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Image deblurring problem is a tough work for improving the quality of images, in this paper; we develop an efficient and fast thresholding algorithm to handle such problem. We observe that the improved fast iterative thresholding algorithm (IFISTA) can be further accelerated by using a sequence of over relaxation parameters which do not satisfy the Nesterov's rule. Our proposed algorithm preserves the simplicity of the IFISTA and fast iterative shrinkage thresholding algorithm (FISTA). In addition, we theoretically study the convergence of our proposed algorithm and obtain some improved convergence rate. Furthermore, we investigate the local variation of iterations which is still unknown in FISTA and IFISTA algorithms so far. Extensive experiments have been conducted and show that our proposed algorithm is more efficient and robust. Specifically, we compare our proposed algorithm with FISTA and IFISTA algorithms on a series of scenarios, including the different level noise signals as well as different weighting matrices. All results demonstrate that our proposed algorithm is able to achieve better recovery performance, while being faster and more efficient than others.

A Novel Thresholding Algorithm for Image Deblurring Beyond Nesterov’s Rule