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Spectral computed tomography (SCT) is used to perform material characterization in 3D images, a feature that is not possible with conventional computed tomography (CT) systems. Currently, photon-counting detectors are used to obtain the energy binned images in SCT, however, these detectors are costly and the measured data have low signal to noise ratios. This paper presents a new approach for SCT which circumvents the limitations of current SCT systems. It combines conventional X-ray imaging systems with K-edge coded aperture masks. In this scheme, a particular filter pair is aligned with each X-ray beam in a multi-shot architecture, therefore obtaining compressive measurements in both the spectral and spatial domains. Then, the energy binned images are reconstructed using the alternating direction method of multipliers (ADMM) to solve a joint sparse and low-rank optimization problem that exploits the structure of the spectral data-cube. Simulations using coded fan-beam X-ray projections demonstrate the feasibility of the proposed approach. 

Spectral computed tomography (SCT) makes use of the spectral dependence of X-ray attenuation in tissues and contrast agents to separate the attenuation data into more than two energy bins. Current SCT detectors are costly and the measured data have low signal to noise ratio due to the detector's narrow bin bandwidth and quantum noise. A new approach called coded aperture compressive X-ray SCT that combines a conventional rotating X-ray CT system with a set of pixelated K-edge coded apertures is introduced. In this method, the amplitude and spectra of the X-ray source are filtered by a particular pattern of K-edge filters in each view angle. Compressed sensing (CS) reconstruction algorithms are then used to recover the spectral CT image from the coded measurements. Simulations results for random coded apertures are shown, and their performance is compared to the use of uncoded measurements.