基于X射线木材断层扫描反投影算法中的最优滤波器选取

Selection of the Optimum Filter in the Back Projection Algorithm Based on X-Ray Wood Tomography

【目的】对比X射线计算机断层扫描图像重建算法中常用R-L、S-L、Cosine、Hamming和Hanning滤波器的重建图像效果,分析滤波函数重建图像质量,优选木材断层扫描图像重建中的最佳滤波器,为木材断层成像技术研究提供科学方法。【方法】依据CT成像原理,分析图像滤波过程,探讨不同滤波器工作特性和滤波器的设计步骤。首先将投影数据存放于二进制的二维数组,通过探测点编号和旋转角度确定每一点投影值,根据投影数据序列长度确定滤波器长度,将不同角度下的投影数据前后补零,使其构成3倍于原始长度的投影数据。然后进行一维快速傅里叶变换,并将频域结果与滤波器频域离散形式作乘积,对投影数据进行逐行滤波。最后,将乘积后的滤波结果进行傅里叶反变换得到时域中的投影数据,对比不同滤波器成像结果,对不同滤波器进行评价与分析。【结果】与未进行滤波的反投影重建图像相比,滤波后断层图像生长轮边界更清晰、伪影较少,边缘平滑;未经滤波处理直接反投影重建图像伪影严重,重建效果极差,生长轮、裂缝结构特征不清晰。采用R-L、S-L、Cosine滤波器滤波后断层图像边缘平滑、清晰,无向周边扩散现象,采用Hamming、Hanning滤波器滤波后图像伪影轻微,存在比较明显的波纹状伪影。从各滤波图像与检测模型图像的差异性来看,R-L滤波器滤波后图像质量最高,而Hamming滤波器滤波后结果误差最大。【结论】采用R-L滤波器得到的重建图像误差最小,图像最清晰,空间分辨率高,能有效去除伪影,滤波后的木材断层图像可准确判断缺陷形状、位置和大小。

【Objective】In order to optimize the best filter in wood tomography image reconstruction and provide scientific methods for the study of wood tomography, the reconstructed image effects of R-L, S-L, Cosine, Hamming and Hamming filters commonly used in X-ray computed tomography scanning reconstruction algorithm were compared in this study, and the reconstructed image quality of filter function were also analyzed.【Method】 According to the CT imaging principle, the image filtering process was analyzed, and the working characteristics of different filters and the design steps of the filters were discussed. Firstly, the projection data is stored in a binary two-dimensional array. The projection value of each point is determined by the probe point number and the rotation angle. The filter length is determined according to the length of the projection data sequence, and the projection data at different angles are zero-padded before and after, so that it constitutes a series of new projection data that is three times the ones of the original length. Then, a one-dimensional fast Fourier transform is performed, and the frequency domain result is multiplied by the filter frequency domain discrete form, and the projection data is filtered line by line. Finally, the filtered result of the product is inversely transformed by Fourier to obtain the projection data in the time domain. The imaging result of different filters are compared, and different filters are evaluated and analyzed.【Result】 After comparing with the back-projected reconstruction image without filtering, the boundary of the growth ring of the five filtered images is clearer, the artifacts are less, and the edges are smoother. The image artifacts are directly reconstructed by the back projection without filtering with an extremely poor reconstruction effect, with the structural characteristics of the growth wheel and crack are not clear. After reconstruction with R-L, S-L and Cosine filters, respectively, the edges of the tomographic image are smooth and clear, and the non-directional periphery is diffused. After the Hamming and Hamming filters are reconstructed,respectively, the image artifacts are slight, and there are obvious corrugated artifacts. From the difference of each filtered image and the detection model, the image quality is the highest after reconstruced by the R-L filter, and the error of the Hamming filter is the largest after reconstruction.【Conclusion】 The reconstructed image obtained by R-L filter has the smallest error, the reconstructed image is the clearest, the spatial resolution is high, and the artifact can be effectively removed. The filtered wood tomographic image can accurately determine the shape, position and size of the defect.