In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading\nthe image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a\nlimited number of projections.However, conventional CS-based algorithms are computationally intensive and time-consuming.We\npropose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform\nand rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior\napproach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on\nthe statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning\ninterpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and\ninterpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 Ã?â?? 512 Shepp-Logan phantom\nwhen reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed\nmethod the reconstruction error was less than 1%.Moreover, computation times of less than 30 sec were obtained using a standard\ndesktop computer without numerical optimization.
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