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.

Image reconstruction from sparse data in synchrotron-radiation-based microtomography.

Synchrotron-radiation-based microcomputed-tomography (SR-µCT) is a powerful tool for yielding 3D structural information of high spatial and contrast resolution about a specimen preserved in its natural state. A large number of projection views are required currently for yielding SR-µCT images by use of existing algorithms without significant artifacts. When a wet biological specimen is imaged, synchrotron x-ray radiation from a large number of projection views can result in significant structural deformation within the specimen. A possible approach to reducing imaging time and specimen deformation is to decrease the number of projection views. In the work, using reconstruction algorithms developed recently for medical computed tomography (CT), we investigate and demonstrate image reconstruction from sparse-view data acquired in SR-µCT. Numerical results of our study suggest that images of practical value can be obtained from data acquired at a number of projection views significantly lower than those used currently in a typical SR-µCT imaging experiment.

An Investigation of Compressive-sensing Image Reconstruction from Flying-focal-spot CT Data.

Flying-focal-spot (FFS) technique has been used for improving the sampling condition in advanced clinical CT by collecting multiple cone-beam data sets with the focal-spot at different locations at each "projection view". It has been demonstrated that the increased sampling rate in FFS scans can substantially reduce aliasing artifacts in reconstructed images. However, the increase of the sampling density through multiple illuminations at each view can result in the increase of radiation dose to the imaged subject. In this work, we have applied a compressive-sensing (CS)-based algorithm to image reconstruction from data acquired in FFS scans. The results of the study demonstrate that aliasing artifacts observed images reconstructed by use of analytic algorithms can be suppressed effectively in images reconstructed with this CS-based algorithm from only data acquired at one FFS scan.