Improved Integral Transform Method Based on Gaussian Kernel for Image Reconstruction

Tomography has been widely used in many fields. The theoretical basis of tomography is the Radon transform, which is the line integral along a radial line oriented at a specific angle. In practice, the detector that collects the projection has a certain width, which does not coincide with the line integral. Therefore, the resolution of the reconstructed image will be reduced. In order to overcome the effect of the detector width on the reconstruction quality, some reconstruction methods have taken the influence of the detector width into account and have achieved high reconstruction quality, such as the distance-driven model (DDM) and the area integral model (AIM). They have no exact analytic inversion formula, just numerical processing means to improve the reconstruction quality. According to the characteristics of DDM and AIM projection functions, a new integral transform is established, which is called Gaussian weighted Radon transform (GWRT). The width of integral line can be controlled by parameter in GWRT. GWRT is the generalized Radon transform in theory. We derive the analytical inversion formula of GWRT and establish a new numerical inversion algorithm based on it, i.e., optimized FBP. GWRT has a perfect theoretical framework, which can realize the accurate inversion of integral transform with integral line of a certain width. The experimental results show that the GWRT is feasible, and the image reconstruction quality is higher when the detector has a certain width than that of Radon transform implemented by FBP. And GWRT has better anti-noise ability than Radon transform.