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Isaac Newton Institute for Mathematical Sciences

Empirical phase transitions in computed tomography

2014-02-07

Presenter: Jakob Sauer Joergensen (Technical University of Denmark)

Co-authors: Christian Kruschel (Technical University of Braunschweig), Dirk Lorenz (Technical University of Braunschweig), Per Christian Hansen (Technical University of Denmark), Emil Sidky (University of Chicago), Xiaochuan Pan (University of Chicago)

Abstract

Sparse reconstruction methods such as total variation (TV) minimization have shown potential for dose-reduction in x-ray computed tomography. The fundamental question of how many measurements ensure unique recovery is open, as standard recovery guarantees from compressed sensing do not apply to the deterministic CT sampling matrices. Recent theoretical analysis take important steps forward for certain special sampling patterns but for conventional CT sampling patterns the question of sufficient sampling remains unanswered. We study the question empirically in the spirit of the Donoho-Tanner phase diagram, i.e, by investigating the fraction of recovered image instances as function of sparsity and sampling.

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