<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Objective: Improve the reconstructed image with fast and multiclass dictionaries learning when magnetic resonance imaging is accelerated by undersampling the k-space data. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods: A fast orthogonal dictionary learning method is introduced into magnetic resonance image reconstruction to provide adaptive sparse representation of images. To enhance the sparsity, image is divided into classified patches according to the same geometrical direction and dictionary is trained within each class. A new sparse reconstruction model with the multiclass dictionaries is proposed and solved using a fast alternating direction method of multipliers. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Results: Experiments on phantom and brain imaging data with acceleration factor up to 10 and various undersampling patterns are conducted. The proposed method is compared with state-of-the-art magnetic resonance image reconstruction methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusion: Artifacts are better suppressed and image edges are better preserved than the compared methods. Besides, the computation of the proposed approach is much faster than the typical K-SVD dictionary learning method in magnetic resonance image reconstruction. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Significance: The proposed method can be exploited in undersampled magnetic resonance imaging to reduce data acquisition time and reconstruct images with better image quality.

Fast Multiclass Dictionaries Learning With Geometrical Directions in MRI Reconstruction