Related papers: Stopping Rules for Algebraic Iterative Reconstruct…
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…
We propose two new algebraic reconstruction techniques based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. Tomography problems exhibit semi-convergence when iterative methods are employed, and the…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
This is a review paper on some of the physics, modeling, and iterative algorithms in proton computed tomography (pCT) image reconstruction. The primary challenge in pCT image reconstruction lies in the degraded spatial resolution resulting…
Computed Tomography is one of the efficient and vital modalities of non-destructive techniques (NDT). Various factors influence the CT reconstruction result, including limited projection data, detector electronics optimization, background…
We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
Performing X-ray computed tomography (CT) examinations with less radiation has recently received increasing interest: in medical imaging this means less (potentially harmful) radiation for the patient; in non-destructive testing of…
Background: Whereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce…
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…
With the availability of more powerful computers, iterative reconstruction algorithms are the subject of an ongoing work in the design of more efficient reconstruction algorithms for X-ray computed tomography. In this work, we show how two…
Dose reduction in computed tomography (CT) is essential for decreasing radiation risk in clinical applications. Iterative reconstruction is one of the most promising ways to compensate for the increased noise due to reduction of photon…
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…
Computed Tomography (CT) reconstruction of objects with cylindrical symmetry can be performed with a single projection. When the measured rays are parallel, and the axis of symmetry is perpendicular to the optical axis, the data can be…
X-Ray based computed tomography (CT) is a well-established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the…
While Computerized Tomography (CT) images can help detect disease such as Covid-19, regular CT machines are large and expensive. Cheaper and more portable machines suffer from errors in geometry acquisition that downgrades CT image quality.…
With the availability of more powerful computing processors, iterative reconstruction algorithms have recently been successfully implemented as an approach to achieving significant dose reduction in X-ray CT. In this report, we describe our…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…