Real-time cardiac MRI is a very challenging problem because of limitations on imaging speed and resolution. To address this problem, the (k, t) - space MR signal is modeled as being partially separable along the spatial and temporal dimensions, which results in a rank-deficient data matrix. Image reconstruction is then formulated as a low-rank matrix recovery problem, which is solved using emerging low-rank matrix recovery techniques. In this paper, the Power Factorization algorithm is applied to efficiently recover the cardiac data matrix. Promising results are presented to demonstrate the performance of this novel approach.
The partially separable function (PSF) model has been successfully used to reconstruct cardiac MR images with high spatiotemporal resolution from sparsely sampled (k,t)-space data. However, the underlying model fitting problem is often ill-conditioned due to temporal undersampling, and image artifacts can result if reconstruction is based solely on the data consistency constraints. This paper proposes a new method to regularize the inverse problem using sparsity constraints. The method enables both partial separability (or low-rankness) and sparsity constraints to be used simultaneously for high-quality image reconstruction from undersampled (k,t)-space data. The proposed method is described and reconstruction results with cardiac imaging data are presented to illustrate its performance.
Athinoula A. Martinos Center for Biomedical Imaging