This paper proposes a weighted nuclear norm minimization (WNNM) method for image denoising, which improves upon the standard nuclear norm minimization (NNM) by assigning different weights to singular values. The standard NNM treats all singular values equally, which limits its flexibility in handling practical problems where singular values have different importance. WNNM assigns weights to singular values based on their importance, allowing for more effective denoising. The WNNM algorithm is applied to image denoising by exploiting the nonlocal self-similarity of images. Experimental results show that WNNM outperforms state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measures (e.g., PSNR) and visual quality. The WNNM method is shown to be more robust to noise and better preserves image structures. The algorithm is efficient and can be applied to various image denoising scenarios. The paper also discusses the theoretical properties of WNNM, including its convexity under certain weight conditions and the use of iterative algorithms for non-convex cases. The results demonstrate that WNNM provides superior denoising performance compared to existing methods.This paper proposes a weighted nuclear norm minimization (WNNM) method for image denoising, which improves upon the standard nuclear norm minimization (NNM) by assigning different weights to singular values. The standard NNM treats all singular values equally, which limits its flexibility in handling practical problems where singular values have different importance. WNNM assigns weights to singular values based on their importance, allowing for more effective denoising. The WNNM algorithm is applied to image denoising by exploiting the nonlocal self-similarity of images. Experimental results show that WNNM outperforms state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measures (e.g., PSNR) and visual quality. The WNNM method is shown to be more robust to noise and better preserves image structures. The algorithm is efficient and can be applied to various image denoising scenarios. The paper also discusses the theoretical properties of WNNM, including its convexity under certain weight conditions and the use of iterative algorithms for non-convex cases. The results demonstrate that WNNM provides superior denoising performance compared to existing methods.