Reconstruction Of Dynamic Magnetic Resonance Image Based On Sparsity And Low-rank Decomposition

Dynamic magnetic resonance imaging（DMRI）is an important instrument in medical research and clinical diagnosis.Limited by physical and physiological conditions,the scanning time of DMRI is relative long which leads to deterioration of imaging quality and limits the application of magnetic resonance imaging.Compressive sensing（CS）exploits the sparse prior of dynamic magnetic resonance images and is capable of reconstructing dynamic magnetic resonance images under highly undersampled condition,which greatly reduces the number of samples required and scanning time.However,CS only exploits the sparse prior but does not make full use of the internal information of dynamic magnetic resonance images,and there are obvious aliasing artifacts in the aperiodic images reconstructed by the conventional Fourier transform-based CS methods.In this paper,the low-rank prior of dynamic magnetic resonance images is introduced into the optimization model by the robust principal component analysis（RPCA）method for the reconstruction of undersampled dynamic magnetic resonance images.The dynamic magnetic resonance images are decomposed into dynamic foregrounds and static backgrounds by using a L₁ norm on the dynamic foreground matrix to enforce sparse penalty and a nuclear norm on the static background matrix to enforce low-rank penalty.The details in the dynamic magnetic resonance images are effectively reserved and the temporal and spatial resolution of reconstruction images are improved.The existing low-rank and sparse decomposition methods express the dynamic foreground matrix sparsely using fixed bases and cannot obtain the optimal matches of dynamic foreground matrices for various dynamic magnetic resonance images,the quality of reconstructed images is thus decreased.To solve this problem,blind compressive sensing（BCS）is introduced into the existing low-rank and sparse decomposition model.The dynamic foreground is adaptively sparsely represented as a product of a sparse coefficient matrix and the relevant dictionary.A L₁ norm penalty is applied on the sparse coefficient matrix and a Frobenius norm constraint on the dictionary,which enforces the attenuation of noisy basis functions and the reduction of the noisy artifacts.The results of the reconstruction experiments on breath-held cardiac cine images and free breathing cardiac perfusion images show that both the periodic and aperiodic dynamic images reconstructed by the improved method are of high qualities,compared to the conventional low-rank and sparse methods.