Magnetic Resonance Images Reconstruction using Uniform Discrete Curvelet Transform Sparse Prior based Compressed Sensing

Compressed sensing(CS) has shown great potential in speeding up magnetic resonance imaging(MRI) without degrading images quality. In CS MRI, sparsity (compressibility) is a crucial premise to reconstruct high-quality images from non-uniformly undersampled k-space measurements. In this paper, a novel multi-scale geometric analysis method (uniform discrete curvelet transform) is introduced as sparse prior to sparsify magnetic resonance images. The generated CS MRI reconstruction formulation is solved via variable splitting and alternating direction method of multipliers, involving revising sparse coefficients via optimizing penalty term and measurements via constraining k-space data fidelity term. The reconstructed result is the weighted average of the two terms. Simulated results on in vivo data are evaluated by objective indices and visual perception, which indicate that the proposed method outperforms earlier methods and can obtain lower reconstruction error.