Since the Radon transform (RT) consists in a line integral function, some modeling assumptions are made on Computed Tomography (CT) system, making image reconstruction analytical methods, such as Filtered Backprojection (FBP), sensitive to artifacts and noise. In the other hand, recently, a new integral transform, called Scale Space Radon Transform (SSRT), is introduced where, RT is a particular case. Thanks to its interesting properties, such as good scale space behavior, the SSRT has known number of new applications. In this paper, with the aim to improve the reconstructed image quality for these methods, we propose to model the X-ray beam with the Scale Space Radon Transform (SSRT) where, the assumptions done on the physical dimensions of the CT system elements reflect better the reality. After depicting the basic properties and the inversion of SSRT, the FBP algorithm is used to reconstruct the image from the SSRT sinogram where the RT spectrum used in FBP is replaced by SSRT and the Gaussian kernel, expressed in their frequency domain. PSNR and SSIM, as quality measures, are used to compare RT and SSRT-based image reconstruction on Shepp-Logan head and anthropomorphic abdominal phantoms. The first findings show that the SSRT-based method outperforms the methods based on RT, especially, when the number of projections is reduced, making it more appropriate for applications requiring low-dose radiation, such as medical X-ray CT. While SSRT-FBP and RT-FBP have utmost the same runtime, the experiments show that SSRT-FBP is more robust to Poisson-Gaussian noise corrupting CT data.

翻译：由于Radon变换（RT）本质上是线积分函数，在计算机断层扫描（CT）系统中需引入若干建模假设，使得滤波反投影（FBP）等图像重建解析方法对伪影和噪声敏感。另一方面，近年来提出了一种名为尺度空间Radon变换（SSRT）的新型积分变换，其中RT是其特例。凭借良好的尺度空间行为等有趣性质，SSRT已涌现出诸多新应用。本文为改善上述方法的重建图像质量，提出采用尺度空间Radon变换（SSRT）对X射线束进行建模，其中对CT系统元件物理维度的假设更符合实际。在阐述SSRT基本性质及其逆变换后，本文采用FBP算法从SSRT正弦图重建图像，其中FBP中使用的RT频谱被替换为频域表达的SSRT及高斯核函数。以峰值信噪比（PSNR）和结构相似性（SSIM）作为质量评价指标，在Shepp-Logan头部体模和拟人腹部体模上对比了基于RT与SSRT的图像重建效果。初步结果表明，基于SSRT的方法优于基于RT的方法，尤其在投影数量减少时优势更为明显，更适合于医用X射线CT等需要低剂量辐射的应用场景。尽管SSRT-FBP与RT-FBP的运行时间近乎相同，但实验表明SSRT-FBP对污染CT数据的泊松-高斯噪声具有更强的鲁棒性。