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.
This paper improves inverse problem solving with weakly convex regularisers and proves convergence.
problem Improving solution methods for inverse problems.
method Generalised formulation of convergent regularisation using weakly convex regularisers, and proof of convergence for primal-dual hybrid gradient method.
result Proves convergence of primal-dual hybrid gradient method for variational problems and shows improved performance with IWCNNs.
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…
Deep network improves electrical tomography across multiple frequencies.
problem Nonlinear multi-frequency electrical impedance tomography (mfEIT) for tissue conductivity estimation.
method Integrates graph neural networks (GNNs) into the iterative Proximal Regularized Gauss Newton (PRGN) framework to reconstruct tissue concentrations accurately.
result Accurate reconstruction of overlapping tissue fraction concentrations across multiple frequencies.
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…
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…
The distribution of absorbed dose in radionuclide therapy with Lu177 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…
Positron Emission Tomography (PET) is a functional imaging modality widely used in neuroscience studies. To obtain meaningful quantitative results from PET images, attenuation correction is necessary during image reconstruction. For PET/MR hybrid systems, PET attenuation is challenging as Magnetic Resonance (MR) images…
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…
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.…
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…
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.
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 d0 is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not…