Signal restoration combining Tikhonov regularization and multilevel method with thresholding strategy

Abstract

Singular value decomposition (SVD)-based approaches, e.g., truncated SVD and Tikhonov regularization methods, are effective ways to solve problems of small or moderate size. However, SVD, in the sense of computation, is expensive when it is applied in large-sized cases. A multilevel method (MLM) combining SVD-based methods with the thresholding technique for signal restoration is proposed in this paper. Our MLM will transfer large-sized problems to small- or moderate-sized problems in order to make the SVD-based methods available. The linear systems on the coarsest level in the multilevel process will be solved by the Tikhonov regularization method. No presmoothers are implemented in the multilevel process to avoid damaging the parameter choice on the coarsest level. Furthermore, the soft-thresholding denoising technique is employed for the postsmoothers aiming to eliminate the leaving high-frequency information due to the lack of presmoothers. Finally, computational experiments show that our method outperforms other SVD-based methods in signal restoration ability at a shorter CPU-time consumption.