Undersampled dynamic magnetic resonance imaging using kernel principal component analysis

Compressed sensing (CS) is a promising approach to accelerate dynamic magnetic resonance imaging (MRI). Most existing CS methods employ linear sparsifying transforms. The recent developments in non-linear or kernel-based sparse representations have been shown to outperform the linear transforms. In this paper, we present an iterative non-linear CS dynamic MRI reconstruction framework that uses the kernel principal component analysis (KPCA) to exploit the sparseness of the dynamic image sequence in the feature space. Specifically, we apply KPCA to represent the temporal profiles of each spatial location and reconstruct the images through a modified pre-image problem. The underlying optimization algorithm is based on variable splitting and fixed-point iteration method. Simulation results show that the proposed method outperforms conventional CS method in terms of aliasing artifact reduction and kinetic information preservation.