基于超拉普拉斯正则化的冲击波超压层析重建  

Shock wave overpressure tomography reconstruction based on super-Laplace regularization

作　　者：宋一娇 孔慧华[1,3] 李剑 齐子文[1,3] 张然 Song Yijiao;Kong Huihua;Li Jian;Qi Ziwen;Zhang Ran(School of Mathematics,North University of China,Taiyuan 030051,China;School of Information and Engineering,North University of China,Taiyuan 030051,China;Shanxi Key Laboratory of Information Detection and Processing,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,太原030051 [2]中北大学信息与通信工程学院,太原030051 [3]中北大学信息探测与处理山西省重点实验室,太原030051

出　　处：《电子测量技术》2024年第10期160-167,共8页Electronic Measurement Technology

基　　金：国家自然科学基金(62271453)项目资助。

摘　　要：超压层析成像是利用传感器采集到的冲击波信号来反演测试区域的超压分布,是典型的不完全数据重建问题,为了提高求解精度,本文提出了一种基于高斯牛顿迭代联合超拉普拉斯正则化的冲击波超压层析重建方法。由于实际采集到的冲击波信号通常与干扰信号混叠在一起,会影响超压值的测量精度,本文首先采用改进的小波阈值算法对冲击波信号进行去噪处理;其次利用超拉普拉斯先验对图像边缘和二维层析模型进行正则约束;然后采用高斯牛顿迭代算法和交替方向乘子算法,解决大型病态稀疏矩阵的求解问题。实际实验结果表明本文的正则化方法与传统的全变分正则化和广义全变分正则化相比,重建精度可保持在15%左右,在实际场景中具有一定的应用价值。Overpressure tomography is a typical incomplete data reconstruction problem,which uses the shock wave signal collected by the sensor to invert the overpressure distribution in the test area.In order to improve the solution accuracy,a shock wave overpressure tomography reconstruction method based on Gauss-Newton iterative combined superlaplace regularization is proposed in this paper.Because the collected shock wave signal is usually aliased with the interference signal,which will affect the measurement accuracy of the overpressure value,this paper firstly adopts the improved wavelet threshold algorithm to denoise the shock wave signal.Secondly,the image edges and the two-dimensional chromatographic model are constrained by the superlaplace prior.Then Gauss-Newton iterative algorithm and alternating direction multiplier algorithm are used to solve the problem of large ill-conditioned sparse matrix.The experimental results show that compared with the traditional total variational regularization and total generalized variational regularization,the reconstruction accuracy of the proposed method can be maintained at about 15%,which has certain application value in practical scenarios.

关 键 词：层析成像 小波阈值 全变分正则化 广义全变分正则化 超拉普拉斯正则化 超压场重建 

分 类 号：TN911.73[电子电信—通信与信息系统]