Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.

We study local deformations of time-frequency and timescale representations, in the framework of the so-called reassignment methods, which aim at "deblurring" time-frequency representations. We focus on deformations generated by appropriate vector fields defined on time-frequency or time scale plane, and constructed on the basis of geometric and group-theoretical arguments. Such vector fields may be used as such for signal analysis (as quantities generalizing instantaneous frequency or group delay) in the framework of reassignment algorithms.