Research On The Image Reconstruction Algorithms For Compton Back-scattering Tomography Based On Energy Spectrum

Compton back-scattering tomography(CBST) measures the electron densities of the sample utilizing the back scattered photons. Compared to the traditional transmission tomography technologies, CBST has some outstanding advantages, such as freedom in systems construction, high sensitivity for low-Z materials, and low radiation dose, making it has broad application prospects for non-destruction testing, safety inspection, medical diagnosis, and other fields. The CBST based on the energy spectrum has faster scanning speed and less dependence on mechanical accuracy, compared with the traditional accurate collimation type, and become the research hotspot. However, it is very difficult to obtain high quality reconstruction results for the energy spectrum CBST due to some problems. These problems are listed as follows: firstly, the existence of the X(γ)-ray attenuation causes it is impossible to reconstruct the image using only the energy spectrum; secondly, in the Compton back scatter situation the measured energy spectrum is not sufficient; finally, the CBST reconstruction is an ill-posed problem, of which solutions are quite sensitive to noise. Thus research on how to get high-performance reconstruction images in CBST and improve its practicality is of great significance.Aiming at the above mentioned problems in CBST reconstruction, this paper takes the unique features of reconstruction problem under different energy X-ray energy into consideration, and focuses on the research of the reconstruction algorithms with diagnostic and intermediate-energy X(γ)-ray, respectively, as well as the acceleration of the iterative algorithms. The main achievements are included as follows:1. An iterative reconstruction algorithm is proposed based on the attenuation correction factors(ACFs) and Simultaneous Algebraic Reconstruction Technique(SART) for diagnostic range X(γ)-ray. First, compute the ACFs with the primary electron densities and the pre-scatter attenuation coefficients. Second, correct the measurements of each scatter detector through multiplying by their corresponding ACFs. Then reconstruct the electron densities with the measurements calibrated by the SART algorithm, and the reconstructed results can be used as the new primary electron densities of the next iteration. Finally, repeat the process until the established criteria is met. Experimental results shows that the novel algorithm can reconstruct the electron densities and correct the X(γ)-ray attenuation within a few iterations.2. A novel reconstruction algorithm named TVM-ADM is proposed, based on total variation(TV) minimization regularization and alternating direction method for intermediate-energy X(γ)-ray. First, introduce the TV minimization regularization and reformulating the CBST reconstruction problem as an optimization problem to solving the image’ TV minimization function with nonlinear constraint. Second, decompose its corresponding augmented Lagrangian function into a slack variable sub-problem and an electron density sub-problem, and they have closed form solution. Finally, solve the two sub-problems in turn. Numerical experiments show that both the quality and the efficiency of the proposed method are improved compared to that of the similar method.3. A strategy to solve the memory hungry and time-consuming problem of TVM-ADM is proposed based on Sparse Matrix Vector multiplication(SpMV) and Compute Unified Device Architecture(CUDA). Firstly, by analyzing the sparse characteristics of CBST projection matrixes, the CSR(Compressed Sparse Row) and ELL(ELLPACK) sparse format matrix are used to store the projector and back-projector matrixes respectively to reduce the memory consumption and the Sparse Matrix Vector multiplication(SpMV) was used to accelerate the projector and back projector computing process. Then, this paper computes the TVM-ADM parallel with the CUDA and Graphics Processing Unit(GPU) based on the parallel features of this algorithm. Experimental results show that, the TVM-ADM with acceleration strategy can achieve a 188 times memory compression ratio and 96 times speedup ratio with no precision reduction.