Imaging from Incomplete Data through Sinogram Restoration by Hough Transform

E. P. A. Constantino and K. B. Ozanyan

School of Electrical and Electronic Engineering, The University of Manchester, Manchester, M60 1QD, United Kingdom, Email: e.pereira-araujo-c@student.manchester.ac.uk

ABSTRACT

Tomography in most industrial applications is the subject of imaging apparatus that often prohibits line integrals of attenuation to be measured at a sufficiently large number of viewing angles, which discriminates the use of standard algorithms to solve the inverse problem. “Missing angles” can be clustered at a certain range, where access is impossible (limited access), or evenly distributed, but limited in number (limited resources). Consequently, industrial imaging often addresses the predicament of severely incomplete data. In this study, we present a new method that restores the missing information in the 2-D Radon transform (the sinogram) image, pixellated according to the attainable spatial resolution, as a mean to condition the data prior to image reconstruction using standard algorithms e.g. filtered back-projection. The method uses Hough transform to recognise sinusoidal patterns in the sinogram, which corresponds to higher intensity clusters in the object space. Results have shown that the novel method can be a powerful supplement to traditional transform- based image reconstruction methods. The algorithm has achieved satisfactory image reconstruction with good objects’ location and spatial extent from as low as 124 line integrals. This study also indicates that for simple subjects, the HT method allows us to bypass the solving of the inverse problem altogether, by supplying the “Centre of Mass” coordinates of the high intensity clusters and the spatial extent of these clusters in real space.

Keywords Hard-Field Tomography, sinogram, Hough Transform