Fast Multiclass Dictionaries Learning With Geometrical Directions In Sparse Image 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 by K-SVD and the state-of-the-art image quality is achieved in image reconstruction.However,this method is time consuming due to the 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 the dictionary is trained within each class.We propose a sparse reconstruction model with the multi-class dictionaries and solve the problem with 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.In addition,the proposed dictionary learning method is adopted as a sparse representation for salt-and-pepper noise removal.Results demonstrate that the proposed method outperforms adaptive median filtering method and wavelet-based noise removal method in terms of removing noising and preserving image edges.