Static MRI Reconstruction with RPCA Based on Non-local Self-similarity

The main idea of RPCA (Robust Principal Component Analysis) is to decompose a matrix into a low-rank component L and a sparse component S. In dynamic MRI (Magnetic Resonance Imaging) reconstructions, due to the regular movement or pulsation of organs, the change is relatively slight and the similarity between frames is very high. Therefore, the RPCA model is very suitable for the reconstruction of dynamic MR images. However, for static images, their low-rank attribute is not obvious and we cannot achieve better results if we apply the RPCA model to the reconstruction of static images directly. Based on the non-local self-similarity and sparsity of an image, this paper successfully applied the RPCA model to the reconstruction of static MR images and achieved good reconstruction results.