Recently, I saw new published papers like
- Shuhang Gu, Lei Zhang, Wangmeng Zuo, Xiangchu Feng, Weighted Nuclear Norm Minimization with Application to Image Demonising [pdf].
about denoising images using Weighted Nuclear Norm Minimization (WNNM) approach and I am wondering what the physical intuition behind it is.
The main idea is to subdivide the image into patches $Y_j$ then estimate the free-noise patch as the solution of
$$\min\limits_{X_j}{\frac{1}{\sigma_n^2}\|X_j-Y_j\|_F + \sum_i|w_i\sigma_i(X_j)|}$$
where $\sigma_n^2$ is the variance of the noise, $X_j$ is the $j^{th}$ denoised patch to estimate, $\sigma_i(X_j)$ is $i^{th}$ singular value of the matrix $X_j$ and the weights $w_i$'s are non-negative values and chosen in a non-ascending order to satisfy the convexity property.
More specifically, I would like to understand what that means if an image has the singular values of its patches (or regions) constrained to be sparse (according to the expression of the objective function) and I am wondering also if this optimization problem would yield characteristic patterns that are the same in all the images.
