New properties of the V-line Radon transform and their imaging applications

T. T. Truong (1) , M. K. K Nguyen (2)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
2 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

This paper reports on new aspects of the so-called V-line Radon transforms complementing those reported in an earlier work. These new properties are nicely uncovered and described with cartesian coordinates. In particular, we show that the V-line Radon transform belongs to the class of Radon transforms on curves in the plane which can be mapped onto the standard Radon transform on straight lines and thereby are fully characterizable and invertible. Next, we show that the effect of geometric inversion on the V-line Radon transform is to produce a new Radon transform on a pair of supplementary circular arcs, which provides a new access to image reconstruction in the so-called Norton's modality of Compton scatter tomography, a front runner in the race for alternatives to current emission imaging.

Mots clés: Radon transform on a pair of supplementary circular arcs; Compton scatter tomography; Radon transform; V-line Radon transforms; image reconstruction

Domaines: Imagerie; Traitement du signal et de l'image [eess.SP]; Physique mathématique [math-ph]

T. T. Truong, M. K. K Nguyen. New properties of the V-line Radon transform and their imaging applications. Journal of Physics A: Mathematical and Theoretical, 2015, 48(2015) 405204, ⟨10.1088/1751-8113/48/40/405204⟩. ⟨hal-01260337⟩