Related papers: Translation invariant diagonal frame decomposition…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the…
We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We…
We address the estimation of seismic wavefields by means of Multidimensional Deconvolution (MDD) for various redatuming applications. While offering more accuracy than conventional correlation-based redatuming methods, MDD faces challenges…
Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions,…
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
Low-dose computed tomography (LDCT) reduces radiation exposure but suffers from image artifacts and loss of detail due to quantum and electronic noise, potentially impacting diagnostic accuracy. Transformer combined with diffusion models…
The paper deals with totally geodesic Radon transforms on constant curvature spaces. We study applicability of the historically the first Funk-Radon-Helgason method of mean value operators to reconstruction of continuous and $L^p$ functions…
Although sparse-view computed tomography (CT) has significantly reduced radiation dose, it also introduces severe artifacts which degrade the image quality. In recent years, deep learning-based methods for inverse problems have made…
This work aims to tackle the all-in-one image restoration task, which seeks to handle multiple types of degradation with a single model. The primary challenge is to extract degradation representations from the input degraded images and use…
Light field (LF) cameras can record scenes from multiple perspectives, and thus introduce beneficial angular information for image super-resolution (SR). However, it is challenging to incorporate angular information due to disparities among…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation…