Three-Dimensional Tomographic Image Reconstruction From Limited Angle Projection Data Based On GPU

Computed tomography (CT) is becoming an increasingly important tool in medical diagnosis and treatment as well as in non-destructive testing. This is why its image reconstruction techniques have been intensively addressed and studied. The transform-based image reconstruction techniques are commonly adopted in the CTs for medical purpose. This is because that the sufficient number of projections needed for transform-based data reconstruction can be achieved in the image acquisition procedure. However, in many situations, it is intractable for the imaging devices to collect the complete data required for transform-based reconstructions. For example, the use of cone beam projections often leads to an inadequate number of projections and therefore forms an incomplete dataset for tomographic reconstruction in treatment planning for clinical medication. To overcome this operational difficulty, the iterative algorithm has to be applied for the sake of achieving a desirable image quality even if the computational cost is unrealistically high. But how to balance the image quality and the speed of image reconstruction is becoming an extensive interest that many researchers pursue, which is the main motivation of this presentation. The main focus of this thesis is to study the 3D tomographic image reconstruction algorithm based on limited angle projection data. In particular, we have investigated the so-called TV reconstruction which is an iterative image reconstruction algorithm based on the minimization of the image total variation (TV). The TV reconstruction algorithm was exploited to the benefit of a fast implementation based on GPU (Graphic Process Unit) technology as well as a refinement of its optimization procedure We have extended the TV algorithm from two-dimensional space to the case of solving 3D reconstruction problem based on limited angle projection data. The implementation of the 3D TV algorithm was originally done using C++ in a sense of running the algorithm on the CPU of personal computers. But the algorithmic performance is severely offset by an expensively computational cost. To this end, we proposed an efficient implementation for the 3D TV algorithm by utilizing the parallel computing power of GPU. Numerical simulations were conducted to validate the 3D TV algorithm using a revised 3D Shepp-Logan phantom. The performance of the underlying image reconstruction was evaluated in a comparison to the two other image reconstruction methods: FDK and ART algorithm. Numerical simulation results demonstrated that the 3D TV algorithm was superior to the FDK and ART algorithm whereas the GPU based implementation has significantly speed-up the reconstruction procedure by almost 10 times.We also revisited the optimization procedure of the 2D TV algorithm and implemented a refinement without changing the original optimization objectives. Numerical simulations over a 2D Shepp-Logan phantom have demonstrated that the improved algorithm is indeed able to accelerate the data reconstruction without sacrificing the resulting image quality.The main contribution of this thesis is that we expanded the framework of the TV algorithm from the two dimensional space to the case of solving 3D reconstruction problem incurred by the limited angle projection data. More importantly, by using GPGPU (General Purpose GPU) technology, the implementation of 3D reconstruction was accomplished to be feasible for engineering practice. Besides, a refinement of optimization procedure for the 2D TV algorithm has been implemented in main purpose for speed-up of data reconstruction.