基于lp-范数的ECT图像重建算法研究

Research on ECT Image Reconstruction Algorithm Based on lp -norm

针对在ECT图像重建过程中,基于lp-范数的非凸压缩感知算法常存在计算量较大以及现有的近端映射算法受一些特定的p值限制而导致成像分辨率较低的问题,利用改进的插值函数替换lp-范数||x||^pp,通过调整参数使得改进的函数无限逼近lp-范数||x||^pp,同时引入阈值表示理论,并在此基础上提出新的自适应阈值迭代算法对新模型进行求解。实验结果表明,改进后的自适应lp-范数重构算法相对于Landwebr算法、迭代重加权最小二乘法具有更强的适应性,更高的图像分辨率,更快的成像速度。

In the process of ECT image reconstruction,non-convex compressed sensing algorithm based on lp-norm often has the problem of large computational complexity,and the algorithms corresponding to the proximal mapping of the regularization lp-norm minimization are limited to few specific values of parameter p,which leads to low image resolution.The improved interpolation function is used to replace ||x||^pp,by adjusting the parameters,the improved function is infinitely approximated to ||x||^pp.At the same time,the threshold representation theory is introduced,and based on it.A new adaptive threshold iterative algorithm is proposed to solve the new model.The experimental results show that the improved algorithm has stronger adaptability,higher image resolution and faster imaging speed than the Lanweber algorithm and iterative reweighted least squares method.