中文摘要：

为了解决FDK重建算法在锥束CT重建中运算量大，耗时较多，以及针对不同的应用环境提供不同分辨率的3维医学图像问题，该文提出一种基于小波变换的多分辨率锥束CT图像快速3维重建算法。首先对采集到的投影图像进行相应尺度的小波变换，得到各尺度小波分解系数，选择相应尺度的小波系数进行FDK重建，可以得到相应低分辨率的3维图像数据，还可根据需要由得到的低分辨率重建数据分别沿着径向取断层图像，进行相应的小波逆变换，进而得到高分辨率的3维图像数据。实验数据表明，该方法不仅能够得到不同分辨率的3维图像数据，而且相较于传统的FDK算法生成分辨率相同、精度相近的高分辨率3维图像数据，重建速度可以提高1倍以上。

英文摘要：

To solve the large amount of computation, time-consuming problems of the FDK reconstruction algorithm for cone beam CT reconstruction, and different resolutions for different application environments of 3D medical image, this paper proposes a fast reconstruction algorithm of multi-resolution cone beam CT image based on wavelet transform. Firstly, the corresponding wavelet transform for projection images are obtained, and the corresponding scale wavelet coefficients are selected for FDK reconstruction. Thus, 3D image data of the low resolution are obtained. According to need, the high resolution 3D image data can also be obtained by the inverse wavelet transform of the radial images obtained from low resolution. The experimental data shows that this method can not only provide a different resolution of the 3D image data, but also increase the reconstruction speed more than one times when the same resolution and similar precision high resolution 3D image data is obtained compared with the traditional FDK algorithm.