Simultaneous Magnitude And Phase Reconstruction Based On Compressed Sensing Magnetic Resonance Imaging

Magnetic resonance imaging is a widely applied non-invasive medical diagnostic method,which can provide rich anatomical and visual information compared with other medical imaging methods.The acquisition of magnetic resonance images requires the inverse Fourier transform of the complex data acquired in K space,but the full Nyquist sampling of K space data requires hundreds of phase encodings to complete,resulting in too long scanning time.Spontaneous or involuntary movements of the patient during prolonged scanning will produce obvious artifacts in the images,which can seriously interfere with the diagnosis.Compressed sensing technology can reduce the sampling rate,thereby shortening the imaging time.However,the traditional magnetic resonance imaging methods based on compressed sensing mostly focuses on the reconstruction of the magnetic resonance magnitude image and ignores the phase information,but the phase information also has great medical value in medical diagnosis and needs to be reconstructed accurately.Therefore,based on compressed sensing,this paper reconstructs high-quality magnetic resonance magnitude and phase images for diagnosis while reducing data acquisition time.The details are as follows:（1）An algorithm for magnetic resonance image reconstruction based on the sparsity of phase trigonometric function is proposed.Aiming at the problem of insufficient expression of image features by a single traditional two-dimensional wavelet transform,the algorithm performs trigonometric function operations before the wavelet transform of the magnetic resonance phase image.With the help of the periodicity of trigonometric function,this operation can effectively eliminate the influence of phase wrapping and enhance the phase sparsity,thereby obtaining better compressed sensing imaging results.In the paper,the multi-coil brain datasets and single-coil simulated datasets with phase wrapping are used to verify the algorithm.The results show that the algorithm has stronger sparse expression ability,higher quality of reconstructed magnetic resonance images,and faster convergence speed.（2）A simultaneous reconstruction algorithm of magnetic resonance magnitude and phase based on dual tree complex wavelet transform is proposed.Aiming at the shortcomings of the traditional real valued discrete wavelet transform,the algorithm uses dual tree complex wavelet transform as sparse basis.Since the dual tree complex wavelet transform not only has the advantages of real valued discrete wavelet transform,but also can separate the high-frequency subband information of magnitude and phase with multi-directional selectivity,and has the characteristics of shift invariance and limited redundancy,so the dual tree complex wavelet transform operation on the magnetic resonance imaging magnitude and phase images can increase sparsity and show more directional information.The multi-coil brain datasets with phase wrapping and single-coil brain datasets without phase wrapping are used for experimental verification,the results show that the algorithm can recover more image contour and edge information,and can eliminate the artifacts in the magnitude images caused by phase jump.