Dynamic magnetic resonance imaging using compressed sensing with self-learned nonlinear dictionary (NL-D)

Compressed Sensing (CS) is a new paradigm in signal processing and reconstruction from sub-nyquist sampled data. CS has shown promising results in accelerating dynamic Magnetic Resonance Imaging (dMRI). CS based approaches hugely rely on sparsifying transforms to reconstruct the dynamic MR images from its undersampled k-space data. Recent developments in dictionary learning and nonlinear kernel based methods have shown to be capable of representing dynamic images more sparsely than conventional linear transforms. In this paper, we propose a novel method (NL-D) to represent the dMRI more sparsely using self-learned nonlinear dictionaries based on kernel methods. Based on the proposed model, a new iterative approach for image reconstruction relying on pre-image reconstruction is developed within CS framework. Simulation results have shown that the proposed method outperforms the conventional CS approaches based on linear sparsifying transforms.