How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray computed tomography.
We introduce phase-diagram analysis, a standard tool in compressed sensing (CS), to the X-ray computed tomography (CT) community as a systematic method for determining how few projections suffice for accurate sparsity-regularized reconstruction. In CS, 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 comparably with a near-optimal CS 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 with 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.
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Richard Petersens Plads, Kongens Lyngby 2800, Denmark jakj@dtu.dk.
J S
JS
Jørgensen
Department of Radiology MC-2026, University of Chicago, 5841 South Maryland Avenue, Chicago, IL 60637, USA.
E Y
EY
Sidky
D000465:Algorithms; D003198:Computer Simulation; D044962:Data Compression / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*
compressed sensing; computed tomography; image reconstruction; sampling; sparsity regularization