相关论文: Reconstruction algorithms for a class of restricte…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
Computed tomography for region-of-interest (ROI) reconstruction has advantages of reducing X-ray radiation dose and using a small detector. However, standard analytic reconstruction methods suffer from severe cupping artifacts, and existing…
Classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms including the hybrid input-output (HIO) method, the…
Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
Limited-angle electron tomography aims to reconstruct 3D shapes from 2D projections of Transmission Electron Microscopy (TEM) within a restricted range and number of tilting angles, but it suffers from the missing-wedge problem that causes…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network…
This paper studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$. The…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
X-ray single particle imaging involves the measurement of a large number of noisy diffraction patterns of isolated objects in random orientations. The missing information about these patterns is then computationally recovered in order to…
Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different…
In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general…
Scene and object reconstruction is an important problem in robotics, in particular in planning collision-free trajectories or in object manipulation. This paper compares two strategies for the reconstruction of nonvisible parts of the…
Symbolic regression aims to recover closed-form expressions from numerical data, but in differentiable symbolic regression the recovered expression depends not only on the grammar but also on the fixed architecture through which variables…
The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…
The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…
We introduce a new versatile method for constructing solution operators (i.e., right-inverses up to a finite rank operator) for a wide class of underdetermined PDEs $P u = f$, which are regularizing of optimal order and, more interestingly,…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
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…