Sinogram recovery for sparse angle tomography using a sinusoidal Hough transform

In hard-field tomography, where access restrictions forbid continuous scanning around the subject, the measurements represent an under-sampled forward transform resulting in a sparse-angle sinogram and a reconstructed image with substantial artefacts. We introduce a method whereby the under-sampled sinogram is treated as a pixellated image, to which an image analysis technique, the Hough transform, is applied. The analytical description is obtained of sinusoidal data patterns (centre of mass, spatial support and total mass), corresponding to the major objects' distribution in the imaged subject. Furthermore, the sampling of the sinogram is recovered to a degree required for standard algorithms for data inversion. Results are presented from the implementation of the proposed algorithm on simulated phantoms, as well as experimental data from guided-path tomography. It is shown that the algorithm is capable of recovering a complete sinogram from as little as 32 measurements at four angular projections with good centre-of-mass estimates and boundary definition, together with substantial suppression of errors in subsequent image reconstruction.