CS-MRI中稀疏信号支撑集混合检测方法

Hybrid Detection Method of Sparse Signal Support Set in CS-MRI

针对磁共振成像技术采样过程过慢的问题,给出一种新的基于压缩感知的图像重建方法。通过分析一种特殊的基于奇异值分解(SVD)的信号稀疏表示方法,提出一种结合稀疏信号位置和大小信息的支撑集混合检测方法,并根据该方法改进稀疏信号重建算法FCSA。实验结果证明,在相同的欠采样率下,改进FCSA算法重建图像的峰值信噪比(PSNR)比传统的基于小波稀疏基的FCSA算法重建图像的PSNR高2.21 dB^12.72 dB,比基于SVD稀疏基的FCSA算法重建图像的PSNR高0.87 dB^2.05 dB,且重建时间从基于小波稀疏基的FCSA算法的103.21 s下降至改进FCSA算法的36.91 s。

Aiming at the problem of slow sampling time in Magnetic Resonance Imaging（MRI）, a new Compressed Sensing（CS） method is proposed. Singular Value Decomposition（SVD）-based sparse representation is an effective but not widely studied method in the CS-MRI field. This sparse representation is improved using the partially known signal support method. A hybrid support detection method is proposed to make use both the position and magnitude knowledge of the sparse signals. This hybrid support detection method is further applied in Fast Composite Splitting Algorithm（FCSA）, which is an effective reconstruction algorithm for CS-MRI problem. Experimental results show that the proposed FCSA algorithm outperforms the FCSA with Wavelet method and the FCSA with SVD method in the reconstructed image qualities, its PSNR is 2.21 dB^12.72 dB higher than the FCSA with Wavelet method, 0.87 dB^2.05 dB higher than the FCSA with SVD method, and the reconstruction time is 36.91 s compared with 103.21 s of the FCSA with Wavelet method.