Tree structure based MR image reconstruction with partially known support

As a promising sampling scheme, compressed sensing (CS) has been successfully used for magnetic resonance imaging (MRI). By exploiting the sparse property, MR images can be reconstructed from undersampled k-space data. However, images involved in practical applications display structural information in addition to the sparsity. In this paper, we simultaneously take advantage of the wavelet tree structure and the support information, thereby proposing a new MR image reconstruction method. The resulting reconstruction model is composed of a data fidelity term, a total variation (TV) regularization term and a mixed l₂-l₁ norm term penalizing the parent-child pairs within the complement of the known support. The proposed method has been validated by experiments both on synthetic and practical MRI data. The results demonstrate the competitive performance of our method over the conventional CS reconstruction method.