Exploiting Non-local Low Rank Structure in Image Reconstruction

Constrained image models based on linear dependence are commonly used in high dimensional imaging and computer vision to exploit or extract structure, which can be expressed with low rank matrix approximations. Natural images also have a self-similarity property, where features tend to repeat themselves all over the image, and linear dependence relationships may be non-local. To exploit non-local linear dependence structure for image reconstruction, we develop a novel and flexible framework using low rank matrix reconstruction and a union of subspaces model, which is learned using subspace clustering. Subspace clustering makes weaker assumptions about the image than similar methods and also scales to very large-sized problems. We extend this approach for tensors, which are natural representations for images. We demonstrate a benefit of non-local low rank modeling for image denoising and reconstruction of MRI and light field images.