Low-rank plus 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 is used 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, and 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.