Low-rank recovery has emerged as a powerful methodology for the restoration of degraded images. Conventional low-rank recovery techniques, however, predominantly rely on nuclear norm or weighted nuclear norm minimization to separate sparse noise. A significant limitation of this approach is its dependence on full singular value decomposition, which imposes a substantial computational burden, thereby hindering its practical applicability. This paper presents a novel image denoising model integrating the weighted nuclear norm and deep image prior. The weighted nuclear norm is introduced to accurately characterize the global structural properties of images, ensuring the consistency of the overall image structure after denoising. Meanwhile, the deep image prior is employed to effectively capture local details, which helps avoid the blurring of textures and edges often caused by excessive noise removal. The complementary advantages of the two components enable the proposed model to achieve superior performance compared with existing denoising methods. To efficiently compute the proposed model, we design the bilinear factorization method and the alternating direction method of multipliers. Experiments show that the proposed method outperforms mainstream approaches in both restoration accuracy and computational efficiency, exhibiting rapid convergence and robust algorithm stability, thereby demonstrating excellent comprehensive performance.
Feng et al. (Sun,) studied this question.