Related papers: Using the Notion of Copula in Tomography
This paper establishes $L^p$-improving estimates for a variety of Radon-like transforms which integrate functions over submanifolds of intermediate dimension. In each case, the results rely on a unique notion of curvature which relates to,…
In this paper, we deal with the problem of reconstruction from Radon random samples in local shift-invariant signal space. Different from sampling after Radon transform, we consider sampling before Radon transform, where the sample set is…
Here we present a novel microlocal analysis of a new toric section transform which describes a two dimensional image reconstruction problem in Compton scattering tomography and airport baggage screening. By an analysis of two separate…
Recent technical advances in collecting spatial data have been increasing the demand for methods to analyze large spatial datasets. The statistical analysis for these types of datasets can provide useful knowledge in various fields.…
The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for…
Change detection (CD) in heterogeneous remote sensing images has been widely used for disaster monitoring and land-use management. In the past decade, the heterogeneous CD problem has significantly benefited from the development of deep…
Computed Tomography (CT) using synchrotron radiation is a powerful technique that, compared to lab-CT techniques, boosts high spatial and temporal resolution while also providing access to a range of contrast-formation mechanisms. The…
For conventional computed tomography (CT) image reconstruction tasks, the most popular method is the so-called filtered-back-projection (FBP) algorithm. In it, the acquired Radon projections are usually filtered first by a ramp kernel…
We introduce single-shot X-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number…
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…
X-ray tomographic image reconstruction consists of determining an object function from its projections. In many applications such as non-destructive testing, we look for a fault region (air) in a homogeneous, known background (metal). The…
Objective: There exist several X-ray computed tomography (CT) scanning strategies to reduce a radiation dose, such as (1) sparse-view CT, (2) low-dose CT, and (3) region-of-interest (ROI) CT (called interior tomography). To further reduce…
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…
Local reconstruction analysis (LRA) is a powerful and flexible technique to study images reconstructed from discrete generalized Radon transform (GRT) data, $g=\mathcal R f$. The main idea of LRA is to obtain a simple formula to accurately…
We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems,…
When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…
Cosmography is a phenomenological and relatively model-independent approach to cosmology, where physical quantities are expanded as a Taylor series in the cosmological redshift, or in related variables. Here we apply this methodology to…
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for…
In clinical CT, the x-ray source emits polychromatic x-rays, which are detected in the current-integrating mode. This physical process is accurately described by an energy-dependent non-linear integral model on the basis of the Beer-Lambert…