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We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
Thomson scattering spectra measure the response of plasma particles to incident radiation. In warm dense matter, which is opaque to visible light, x-ray Thomson scattering (XRTS) enables a detailed probe of the electron distribution and has…
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in $\mathbb{R}^3$ by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering…
Within the quantum sine-Gordon model a transmission matrix describing the scattering of a soliton with a fused pair of integrable defects is proposed. The result is consistent with the classical picture of scattering and highlights the…
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…
Muography is an imaging tool based on the attenuation of cosmic muons to observe the density distribution of large objects, such as underground caves or fractured zones. Tomography based on muography measurements -- that is, three…
The star transform is a generalized Radon transform mapping a function on $\mathbb{R}^n$ to the function whose value at a point is the integral along a union of rays emanating from the point in a fixed set of directions, called branch…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
Ultrasound imaging is a cost-effective and radiation-free modality for visualizing anatomical structures in real-time, making it ideal for guiding surgical interventions. However, its limited field-of-view, speckle noise, and imaging…
This paper aims to solve a fundamental problem in intensity-based 2D/3D registration, which concerns the limited capture range and need for very good initialization of state-of-the-art image registration methods. We propose a regression…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…
We describe decomposition formulas for rotations of $R^3$ and $R^4$ that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions…