Related papers: Generalized SART Methods for Tomographic Imaging
In this paper, we consider the standard forms of two kinds of Kaczmarz-Tanabe type methods, one is derived from the Kaczmarz method and the other is derived from the symmetric Kaczmarz method. As a famous image reconstruction method in…
The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often observe and appreciate its fast convergence in the first few…
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…
Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…
Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step…
Computed tomography (CT) provides high spatial resolution visualization of 3D structures for scientific and clinical applications. Traditional analytical/iterative CT reconstruction algorithms require hundreds of angular data samplings, a…
Modern tomography involves gathering projection data from multiple directions and feeding them into a software algorithm for tomographic reconstruction. We focus our study on image reconstruction from Radon data in the setting of…
The randomized Kaczmarz algorithm is one of the most popular approaches for solving large-scale linear systems due to its simplicity and efficiency. In this paper, we propose two classes of global randomized Kaczmarz methods for solving…
Classical total variation (TV) based iterative reconstruction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
The Kaczmarz algorithm is one of the most popular methods for solving large-scale over-determined linear systems due to its simplicity and computational efficiency. This method can be viewed as a special instance of a more general class of…
Medical imaging modalities have revolutionized health-care approaches by offering a better understanding of the human anatomy. Discovery of x-rays allowed the exploiting of the micro-scaled information of human anatomy. Computed tomography…
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a…
As Computed Tomography (CT) scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to…
The MARS scanner is designed for the x-ray spectroscopic study of samples with the aid of computer tomography methods. Computer tomography allows the reconstruction of slices of an investigated sample using a set of shadow projections…
Tomography has made a revolutionary impact on diverse fields, ranging from macro-/mesoscopic scale studies in biology, radiology, plasma physics to the characterization of 3D atomic structure in material science. The fundamental of…
Purpose: We analyze a recently proposed polyenergetic version of the simultaneous algebraic reconstruction technique (SART). This algorithm, denoted pSART, replaces the monoenergetic forward projection operation used by SART with a…
In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…
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…
Terahertz (THz) tomography is a rather novel technique for nondestructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from…