When developing a Filtered Backprojection (FBP) algorithm, considering the Radon transform (RT) as a line integral necessitates assuming that all elements of the Computed Tomography (CT) system, such as the detector cell, are dimensionless. It is generally the result of such inadequate CT modeling that analytical methods are sensitive to artifacts and noise. Then, to address this problem, several algebraic reconstruction techniques utilizing iterative models are suggested. The high computational cost of these methods restricts their application. In this paper, we propose the utilization of the Scale Space Radon Transform (SSRT), recognized for its good behavior in the scale space where, the detector width is already considered into the SSRT design and is controlled by the Gaussian kernel standard deviation. After depicting the basic properties and the inversion of SSRT, the FBP algorithm is used in two different ways to reconstruct the image from the SSRT sinogram: (1) Deconv-Rad-FBP: Deconvolve SSRT to estimate RT and apply FBP or (2) SSRT-FBP: Modify FBP such that RT spectrum used in FBP is replaced by SSRT, expressed in the frequency domain. Comparison of image reconstruction using SSRT and RT are performed on Shepp-Logan head and anthropomorphic abdominal phantoms by using, as quality measures, PSNR and SSIM. The first findings show that the SSRT-based image reconstruction quality is better than the one based on RT where, the SSRT-FBP method reveals to be the most accurate, 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 algorithm have utmost the same execution time, the former is much faster than Deconv-Rad-FBP. Furthermore, the experiments show that the SSRT-FBP method is more robust to CT data Poisson-Gaussian noise.

翻译：在开发滤波反投影（FBP）算法时，将Radon变换（RT）视为线积分需假定CT系统所有元件（如探测器单元）均为无尺寸点。此类不精确CT建模通常导致解析方法对伪影和噪声敏感。为解决该问题，研究者提出多种基于迭代模型的代数重建技术，但这些方法的高计算成本限制了其应用。本文提出利用尺度空间Radon变换（SSRT）——该变换在尺度空间中表现出优异特性，探测器宽度已纳入SSRT设计，并由高斯核标准差控制。在阐述SSRT基本性质及其逆变换后，采用两种不同方式从SSRT正弦图重建图像：（1）Deconv-Rad-FBP：对SSRT反卷积以估计RT并应用FBP；（2）SSRT-FBP：修改FBP使其频域表达式中的RT谱被SSRT替代。通过PSNR和SSIM质量指标，在Shepp-Logan头部模体和拟人腹部模体上比较SSRT与RT的图像重建效果。初步结果表明，基于SSRT的图像重建质量优于基于RT的方法，其中SSRT-FBP方法精度最高，尤其在投影数减少时更为显著，故更适用于需低剂量辐射的应用场景（如医用X射线CT）。虽然SSRT-FBP与RT-FBP算法执行时间几乎相同，但前者比Deconv-Rad-FBP快得多。此外，实验表明SSRT-FBP方法对CT数据的泊松-高斯噪声具有更强鲁棒性。