A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper develops a new method for solving IBVPs on star-shaped domains.
Extends magnetic flow theory results to higher dimensions.
Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.
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.
We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a symmetry condition at the reflecting part of the boundary and vanishes on the rest. This is done in a geometry with non-positive sectional cur…
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.
Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass …
Sharp stability estimate for tensor tomography in non-positive curvature.
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 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.
CRC method provides tighter uncertainty intervals for CT images.
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors are symmetric differentials of any order as well as other types obtained after ta…
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…
Study reveals how travel times on cylindrical boundaries can identify spacetime structure.
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…
Study sparse function recovery from indirect noisy observations using -regularization.
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.…
Research on unique continuation principles in medical and seismic imaging.
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.
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …
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.
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…
We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
New quantum state reconstruction method accelerates convergence.
Interior tomography for the region-of-interest (ROI) imaging has advantages of using a small detector and reducing X-ray radiation dose. However, standard analytic reconstruction suffers from severe cupping artifacts due to existence of null space in the truncated Radon transform. Existing penalized reconstruction meth…
Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not…
Develops support theorem for analytic transforms in tomography.
Noise2Filter improves 3D tomography reconstruction efficiency and accuracy.