A different kind of phase transition can be seen in the figure above, either the solver fails or it breaks. When it breaks, it means the solver found a sparser solution given the measurements. : Nonconvex compressive sensing for X-ray CT: an algorithm comparison by Rick Chartrand, Emil Y. Sidky, Xiaochuan Pan

Compressive sensing makes it possible to reconstruct images from severely underdetermined linear systems. For X-ray CT, this can allow high-quality images to be reconstructed from projections along few angles, reducing patient dose, as well as enable other forms of limited -view tomography such as tomosynthesis. Many previous results have shown that using nonconvex optimization can greatly improve the results obtained from compressive sensing, and several efﬁcient algorithms have been developed for this purpose. In this paper, we examine some recent algorithms for CT image reconstruction that solve non-convex optimization problems, and compare their reconstruction performance and computational efﬁciency.

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