An Improved Denoising Model Based on the Analysis K-SVD Algorithm

Denoising models play an important role in various applications, such as signal denoising. Recently, the analysis K- singular-value decomposition (SVD) (AK-SVD) algorithm has emerged as an efficient dictionary learning algorithm derived from the analysis sparse model, which has achieved promising performance in various problems. In this paper, we propose a new method that uses AK-SVD for signal denoising. Specifically, we divide input signals into redundant signal segments, which are used to generate denoised segments and train the analysis dictionary using AK-SVD. The maximum a posteriori estimator, which is defined as the minimizer of a global penalty term, is used to integrate multiple local denoised segments to attain the global denoised signals. Furthermore, the basis functions of the denoised signal are constructed based on the previously built analysis dictionary. Numerical experiments demonstrate that the proposed method can outperform the existing state-of-the-art denoising approaches.