Abstract:

A Filtered Back-Projection （FBP） ultrasonic tomography reconstruction algorithm based on sparse representation was proposed to solve the difficulty of traditional ultrasonic Lamb wave in detecting and vividly describing the delamination defects composite materials. Firstly， the Lamb wave time-of-flight signals in the composite plate with defect were used as the projection values， the one-dimensional Fourier transform of the projection was equivalent to the two-dimensional Fourier transform of the original image， and the FBP reconstructed image was obtained by convolution with the filter function and projection along different directions. Then， the sparse super-resolution model was constructed and jointly trained by constructing a dictionary of low-resolution image blocks and high-resolution image blocks in order to strengthen the sparse similarity between low- and high-resolution blocks and real image blocks， and a complete dictionary was constructed using low- and high-resolution blocks. Finally， the images obtained by FBP were substituted into the constructed dictionary to obtain the complete high-resolution images. Experimental results show that the proposed algorithm improves Peak Signal-to-Noise Ratio （PSNR）， Structural Similarity （SSIM）， and Edge Structural Similarity （ESSIM） values in the reconstructed image by 9.22%， 2.90%， 80.77%， and 4.75%， 1.52%， 16.5%， respectively compared with the linear interpolation and bicubic spline interpolation algorithms. The proposed algorithm can detect delamination defects in composite materials， improve the resolution of the obtained images with delamination defects and enhance the edge details of the images.

Key words: sparse algorithm, ultrasonic tomography, composite material, delamination defect, non-destructive testing

摘要：

针对传统超声Lamb波难以检测复合材料分层缺陷以及直观描绘缺陷形状的问题，提出一种基于稀疏表示的滤波反投影（FBP）超声层析成像重建算法。首先，提取超声Lamb波在复合材料缺陷板中的走时信号作为投影值，把对投影的一维傅里叶变换等效于对原图像进行的二维的傅里叶变换，与滤波器函数进行卷积运算并沿不同方向投影，从而得到FBP重建图像；然后，构建稀疏超分辨率模型，通过构建低分辨率图像块和高分辨图像块字典进行联合训练，以强化低分辨率和高分辨率块与真实图像块之间的稀疏相似性，并使用低分辨率块和高分辨率块构建完备的字典；最后，将FBP得到的图像代入构建的字典中得到完整的高分辨率图像。实验结果表明，相较于使用线性插值的算法重建的图像，所提算法重建图像的峰值信噪比（PSNR）、结构相似度（SSIM）和边缘结构相似度（ESSIM）值分别提高9.22%、2.90%与80.77%；相较于双三次样条插值算法重建的图像，所提算法重建图像的PSNR、SSIM、ESSIM分别提高4.75%、1.52%与16.5%。所提算法能够有效检测复合材料的分层缺陷，提高获得的分层缺陷图像的分辨率，强化图像的边缘细节。

关键词: 稀疏算法, 超声层析成像, 复合材料, 分层缺陷, 无损检测