Spread spectrum compressed sensing magnetic resonance imaging via fractional Fourier transform

Compressed sensing (CS) has shown great potential in accelerating data acquisition procedure for magnetic resonance imaging (MRI). For compressed sensing magnetic resonance imaging (CS-MRI), the incoherence between the sensing and the sparsity matrices is a key role of the performance . However, in conventional MRI, the sensing matrix is Fourier matrix and the sparsifying transform matrix is Wavelet matrix, respectively. They are not optimally incoherent. Moreover, Fourier encoding weakly spreads out energy and concentrates the energy in the center of the k-space. This will further reduce the randomness of the under-sampling pattern. Therefore, for the CS-MRI, incoherence between the sensing and the sparsity matrices will be weak and lead to a degradation of images reconstruction quality for highly under-sampling factors. In this paper, we investigate spread spectrum incoherent sampling compressed sensing MRI using fractional Fourier transform. Simulation results shown that the fractional Fourier transform encoding can spread out the energy more uniformly than the conventional Fourier encoding. Then it is beneficial for designing the incoherent sampling pattern to satisfy the incoherent requirements of the CS-MRI.