Fast parallel implementation for total variation constrained algebraic reconstruction technique

Abstract

In computed tomography (CT), the total variation (TV) constrained algebraic reconstruction technique (ART) can obtain better reconstruction quality when the projection data are sparse and noisy. However, the ART-TV algorithm remains time-consuming since it requires large numbers of iterations, especially for the reconstruction of high-resolution images. In this work, we propose a fast algorithm to calculate the system matrix for line intersection model and apply this algorithm to perform the forward-projection and back-projection operations of the ART. Then, we utilize the parallel computing techniques of multithreading and graphics processing units (GPU) to accelerate the ART iteration and the TV minimization, respectively. Numerical experiments show that our proposed parallel implementation approach is very efficient and accurate. For the reconstruction of a 2048 × 2048 image from 180 projection views of 2048 detector bins, it takes about 2.2 seconds to perform one iteration of the ART-TV algorithm using our proposed approach on a ten-core platform. Experimental results demonstrate that our new approach achieves a speedup of 23 times over the conventional single-threaded CPU implementation that using the Siddon algorithm.

Application of a curve reconstruction-based seismic identification method for flooded layers in the x-block

“…To ensure the fitting effect, the least squares method is selected to determine the reconstruction parameters, which is the optimal solution to solve the equation when the number of equations in mathematics is more than the number of unknowns and the error in the equation is guaranteed to be minimal, as shown in equation (1). The method is used in the paper to find the optimal parameters in two sets of data points, natural gamma and deep lateral resistivity, and the sum of squared errors of each set of data is used as the criterion for judging the merit of the fitted parameters [5] { 𝑦 Firstly, the error e=K * (xi)-yi, (i=1, 2,..., n) is demanded, then the error sum of squares is ‖e 2 ‖, and in the operation, ‖e 2 ‖ is considered as a weighted sum of squares, i.e.…”

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].…”