Improved regularisation constraints for compressed sensing of multi-slice MRI

In magnetic resonance imaging, the long acquisition time required to capture k-space data according to the Nyquist sampling rule is a major limitation. Methods for reducing the scan time for these types of imaging procedures have attracted considerable research interest. Compressed sensing approaches have recently been applied to allow faster acquisition by undersampling the k-space data. However, random undersampling introduces noise-like artefacts. To address this issue, a number of nonlinear reconstruction methods have been proposed that use (Formula presented.) norm regularisation with a sparsifying transform. In this paper, we present a reconstruction method in which a Gaussian scale mixture model constraint in the wavelet domain is combined with a total variation constraint for use as a regularisation prior. A series of experimental evaluations are conducted to validate our method using synthetic and real multi-slice MRI data for the purposes of faster acquisition. Our results show that the volume reconstructed by our method has superior quality to the volumes reconstructed by other approaches.