Wavelet-Based Reconstruction for Rapid MRI

In magnetic resonance imaging (MRI), slow data acquisition times often introduce artefacts due to motion and also limit the resolution of the images captured. To address this issue, compressed sensing (CS) techniques have recently been applied to allow under-sampling of the k-space data providing faster acquisition times. To reconstruct the image from the under-sampled measurements, a number of image reconstruction methods have been used. These techniques typically make use of l1-regularization and sparsifying transforms such as the wavelet transform. In this paper, we present a wavelet domain reconstruction method that utilises wavelet regularization with a Gaussian scale mixture (GSM) model prior combined with a Total Variation (TV) constraint in the complex wavelet domain. Our results show that, when compared to the results of previous approaches, the volume reconstructed using our proposed method has superior quality both visually and quantitatively.