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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. 

Abstract: Coded aperture X-ray computed tomography (CT) has the potential to revolutionize X-ray tomography systems in medical imaging and air and rail transit security - both areas of global importance. It allows either a reduced set of measurements in X-ray CT without degrada- tion in image reconstruction, or measure multiplexed X-rays to simplify the sensing geometry. Measurement reduction is of particular interest in medical imaging to reduce radiation, and airport security often imposes practical constraints leading to limited angle geometries. Coded aperture compressive X-ray CT places a coded aperture pattern in front of the X-ray source in order to obtain patterned projections onto a detector. Compressive sensing (CS) reconstruction algorithms are then used to recover the image. To date, the coded illumination patterns used in conventional CT systems have been random. This paper addresses the code optimization prob- lem for general tomography imaging based on the point spread function (PSF) of the system, which is used as a measure of the sensing matrix quality which connects to the restricted isom- etry property (RIP) and coherence of the sensing matrix. The methods presented are general, simple to use, and can be easily extended to other imaging systems. Simulations are presented where the peak signal to noise ratios (PSNR) of the reconstructed images using optimized coded apertures exhibit significant gain over those attained by random coded apertures. Additionally, results using real X-ray tomography projections are presented. 

Abstract: Coded aperture X-ray computed tomography (CT) has the potential to revolutionize X-ray tomography systems in medical imaging and air and rail transit security - both areas of global importance. It allows either a reduced set of measurements in X-ray CT without degrada- tion in image reconstruction, or measure multiplexed X-rays to simplify the sensing geometry. Measurement reduction is of particular interest in medical imaging to reduce radiation, and airport security often imposes practical constraints leading to limited angle geometries. Coded aperture compressive X-ray CT places a coded aperture pattern in front of the X-ray source in order to obtain patterned projections onto a detector. Compressive sensing (CS) reconstruction algorithms are then used to recover the image. To date, the coded illumination patterns used in conventional CT systems have been random. This paper addresses the code optimization prob- lem for general tomography imaging based on the point spread function (PSF) of the system, which is used as a measure of the sensing matrix quality which connects to the restricted isom- etry property (RIP) and coherence of the sensing matrix. The methods presented are general, simple to use, and can be easily extended to other imaging systems. Simulations are presented where the peak signal to noise ratios (PSNR) of the reconstructed images using optimized coded apertures exhibit significant gain over those attained by random coded apertures. Additionally, results using real X-ray tomography projections are presented. 

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.