arXiv research

Study reveals how travel times on cylindrical boundaries can identify spacetime structure.

Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.

Summary of tensor tomography proofs on manifolds with boundaries.

Paper addresses travel time tomography stability and statistical inversion.

Study uses machine learning to solve photoacoustic tomography's inverse problem.

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical details and minimal assumptions. Only very basic functional analysis is assumed as bac…

Sketch Tomography improves quantum state estimation accuracy.

Deep network improves electrical tomography across multiple frequencies.

A new method speeds up quantum state estimation.

Improved computed tomography reconstruction with deep learning and deep image prior.

We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…

New method uses MRI data to improve PET tomography uncertainty quantification.

Study inverse problems for twisted geodesic flows on manifolds.

We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…

TomOpt optimizes muon detector designs using differentiable programming.

Dissertation tackles geodesic ray transform on Riemannian manifolds.

The distribution of absorbed dose in radionuclide therapy with Lu$^{177}$ can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but inaccurate approximation is unsuitable for personalised dosimetry because it negle…

Study online learning of quantum processes, showing feasibility for certain types.

Extends magnetic flow theory results to higher dimensions.

CRC method provides tighter uncertainty intervals for CT images.

Paper develops a new method for solving IBVPs on star-shaped domains.

This work tackles uncertainty quantification in tomography reconstruction.

In the recent articles \cite{PSU1,PSU3}, a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the surjectivity of the adjoint of the geodesic ray transform, or equivalently the exi…

We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…

Framework for confidence estimation in deep CT reconstructions.

Score-based models improve diffuse optical tomography accuracy.

Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections.…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Research on unique continuation principles in medical and seismic imaging.

We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…

We survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. We also propose several open problems.

Unique continuation for X-ray transforms of one-forms with partial data.

Jebsen-Birkhoff theorem extended to Berwald spacetimes.

The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.

The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

The study characterizes GRW spacetimes with gradient solitons and phantom era.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

Kernel estimator optimally recovers function from noisy exponential Radon transform.

In the classic sparsity-driven problems, the fundamental L-1 penalty method has been shown to have good performance in reconstructing signals for a wide range of problems. However this performance relies on a good choice of penalty weight which is often found from empirical experiments. We propose an algorithm called t…

The thesis optimizes quantum state exploration using bandit algorithms.

We prove a sharp stability estimate for the problem of reconstructing a symmetric 2-tensor from its integrals along all maximal geodesics on a simple manifold.

New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.

Study of quasilocal mass using isometric embedding in various spacetimes.

Despite significant advances in artificial intelligence (AI) for computer vision, its application in medical imaging has been limited by the burden and limits of expert-generated labels. We used images from optical coherence tomography angiography (OCTA), a relatively new imaging modality that measures perfusion of the…

Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.