Algebraic reconstruction approach for the circular radon transform.

The normal Radon transform as well as the circular Radon transform are reviewed in this work. Traditionally, the first is linked to computerized tomography and the second is linked to synthetic aperture techniques that are well-established in both, radar, and ultrasound imaging systems. A new method that adapts the ordinary algebraic reconstruction methods to numerically reconstruct an image from its circular Radon transform is presented. To this end, a representation of an image using the unit box functions is employed, this representation facilitates the formation of an exact matrix of coefficients for a linear system to be solved. Regularized least square is used to solve the relatively small systems, and a machine learning approach is used for large systems. Several experiments are conducted for validation of the built system as well the reconstruction of images from their circular Radon transform. [ABSTRACT FROM AUTHOR]