相关论文: Approximation and Reconstruction from Attenuated R…
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…
Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis.…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on…
This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
We give new formulas for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} v$ given within the ball $B_r$. For the one-dimensional case, these formulas are based on the theory…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
We consider weighted ray-transforms $P\_W$ (weighted Radon transforms along straight lines) in $\mathbb{R}^d, \, d\geq 2,$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space…
We characterize Radon measures $\mu$ in $\mathbb{R}^{n}$ that are $d$-rectifiable in the sense that their supports are covered up to $\mu$-measure zero by countably many $d$-dimensional Lipschitz graphs and $\mu \ll \mathcal{H}^{d}$. The…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…
A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form,…
The conical Radon transform is an integral transform that maps a given function $f$ to its integral over a conical surface. In this study, we invesgate the conical Radon transform with a fixed central axis and opening angle, considering 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…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
The problem of reconstruction a function from spherical means is at the heart of several modern imaging modalities and other applications. In this paper we derive universal back-projection type reconstruction formulas for recovering a…
High density implants such as metals often lead to serious artifacts in the reconstructed CT images which hampers the accuracy of image based diagnosis and treatment planning. In this paper, we propose a novel wavelet frame based CT image…
Ptychographic reconstructions in reflection geometries are commonly interpreted with the same two-dimensional thin-sample model used in transmission, yet the validity of this approximation has not been established. We develop a…
We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabilized active subspace. We prove that this recursion can be…