arXiv:2205.05188v1 [cs.CV] 10 May 2022 On Scale Space Radon Transform, Properties and Image Reconstruction Nafaa Nacereddine a,∗ , Djemel Ziou b , Aicha Baya Goumeidane a a Research Center in Industrial Technologies CRTI, P.O.Box 64, Ch´ eraga, Algiers 16014, Algeria b DMI, Universit´ e de Sherbrooke, Qu´ ebec, QC J1K 2R1, Canada Abstract 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 trans- form 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, recon- struct 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 tech- niques 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. Keywords: Scale space Radon transform, SSRT properties, SSRT inversion, Deconvolution, Filtered back projection, Image reconstruction 1. Introduction Scale Space Radon Transform (SSRT), introduced recently in [1], is a matching of an embedded shape in an image and the Gaussian kernel. The choice of the latter should satisfy several requirements such as nice behaviour in scale space, robustness to noise, uniqueness of transform maximum, etc. [1]. It follows that Radon transform [2] is a particular case of SSRT where, the Gaussian kernel is replaced by a Dirac distribution δ . As for the Radon transform, several properties could be derived from SSRT and which could be very useful in computer vision applications such as remote sensing, in- ∗ Corresponding author Email addresses: n.nacereddine@crti.dz (Nafaa Nacereddine), djemel.ziou@usherbrooke.ca (Djemel Ziou), a.goumeidane@crti.dz (Aicha Baya Goumeidane) Preprint submitted to Elsevier May 12, 2022