The Modulo Radon Transform and its Inversion

Abstract

In this paper, we introduce the Modulo Radon Transform (MRT) which is complemented by an inversion algorithm. The MRT generalizes the conventional Radon Transform and is obtained via computing modulo of the line integral of a two-dimensional function at a given angle. Since the modulo operation has an aliasing effect on the range of a function, the recorded MRT sinograms are always bounded, thus avoiding information loss arising from saturation or clipping effects. This paves a new pathway for imaging applications such as high dynamic range tomography, a topic that is in its early stages of development. By capitalizing on the recent results on Unlimited Sensing architecture, we prove that the Modulo Radon Transform can be inverted when the resultant (discrete/continuous) measurements map to a band-limited function. Thus, the MRT leads to new possibilities for both conceptualization of inversion algorithms as well as development of new hardware, for instance, for single-shot high dynamic range tomography.