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Because the X-ray CT imaging has high spatial resolution, it becomes more important in diagnostic imaging. However the techniques of low dose imaging at X-ray mass examination or thin slice imaging provide degraded CT images by noise. The CT images have specific noise, called streak artifact. In this paper, we apply an adaptive Wiener filter (AWF) based on the Gaussian mixture distribution model (GMM), proposed previously to reduce Gaussian white noise. Simulation results show that a new AWF-GMM designed using high dose (original) CT image and low dose (observed) CT image pairs of chest phantom for training image set provides high restoration ability.