An algorithm for constrained one-step inversion of spectral CT data

Rina Foygel Barber,Xiaochuan Pan,Emil Y Sidky,Taly Gilat Schmidt

doi:10.1088/0031-9155/61/10/3784

Rina Foygel Barber, Xiaochuan Pan + Show 2 more

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https://doi.org/10.1088/0031-9155/61/10/3784

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Abstract

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.

Highlights

The recent research activity in photon-counting detectors has motivated a resurgence in the investigation of spectral computed tomography (CT)
We demonstrate the algorithm with the use of total variation (TV) constraints, but the framework allows for other constraints such as non-negativity, upper bounds, and sum bounds applied to either the basis maps or to a composite image such as an estimated mono-chromatic attenuation map
We have developed a constrained minimization algorithm for inverting spectral CT transmission data directly to basis material maps

Summary

Introduction

The recent research activity in photon-counting detectors has motivated a resurgence in the investigation of spectral computed tomography (CT). Photon-counting detectors detect individual x-ray quanta and the electronic pulse signal generated by these quanta has a peak amplitude proportional to the photon energy (Taguchi and Iwanczyk 2013). Thresholding these amplitudes allows for coarse energy resolution of the x-ray photons, and the transmitted flux of x-ray photons can be measured simultaneously in a number of energy windows. For photon-counting detectors where the number of energy windows can be three or greater, the new advantage with respect to quantitative imaging is the ability to image contrast agents that possess a K-edge in the diagnostic x-ray energy range (Roessl and Proksa 2007, Schlomka et al 2008, Cormode et al 2010, Roessl et al 2011a, 2011b, Schirra et al 2013)

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