Application of dictionary learning in compressed sensing of data in MRI

In recent years, it is now well established that for the data like MRI images that admit the sparse representation in some transformed domain, Compressed Sensing (CS) approach is well suited for the accurate restoration tasks. Various analytical sparsifying transforms such as wavelets, finite differences and curvelets are used extensively in many CS methods. In this paper, a general framework for the adaptive learning of the sparsifying transform (dictionary) and reconstruction of the MR image from undersampled k-space data simultaneously is proposed. Here, we also propose the supervised dictionary learning framework adapted to specific task of MR image reconstruction and an efficient algorithm to solve the corresponding optimization problem. In this framework, overlapping image patches are used to exploit the local structure in the image to enforce the sparsity. Dictionary is trained using training images corresponding to particular class the given image belongs to. This results in better sparsities hence the higher undersampling rate. In this alternating reconstruction algorithm, firstly the sparsifying dictionary is learnt to remove aliasing effect and then restoring and filling of the k-space data is performed in the other step. Experiments are conducted on the brain MR image data set with different sampling methods. Results of these experiments show the improvement of around 2.5 dB in PSNR and improvement of around 0.1 in the HFEN value of the reconstructed image. Performance with various sampling schemes is evaluated and the results show that 2D variable density random undersampling scheme is best suited for the MRI application.