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For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an…
While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…
Computed Tomography (CT) reconstruction is a fundamental component to a wide variety of applications ranging from security, to healthcare. The classical techniques require measuring projections, called sinograms, from a full 180$^\circ$…
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
For cone-beam three-dimensional computed tomography (3D-CT) scanning system, voxel size is an important indicator to guarantee the accuracy of data analysis and feature measurement based on 3D-CT images. Meanwhile, the voxel size changes…
We present a description of our method to process a set of autocollimator-based deflectometer 1-dimensional line-scans taken over a large optical surface and reconstruct them to a best-fit conic-section surface. The challenge with our task…
This paper proposes a RANSAC-based algorithm for determining the axial rotation angle of an object from a pair of its tomographic projections. An equation is derived for calculating the rotation angle using one correct keypoints…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
Computed tomography (CT) has become an essential part of modern science and medicine. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source, a detector captures X-rays…
In the last decade C-arm-based cone-beam CT became a widely used modality for intraoperative imaging. Typically a C-arm scan is performed using a circle-like trajectory around a region of interest. Therefor an angular range of at least…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
In this paper, we address analytically and numerically the inversion of the integral transform (\emph{cone} or \emph{Compton} transform) that maps a function on $\mathbb{R}^3$ to its integrals over conical surfaces. It arises in a variety…
The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object given tomographic projection images from different…
We present a new algorithm for 3D cone-beam tomography. The algorithm is based on decomposition of the cone-beam backprojection operation and angular decimation. It has computational complexity of $O(N^{3.5})$ and allows considerable…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…