Color Image Denoising via Quaternion-Based Nonconvex Half-Quadratic Regularized Robust PCA
Authors: Gu, Q., Ma, X., Li, H.Y., Liao, L., Zhao, J., Chen, H.Z., Zhao, S., Zhao, Q., Yu, H., Wang, X.
Journal: IEEE Access
Publication Date: 01/01/2026
eISSN: 2169-3536
DOI: 10.1109/ACCESS.2026.3710921
Abstract:We propose a novel method for color image denoising, termed Quaternion Robust Principal Component Analysis with a non-convex Half-Quadratic Function (QRPCA-HQF). By representing color pixels as quaternions, our model extends the RPCA framework to holistically process the three color channels, effectively preserving their inherent inter-channel correlations. Critically, our proposed algorithm employs a matrix factorization approach that circumvents the computationally expensive Quaternion Singular Value Decomposition (QSVD) typically required in quaternion-based low-rank approximations, leading to a significant improvement in com putational efficiency. Furthermore, to address the challenge of robustly estimating the noise level from the residual matrix, we introduce a novel Component-Wise Generalized Median Absolute Deviation (CW-GMAD) algorithm, and further extend this algorithm. Derived from M-estimation theory, this method enhances the statistical efficiency of outlier detection compared to the standard MAD estimator, assuming the background noise is Gaussian. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed QRPCA-HQF model outperforms several state-of-the-art methods, particularly under challenging high-intensity Gaussian noise conditions.
Source: Scopus