基于迭代p阈值投影算法的压缩感知磁共振成像

Compressed Sensing Magnetic Resonance Imaging Based on Projected Iterative p‑Thresholding Algorithm

针对迭代软阈值投影算法中的软阈值函数收缩功能较差的问题,提出了迭代p阈值投影算法。用p阈值函数替换迭代软阈值投影算法中的软阈值函数,对小系数的惩罚更大,对大系数产生更小的偏置,以抑制噪声,减少重建误差。为加快算法速度,利用Nesterov梯度加速技术,设计了快速迭代p阈值投影算法,用于磁共振图像重建。在紧标架为平移不变离散小波变换和轮廓波下,将快速迭代p阈值投影算法用于压缩感知磁共振成像。与光滑化的快速迭代软阈值算法、迭代软阈值投影算法和交替方向乘子法进行仿真对比分析的结果表明,快速迭代p阈值投影算法提高了磁共振成像的重建速度和重建质量。分析了p值对算法性能的影响,给出了适合的p值选择方法,以获得较好的收敛速度、减小重构误差。

Aiming at the problem of poor shrinkage of the soft thresholding function in the projected iterative soft thresholding algorithm,a projected iterative p-thresholding algorithm is proposed.It replaces the soft thresholding function in the projected iterative soft thresholding algorithm with p-thresholding function,which will bring greater penalty for small coefficients and produce smaller bias for large coefficients to suppress the noise and reduce reconstruction errors.To speed up the algorithm,using the Nesterov gradient acceleration technology,a projected fast iterative p-thresholding algorithm is designed for magnetic resonance image reconstruction.When the tight frames are shift-invariant discrete wavelet transform and Contourlets,the projected fast iterative p-thresholding algorithm is used for compressed sensing magnetic resonance imaging.Compared with the smoothed fast iterative soft thresholding algorithm,projected iterative soft thresholding algorithm and alternating direction multiplier method,simulation results show that the projected fast iterative p-thresholding algorithm promotes the reconstruction speed and the reconstruction quality of magnetic resonance imaging.And the influence of the p value on the performance of the algorithm is analyzed,and a suitable p value selection method is given to obtain a better convergence speed and reduce the reconstruction error.