Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction

Compressed sensing magnetic resonance imaging has shown great capability to accelerate data acquisition by exploiting sparsity of images under a certain transform or dictionary. Sparser representations usually lead to lower reconstruction errors, thus enduring efforts have been made to find dictionaries that provide sparser representation of magnetic resonance images. Previously, adaptive sparse representations are typically trained with K-SVD and the state-of-the-art image quality is achieved in image reconstruction. However, this reconstruction is time consuming because of the relatively slow training process. In this paper, we introduce a fast dictionary learning method, which is essentially an adaptive tight frame construction, into magnetic resonance image reconstruction. To enhance the sparsity, images are divided into classified patches according to the same geometrical directions and dictionary is trained within each class. We set up a sparse reconstruction model with the multi-class dictionaries and solve the problem with a fast alternative direction multiplier method. Experiments on real magnetic resonance imaging data demonstrate that the proposed approach achieves the lowest reconstruction error compared with several state-of-the-art methods and the computation is much faster than previous dictionary learning methods.