Color Image Denoising via Quaternion-Based Nonconvex Half-Quadratic Regularized Robust PCA

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 computational 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.