CS-MRI reconstruction via group-based eigenvalue decomposition and estimation

This paper proposes a novel method for compressed sensing MRI (CS-MRI) reconstruction that combines both the sparse representation and statistical estimation. In this work, the low-rank property is observed and utilized to sparsely represent the similar patches based on group singular value decomposition (SVD), and the linear minimum mean square error (LMMSE) estimation is exploited to perform sparse coefficients estimation. Based on this, the proposed approach is named group-based eigenvalue decomposition and estimation (GEDE). Furthermore, in order to improve the estimation accuracy of the coefficients, the original problem is reformulated into an equivalent noise model and a novel method is proposed to assess the noise variance of similar patches. Extensive experimental results on the MRI data demonstrate that the proposed method outperforms the state-of-the-art reconstruction methods in terms of removing artifacts and reconstruction errors.