Thetotal variation (TV) model has been studied extensively because it is able to preserve sharp attributes and capture some sparsely\ncritical information in images. However, TV denoising problem is usually ill-conditioned that the classical monotone projected\ngradient method cannot solve the problem efficiently. Therefore, a new strategy based on nonmonotone approach is digged out as\naccelerated spectral project gradient (ASPG) for solving TV. Furthermore, traditional TV is handled by vectorizing, which makes\nthe scheme farmore complicated for designing algorithms. In order to simplify the computing process, a newtechnique is developed\nin view of matrix rather than traditional vector. Numerical results proved that our ASPG algorithm is better than some state-ofthe-\nart algorithms in both accuracy and convergence speed.
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