Related papers: Resolution analysis of inverting the generalized R…
In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose…
The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to…
Single photon emission computed tomography (SPECT) is a well established clinical tool for functional imaging. A limitation of current SPECT systems is the use of mechanical collimation, where only a small fraction of the emitted photons is…
This paper, a culmination of the authors' theory of the RT-equations, accomplishes the following: (i) We discover there is a true (geometric) regularity associated with every affine connection, its ``essential regularity'', the highest…
We present a renormalization-group perspective on spontaneous stochasticity in hydrodynamic turbulence, viewed through the lens of multiscale dynamical systems. Building on previously established results for a solvable multiscale Arnold's…
Sparse regularization plays a central role in solving inverse problems arising from incomplete or corrupted measurements. Different regularizers correspond to different prior assumptions about the structure of the unknown signal, and…
Despite the tremendous success of deep models in various individual image restoration tasks, there are at least two major technical challenges preventing these works from being applied to real-world usages: (1) the lack of generalization…
Single image super-resolution (SR) is an ill-posed problem which aims to recover high-resolution (HR) images from their low-resolution (LR) observations. The crux of this problem lies in learning the complex mapping between low-resolution…
Let $\phi(x,y)$ be a continuous function, smooth away from the diagonal, such that, for some $\alpha>0$, the associated generalized Radon transforms \begin{equation} \label{Radon} R_t^{\phi}f(x)=\int_{\phi(x,y)=t} f(y) \psi(y)…
While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view…
Despite that convolutional neural networks (CNN) have recently demonstrated high-quality reconstruction for single-image super-resolution (SR), recovering natural and realistic texture remains a challenging problem. In this paper, we show…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT…
Normalization is a fundamental ring-theoretic operation; geometrically it resolves singularities in codimension one. Existing algorithmic methods for computing the normalization rely on a common recipe: successively enlarge the given ring…
Robust scene representation is essential for autonomous systems to safely operate in challenging low-visibility environments. Radar has a clear advantage over cameras and lidars in these conditions due to its resilience to environmental…