Low-Rank and Sparse Matrix Decomposition for Accelerated Dynamic MRI with Separation of Background and Dynamic Components

Purpose: To apply the low-rank plus sparse (L+S) matrix decomposition model to reconstruct undersampled dynamic MRI as a superposition of background and dynamic components in various problems of clinical interest. Theory and Methods: The L+S model is natural to represent dynamic MRI data. Incoherence between k-t space (acquisition) and the singular vectors of L and the sparse domain of S is required to reconstruct undersampled data. Incoherence between L and S is required for robust separation of background and dynamic components. Multicoil L+S reconstruction is formulated using a convex optimization approach, where the nuclear-norm is used to enforce low-rank in L and the l1-norm to enforce sparsity in S. Feasibility of the L+S reconstruction was tested in several dynamic MRI experiments with true acceleration including cardiac perfusion, cardiac cine, time-resolved angiography, abdominal and breast perfusion using Cartesian and radial sampling. Results: The L+S model increased compressibility of dynamic MRI data and thus enabled high acceleration factors. The inherent background separation improved background suppression performance compared to conventional data subtraction, which is sensitive to motion. Conclusion: The high acceleration and background separation enabled by L+S promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.