PSF model-based reconstruction with sparsity constraint: Algorithm and application to real-time cardiac MRI

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.