We prove a unique continuation property for the fractional Laplacian $(-\Delta)^ s $ when $
s\in (-n/2,\infty)\setminus\mathbb {Z} $. In addition, we study Poincar\'e-type inequalities for …

We prove a uniqueness result for the broken ray transform acting on the sums of functions
and 1-forms on surfaces in the presence of an external force and a reflecting obstacle. We …

We propose a thorough analysis of the tensor tomography problem on the Euclidean unit
disk parameterized in fan-beam coordinates. This includes, for the inversion of the Radon …

We study ray transforms on spherically symmetric manifolds with a piecewise $ C^{1, 1} $
metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $ L …

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle,
following earlier work of Mukhometov. If the surface has nonpositive curvature and the …

We study the problem of recovering a function on a pseudo-Riemannian manifold from its
integrals over all null geodesics in three geometries: pseudo-Riemannian products of …

We present a new computed tomography (CT) method for inverting the Radon transform in 2
dimensions. The idea relies on the geometry of the flat torus; hence we call the new method …

We reduce the broken ray transform on some Riemannian manifolds (with corners) to the
geodesic ray transform on another manifold, which is obtained from the original one by …

This work characterizes the range of the single-quadrant approximate discrete Radon
transform (ADRT) of square images. The characterization follows from a set of linear …

While traditionally the computerized tomography of a function f∈ L 2 (R 2) depends on the
samples of its Radon transform at multiple angles, the real-time imaging sometimes requires …