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Compressive spectral X-ray imaging (CSXI) introduces a pixelated spectral modulator called K-edge coded aperture (KCA) in front of the X-ray source, which enables both, lower dosage to the subject, as well as the capability of spectral tomography while using low-cost integrating X-ray detectors. CSXI systems generally use hundreds of different spectral modulators, each with a distinct pattern to uniquely modulate the illumination at every view angle. In contrast, this paper introduces the use of a single and static coded aperture placed in a tomosynthesis gantry. The compressive system thus interrogates the subject with a fixed coded illumination pattern on all view angles. The advantages of the system are many including reduced cost and the feasibility of implementation. Given the reduced set of coded measurement and the limited spectral separation ability in the resulting architecture, the nonlinear inverse reconstruction problem results in a highly ill-posed problem. An efficient alternating minimization method with three-dimensional total variation regularization is developed for image reconstruction. Furthermore, rather than simply using a random pattern, the coded aperture is optimized under a uniform sensing criterion that shapes the spatial and spectral pattern of the coded aperture so as to minimize the overall radiation exposure placed on any volumetric area of the patient. This is of particular importance in medical imaging where patients at risk are recommended to have periodical X-ray tomosynthesis screenings. The coded aperture optimization is then posed as a binary programming problem solved by a gradient-based algorithm with equilibrium constraints. Numerical experiments show that spatial and spectral coding used in the proposed system to interrogate the subject not only reduces the radiation dose but it also improves the quality of image reconstruction. Gains close to 5dB in peak signal to noise ratio are observed in simulations. Furthermore, it is shown that the optimization of the KCA can effectively improve the uniformity of X-ray radiation compared to random KCA modulation, thus reducing the radiation dose throughout all volumetric sub-areas of the subject — an objective that is not possible with the use of random KCAs. 

Coded spectral X-ray computed tomography (CT) based on K-edge filtered illumination is a cost-effective approach to acquire both 3-dimensional structure of objects and their material composition. This approach allows sets of incomplete rays from sparse views or sparse rays with both spatial and spectral encoding to effectively reduce the inspection duration or radiation dose, which is of significance in biological imaging and medical diagnostics. However, reconstruction of spectral CT images from compressed measurements is a nonlinear and ill-posed problem. This paper proposes a material-decomposition-based approach to directly solve the reconstruction problem, without estimating the energy-binned sinograms. This approach assumes that the linear attenuation coefficient map of objects can be decomposed into a few basis materials that are separable in the spectral and space domains. The nonlinear problem is then converted to the reconstruction of the mass density maps of the basis materials. The dimensionality of the optimization variables is thus effectively reduced to overcome the ill-posedness. An alternating minimization scheme is used to solve the reconstruction with regularizations of weighted nuclear norm and total variation. Compared to the state-of-the-art reconstruction method for coded spectral CT, the proposed method can significantly improve the reconstruction quality. It is also capable of reconstructing the spectral CT images at two additional energy bins from the same set of measurements, thus providing more spectral information of the object.