Efficient Algebraic Image Reconstruction Technique for Computed Tomography

Abstract

Industrial computed tomography (CT) has seen widespread adoption within certain areas of non-destructive testing (NDT), with many commercial systems capable of acquisition and reconstruction of cone-beam CT data. The majority of these systems utilise reconstruction algorithms based on the traditional filtered back-projection (FBP) methods, which are imperfect with respect to limited-angle cone-beam data. These techniques are also inherently restricted in the source trajectories that can be utilised due to the use of Fourier slice theorem. This restricts FBP-based techniques to a circular or helical trajectory. Iterative reconstruction algorithms provide a solution to these limitations as the volume reconstruction does not depend on the location or orientation of the source and detector, allowing the possibility of scanning trajectories that satisfy well-known CT data-sufficiency conditions. This paper proposes a method of reconstruction based on computationally efficient computer graphics algorithms with data collected from points in 3D space not restricted to a single circular trajectory, which is useful within NDT for automated robotic inspection. The algorithms developed allow for rapid processing of the algebraic reconstruction technique (ART) for use with X-ray transmission data for CT reconstruction. Experimental results are presented for reconstructions for circular trajectory and points on a sphere to demonstrate the suitability for NDT applications.

Hybrid regularization method for LRT image reconstruction under incomplete projections

“…Then, image reconstruction algorithms can be used on the collected echo wave to obtain a high-resolution contour image of the target [9]. Inverse Radon transform [10], filtered back projection (FBP) [11][12] and algebraic reconstruction technique (ART) [13][14][15] are common reconstruction algorithms in LRT. However, in actual detection, the collected echo data of LRT is usually missing or incomplete in angle owing to the complex and difficult detection conditions [16][17], which greatly reduces the effect of these traditional projection methods.…”

Hybrid regularization method for LRT image reconstruction under incomplete projections

“…Nevertheless, from the viewpoint of mathematics and based on the algebraic reconstruction technique (ART) theory [18][19][20], the image reconstruction problem under the limited angle in LRT is equivalent to solving an underdetermined system of algebraic equations, which belongs to the domain of ill-posed problems [21][22]. Regularization methods [23][24][25][26][27][28][29][30][31][32][33][34] are great ways to deal with the ill-posed inverse problem of LRT, which are mainly divided into two categories: the projection method and the penalty method [23].…”

Volume integral model for algebraic image reconstruction and computed tomography

“…While iterative techniques offer accurate solutions to the image reconstruction problem without geometric transformations and approximations, they come at greater computational cost. Recent technological advancements have allowed for general-purpose computing on graphics processing units (GPUs) [5,6] , enabling high levels of parallelisation to occur during code execution, utilising a brute-force approach to achieve computational speed.…”