Related papers: Resolution analysis of inverting the generalized R…
A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
Generalizable perception is one of the pillars of high-level autonomy in space robotics. Estimating the structure and motion of unknown objects in dynamic environments is fundamental for such autonomous systems. Traditionally, the solutions…
Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as…
Spatially resolved transcriptomics (SRT) has evolved rapidly through various technologies, enabling scientists to investigate both morphological contexts and gene expression profiling at single-cell resolution in parallel. SRT data are…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…
We construct a generalization of the Dolbeault-Grothendieck resolution on a singular complex space. The same construction yields, for each morphism of analytic spaces, a pullback mapping between the respective Dolbeault-Grothendieck…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…
An alternative method to invert the Radon transforms without the use of Courant-Hilbert's identities has been proposed and developed independently from the space dimension. For the universal representation of inverse Radon transform, we…
In this study, we proposed a universal n-th order partial differential equation (PDE) of 2-D Radon transform to disclose the relationship of Radon transform over a neighborhood of the integral line, named as local correlation equation…
Transformer architectures have exhibited remarkable performance in image super-resolution (SR). Since the quadratic computational complexity of the self-attention (SA) in Transformer, existing methods tend to adopt SA in a local region to…
We present a novel microlocal analysis of a non-linear ray transform, $\mathcal{R}$, arising in Compton Scattering Tomography (CST). Due to attenuation effects in CST, the integral weights depend on the reconstruction target, $f$, which has…