Undersampled MRI reconstruction with patch-based directional wavelets

Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a preconstructed basis or dictionary. In this paper, patch-based directional wavelets are proposed to reconstruct images from undersampled k-space data. A parameter of patch-based directional wavelets, indicating the geometric direction of each patch, is trained from the reconstructed image using conventional compressed sensing MRI methods and incorporated into the sparsifying transform to provide the sparse representation for the image to be reconstructed. A reconstruction formulation is proposed and solved via an efficient alternating direction algorithm. Simulation results on phantom and in vivo data indicate that the proposed method outperforms conventional compressed sensing MRI methods in preserving the edges and suppressing the noise. Besides, the proposed method is not sensitive to the initial image when training directions.