Related papers: The attenuated geodesic X-ray transform
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
Gyrations are operations on manifolds that arise in geometric topology, where a manifold $M$ may exhibit distinct gyrations depending on the chosen twisting. For a given $M$, we ask a natural question: do all gyrations of $M$ share the same…
In this paper, we consider the atmospheric tomography operator, which describes the effect of turbulent atmospheric layers on incoming planar wavefronts. Given wavefronts from different guide stars, measured at a telescope, the inverse…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. "xeroxing." The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the…
We systematically analyze the decay of metastable topological defects that arise from the spontaneous breakdown of gauge or global symmetries. Quantum-mechanical tunneling rates are estimated for a variety of decay processes. The decay rate…
Introducing accelerated reconstruction algorithms into clinical settings requires measures of uncertainty quantification that accurately assess the relevant uncertainty introduced by the reconstruction algorithm. Many currently deployed…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
Attenuation of ultrasound waves varies with tissue composition, hence its estimation offers great potential for tissue characterization and diagnosis and staging of pathology. We recently proposed a method that allows to spatially…
This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables.…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction…
In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
The problem of image reconstruction under multiple light scattering is usually formulated as a regularized non-convex optimization. A deep learning architecture, Scattering Decoder (ScaDec), was recently proposed to solve this problem in a…
Complications arising from the non-compact nature of the phase space of N-body systems prevent any asymptotic characterization of chaotic behaviour (since no equilibrium final states can exist). This leads us to revisit some of the old…
In this article, we revisit iterative methods for solving the inverse problem of photoacoustic tomography in free space. Recently, there have been interesting developments on explicit formulations of the adjoint operator, demonstrating that…
We discuss theoretical and phenomenological aspects of the use of boson propagators with energy-dependent widths in predictions for high-energy scattering processes. In general, gauge invariance is violated in such calculations. We discuss…