A kernel-based compressed sensing approach to dynamic MRI from highly undersampled data

Compressed sensing (CS) has been used in dynamic MRI to reduce the data acquisition time. Several sparsifying transforms have been investigated to sparsify the dynamic image sequence. Most existing works have studied linear transformations only. In this paper, we proposed a novel kernel-based compressed sensing approach to dynamic MRI. The method represents the image sequence sparsely and adaptively using nonlinear transformations. Such nonlinearity is implemented using the kernel method, which maps the acquired undersampled k-space data onto a high dimensional feature space, then reconstructs the image sequence in the corresponding feature space using the conventional compressed sensing, and finally convert the image sequence back into the original space. Experimental results demonstrate that the proposed method improves the reconstruction quality of dynamic ASL-based perfusion MRI over the state-of-the-art method where linear transform is used.