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The purpose of this paper is to develop an algorithm for hybrid spectral computed tomography (CT) which combines energy-integrating and photon-counting detectors. While the energy-integrating scan is global, the photon-counting scan can have a local field of view (FOV). The algorithm synthesizes both spectral data and energy-integrating data. Low rank and sparsity prior is used for spectral CT reconstruction. An initial estimation is obtained from the projection data based on physical principles of x-ray interaction with the matter, which provides a more accurate Taylor expansion than previous work and can guarantee the convergence of the algorithm. Numerical simulation with clinical CT images are performed. The proposed algorithm produces very good spectral features outside the FOV when no K-edge material exists. Exterior reconstruction of K-edge material can be partially achieved. [ABSTRACT FROM AUTHOR]