Li Lei

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography (LCT) is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation (TV) minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method (ADM) to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

Fast parallel algorithm for three-dimensional distance-driven model in iterative computed tomography reconstruction

The projection matrix model is used to describe the physical relationship between reconstructed object and projection. Such a model has a strong influence on projection and backprojection, two vital operations in iterative computed tomographic reconstruction. The distance-driven model (DDM) is a state-of-the-art technology that simulates forward and back projections. This model has a low computational complexity and a relatively high spatial resolution; however, it includes only a few methods in a parallel operation with a matched model scheme. This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations. Our proposed model has been implemented on a GPU (graphic processing unit) platform and has achieved satisfactory computational efficiency with no approximation. The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop, respectively, with an image size of 256×256×256 and 360 projections with a size of 512×512. We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation. The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.

Fast local reconstruction by selective backprojection for low dose in dental computed tomography

The high radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer, which becomes a major clinical concern. The backprojection-filtration (BPF) algorithm could reduce the radiation dose by reconstructing the images from truncated data in a short scan. In a dental CT, it could reduce the radiation dose for the teeth by using the projection acquired in a short scan, and could avoid irradiation to the other part by using truncated projection. However, the limit of integration for backprojection varies per PI-line, resulting in low calculation efficiency and poor parallel performance. Recently, a tent BPF has been proposed to improve the calculation efficiency by rearranging the projection. However, the memory-consuming data rebinning process is included. Accordingly, the selective BPF (S-BPF) algorithm is proposed in this paper. In this algorithm, the derivative of the projection is backprojected to the points whose x coordinate is less than that of the source focal spot to obtain the differentiated backprojection. The finite Hilbert inverse is then applied to each PI-line segment. S-BPF avoids the influence of the variable limit of integration by selective backprojection without additional time cost or memory cost. The simulation experiment and the real experiment demonstrated the higher reconstruction efficiency of S-BPF.

Cone-beam local reconstruction based on a Radon inversion transformation

The local reconstruction from truncated projection data is one area of interest in image reconstruction for computed tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-backprojection (FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional (3D) local reconstruction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data truncation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography (ATRACT), not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.

Matrix approach for processing of iterative reconstruction on cone beam CT

Cone-beam computed tomography (CBCT) is an important technique providing new insights into the inner structure of products in industry and medicine physics. Iterative reconstruction methods have been shown to be more robust than analytical algorithm against the noise and limited angles conditions present in CT. Nevertheless, these methods are not extensively used due to their computational demands. In the iteration algorithm, the matrix of projection is massive and it is very time-consuming to calculate the forward projections and back-projections. In this work, we design a matrix approach that the coefficients of the projection matrix are pre-calculated and simultaneously stored with two compressing formats due to the different sparse structures of the matrix and its transposed matrix. And we implement the corresponding SpMV (sparse matrix-vector multiplication) based on the compressing matrices with GPU platform to realize the acceleration. Experimental results indicate that this method allows efficient implementations of reconstruction in CBCT and it can have a better performance than those with serial computing on CPU.

Multiple helical scans and the reconstruction of over FOV-sized objects in cone-beam CT

In cone-beam computed tomography (CBCT), there are often cases where the size of the specimen is larger than the field of view (FOV) (referred to as over FOV-sized (OFS)). To acquire the complete projection data for OFS objects, some scan modes have been developed for long objects and short but over-wide objects. However, these modes still cannot meet the requirements for both longitudinally long and transversely wide objects. In this paper, we propose a multiple helical scan mode and a corresponding reconstruction algorithm for both longitudinally long and transversely wide objects. The simulation results show that our model can deal with the problem and that the results are acceptable, while the OFS object is twice as long compared with the FOV in the same latitude.

A modified interval subdividing based geometric calibration method for interior tomography

The interior tomography is commonly met in practice, whereas the self-calibration method for geometric parameters remains far from explored. To determine the geometry of interior tomography, a modified interval subdividing based method, which was originally developed by Tan et al.,[11] was presented in this paper. For the self-calibration method, it is necessary to obtain the reconstructed image with only geometric artifacts. Therefore, truncation artifacts reduction is a key problem for the self-calibration method of an interior tomography. In the method, an interior reconstruction algorithm instead of the Feldkamp?Davis?Kress (FDK) algorithm was employed for truncation artifact reduction. Moreover, the concept of a minimum interval was defined as the stop criterion of subdividing to ensure the geometric parameters are determined nicely. The results of numerical simulation demonstrated that our method could provide a solution to the self-calibration for interior tomography while the original interval subdividing based method could not. Furthermore, real data experiment results showed that our method could significantly suppress geometric artifacts and obtain high quality images for interior tomography with less imaging cost and faster speed compared with the traditional geometric calibration method with a dedicated calibration phantom.

A Compton scattering image reconstruction algorithm based on total variation minimization

Compton scattering imaging is a novel radiation imaging method using scattered photons. Its main characteristics are detectors that do not have to be on the opposite side of the source, so avoiding the rotation process. The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations, which is ill-posed. This means the solution exhibits instability and sensitivity to noise or erroneous measurements. Using the theory for reconstruction of sparse images, a reconstruction algorithm based on total variation minimization is proposed. The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint. The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality, especially when there are not enough measurements.