Fast reconstruction of highly undersampled MR images using one and two dimensional principal component analysis

Recent compressed sensing techniques allow signal acquisition with less sampling than required by the Nyquist-Shannon theorem which reduces the data acquisition time in magnetic resonance imaging (MRI). However, prior knowledge becomes essential to reconstruct detailed features when the sampling rate is exceedingly low. In this work, one compressed sensing scheme developed in wireless sensing networks was adapted for the purpose of reconstructing magnetic resonance images by using one-dimensional principal component analysis (1D-PCA). Moreover, another related reconstruction method was proposed based on two-dimensional principal component analysis (2D-PCA). When comparing with one wavelet compressed sensing method, we demonstrate that these techniques are feasible and efficient at high undersampling rates.