to systematically determine the minimal number of projections needed for accurate sparse image reconstruction.

Contribution

It introduces phase-diagram analysis as a new empirical tool for X-ray CT, demonstrating its effectiveness in predicting undersampling requirements and comparing sampling strategies.

Findings

X-ray CT can perform comparably to Gaussian sensing matrices in certain cases.

Randomized CT measurements do not outperform structured sampling patterns.

Phase-diagram analysis can predict the number of projections needed for accurate total-variation regularized reconstruction.

Abstract

We introduce phase-diagram analysis, a standard tool in compressed sensing, to the X-ray CT community as a systematic method for determining how few projections suffice for accurate sparsity-regularized reconstruction. In compressed sensing a phase diagram is a convenient way to study and express certain theoretical relations between sparsity and sufficient sampling. We adapt phase-diagram analysis for empirical use in X-ray CT for which the same theoretical results do not hold. We demonstrate in three case studies the potential of phase-diagram analysis for providing quantitative answers to questions of undersampling: First we demonstrate that there are cases where X-ray CT empirically performs comparable with an optimal compressed sensing strategy, namely taking measurements with Gaussian sensing matrices. Second, we show that, in contrast to what might have been anticipated, taking randomized CT measurements does not lead to improved performance compared to standard structured sampling patterns. Finally, we show preliminary results of how well phase-diagram analysis can predict the sufficient number of projections for accurately reconstructing a large-scale image of a given sparsity by means of total-variation regularization.