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Restore lost images due to noise and blurred is a burgeoning subject in imageprocessing and despite the different algorithms on this subject, but the effortto improve is always considered. The definition of fractional derivatives inrecent years has created a powerful tool for this purpose. In the presentpaper, using fractional-order total variation and framelet transform, thenonconvex model for image restoration with impulse noise problem is improved.Then by alternating direction method of multipliers (ADMM) and primal-dualproblem, the proposed model is solved.  The convergence of the proposed algorithm is studied. And the proposedalgorithm is evaluated using different types of tests. The output results showthe efficiency of proposed method.

Color image restoration with impulse noise based on fractional-order total variation and framelet