On Scale Space Radon Transform, Properties and Image Reconstruction

Aware of the importance of the good behavior in the scale space that a mathematical transform must have, we depict, in this paper, the basic properties and the inverse transform of the Scale Space Radon Transform (SSRT). To reconstruct the image from SSRT sinogram, the Filtered backprojection (FBP) technique is used in two different ways: (1) Deconvolve SSRT to obtain the estimated Radon transform (RT) and then, reconstruct image using classical FBP or (2) Adapt FBP technique to SSRT so that the Radon projections spectrum used in classical FBP is replaced by SSRT and Wiener filtering, expressed in the frequency domain. Comparison of image reconstruction techniques using SSRT and RT are performed on Shepp-Logan head phantom image. Using the Mean Absolute Error (MAE) as image reconstruction quality measure, the preliminary results present an outstanding performance for SSRT-based image reconstruction techniques compared to the RT-based one. Furthermore, the method (2) outperforms the method (1) in terms of computation time and adaptability for high level of noise when fairly large Gaussian kernel is used.