Low-Rank and Sparse Matrix Decomposition with a-priori knowledge for Dynamic 3D MRI reconstruction

Abstract

It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of a Low-rank and a Sparse component from compressive measurements. When applied to the problem of construction of 4D Cardiac MR image sequences in real-time from highly under-sampled $k-$space data, our proposed method achieves superior reconstruction quality compared to the other state-of-the-art methods.