The Application of the Accelerated Proximal Gradient Descent Algorithm for the Solution of the Weighted Schatten-p Norm in Sparse Noise Extraction

In this study, we introduce the weighted Schatten-p norm optimization robust principal component analysis model, transforming the nuclear norm into a combination of the Schatten-p norm and the weighted nuclear norm for enhanced flexibility. We adapt the model for compatibility with the Accelerated Proximal gradient descent algorithm (APG) and use APG to solve this new model. In the experimental section, we analyze the algorithm’s adaptability under various conditions through multi-dimensional variation analysis on generated data. Additionally, we assess its practical effectiveness by testing on noisy images for restoration, establishing the proposed method as the most advanced algorithm in terms of performance.