| CT (Computerized tomography) imaging, a technique which combines with Mathematics, Physics, Computer Science, electronic technology, etc, is mainly used for showing the inner structure of an object intuitively and accurately, and it is pervasively used in many areas, such as medical diagnosis, industrial non-destructive detection and material science. In particular, CT imaging becomes one of the indispensable medical imaging techniques in the area of clinical medicine. With the wide application of CT equipment, the X-ray radiation problem is increasingly apparent. Accordingly, more and more researchers pay close attention on how to reconstruct a CT image that meets the demand of clinical application in the case of low X-ray radiation. Therefore, the research of CT image reconstruction through sparse angles projection data that come from low dose CT scanning is significant for academic theory and clinical application.The existing algorithms of CT image reconstruction include two main categories: analytical and iterative algorithms. For complete projection data, using the analytical algorithm can get a high-quality reconstruction image at high speed. In fact, for the sparse projection data, the reconstruction image from analytical algorithm would have many artifacts and affect the observation of normal structure of the scanned object. However, using the iterative algorithm, we can get a higher quality CT reconstruction image. In other words, the iterative algorithm fits better for sparse projection data to reconstruct a CT image. Furthermore, the Compressed Sensing theory indicates that we can reconstruct an accurate initial signal form the sampling data that is far lower than the Nyquist smpling frequency. The iterative algorithm and Compressed Sensing theory provide theoretical basis for the CT image reconstruction under sparse projection data. The topic proposes a CT iterative image reconstruction algorithm based on the frame of Compressed Sensing and aims at sparse projection data, which is called RR-L1 (Rough Reconstruction with L1-norm optimization) algorithm. The CT image reconstruction from sparse projection data, which is equal to the problem of solving the ill-posed linear equations. The RR-L1 algorithm converts the problem into the optimization of the object function with constraints, and finds the solution by the iterative image reconstruction algorithm. Because of the Total Variation (TV) objective function in RR-L1, the TV-induced smoothing reduces the spatial resolution and contrast of CT image, leading negtive effect in practical application. Our topic improve the objective function and use intelligent optimization methods like the Simulated Annealing algorithm to accomplish the step of optimization calculation.In addition, the dual energy CT uses two kinds of different energy X-ray to scan the tested object, and it can reconstruct the material effective atomic number and the electron density distribution of the object to distinguish each material effectively. The problem of X-ray radiation also exists in dual energy CT. To our best knowledge, there is little research on how to reduce the X-ray radiation in dual energy CT effectively to obtain a high quality reconstruction CT image. Therefore, the topic, combined with RR-L1 algorithm, proposes two kinds of technical ideas that are easy to implement and have a clear physical meaning. And we do many experiments so as to verify the effectiveness of the two ideas.For the image reconstruction problem of sparse angles projection data in regular CT and dual energy CT, many experiments are made using simulative and real data. Experiment results show that the RR-L1 algorithm can reconstruct high quality CT images through sparse angles projection data. Our work provides a helpful solution and technical idea on how to reduce X-ray radiation effectively for regular CT and dual energy CT. |
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