Backward projection is one of the most time-consuming steps in method-based iterative reconstruction computed tomography. The 3D back-projection memory access pattern is potentially enough regular to exploit efficiently the computation power of acceleration boards based on GPU or FPGA. This paper proposes an OpenCL acceleration of the voxel-driven 3D back-projection algorithm on an Arria 10 FPGA. This design flow is based initially on an offline memory access analysis, then iteratively on a performance analysis of each new implementation represented on a Berkeley Roofline model.By taking advantage of the FPGAs local memory architecture, we have succeeded to design an efficient pipeline reaching maximum bandwidth with stall-free access underlining this platform’s interest for memory optimization. Our design flow allowed for a significant improvement of our initial algorithm’s computational intensity, resulting in better performance on FPGA. It reaches comparable performance to an embedded GPU implementation and other computed tomography algorithms on FPGAs.

Model-Based Iterative Reconstruction (MBIR) algorithms iteratively use expensive computational operators of forward and backward projections. The irregular memory access pattern of these operators makes them a memory-bound application. Their computation time must be reduced to meet clinical routine constraints. This paper proposes a hardware accelerator architecture based on Field Programmable Gate Arrays (FPGAs) through high-level language, as an alternative to GPU architecture. This acceleration is based on an offline memory access analysis to address the main bottleneck of the algorithm and maximize the data reuse rate. The offline analysis allows for the tuning of the architecture parameters so that they converge to an optimal solution. Then, the Berkeley Roofline model guides our optimization steps by iteratively analyzing the design performance. Our design flow significantly improved the algorithm's computational intensity and overcame the memory bottleneck. Thus, our architecture takes advantage of the FPGA local memory to achieve significant memory bandwidth and efficiently harness the pipeline without stalling the computation. Furthermore, we present the scaling-up strategy from mid-range FPGA to high-end FPGA and any concerns of portability. We used two Intel FPGA devices to implement the algorithm, and then we compared the results with our GPU implementation in terms of speedup and energy efficiency. Our experimental results show that our design has achieved better computational throughput than the works on FPGA architectures reported in the literature.

In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution ( $\mathcal{S}{t}_g$ ), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles.

In order to enhance image quality for controlling the interior of a volume in industry, model-based iterative reconstruction (MBIR) methods in 3D X-ray Computed Tomography (CT) have shown their efficiency compared to analytical reconstruction methods. MBIR methods enforce a prior model on the volume to reconstruct and make fusion of the information contained in the prior model and the projection data. The projections have many uncertainties which have very different origins in 3D CT. They are taken into account in MBIR methods but, despite of their different origins, they are in general gathered in only one term in the forward model. In this paper, we propose to derive a new forward model by adding a further error term in the Poisson statistics of photon-count, corresponding to the deviation of the monochromatic model with respect to the actual polychromacy of the rays. A Taylor expansion of the Poisson log-likelihood leads us to a new algebraic forward model accounting for two terms of uncertainties : we call it the error- splitting forward model. Different prior models are assigned to each of distinguished uncertainties : measurement uncertainties are modeled as Gaussian, while linear model uncertainties are modeled as heavy-tailed to bring robustness to the reconstruction process. We give strategies to fix the parameters of the error-splitting forward model. Next, we use it in a full MBIR method with Gauss-Markov-Potts prior model on the volume, in order to reconstruct piecewise-constant objects for non-destructive testing in industry. Compared to the conventional forward model, we show in our experiments that the use of the error-splitting forward model with Gauss-Markov-Potts prior combines better robustness and accuracy.