Linear Projection-Based Noise Filtering Framework for Image Denoising

Image denoising remains a fundamental challenge in digital image processing due to the inevitable presence of noise during image acquisition and transmission. While existing noise filtering methods predominantly focus on local spatial information, they often overlook crucial structural information from other perspectives, such as local manifold and global structures. To address this limitation, we propose a novel linear projection-based noise filtering (LPNF) framework grounded in linear projection learning theory. This framework innovatively learns a linear projection for noise filtering by incorporating multiple structural information sources- local spatial, local manifold, and global structures- through well-defined criteria. We present two specialized implementations of the LPNF framework: PCA-based LPNF (LPNF-PCA) and LPP-based LPNF (LPNF-LPP). The LPNF-PCA simultaneously leverages local spatial and global information, while LPNF-LPP integrates both local manifold and spatial information for enhanced denoising performance. Comprehensive experiments conducted on four standard test images with various noise types demonstrate that both LPNF-PCA and LPNF-LPP consistently outperform state-of-the-art denoising methods in terms of both quantitative.