Recently, variational models based on non-local regularisation obtain superior results over traditional methods, and many iterative algorithms have been proposed for these models. At present, Xiaoqun Zhang et al. proposed two algorithms based on Bregman iteration for solving non-local regularisation problems, these algorithms converge fast but the calculation quantity is large for each iterative step. Here, based on the idea of variable splitting and penalty techniques in optimisation and fast Fourier transform, the authors present a non-local total variational model and propose a fast iterative algorithm for the model. Under some assumption, q-linear convergence of the iterative algorithm is proved. Experiments demonstrate that the algorithm can efficiently speed up the execution of the variational model and obtain an improvement in signal-to-noise ratio through the selection of penalty parameters.
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