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Transmission and scattering tomography inversion algorithm

Author: XuMaoLin
Tutor: WangYuanMei
School: Zhejiang University
Course: Biomedical Engineering
Keywords: Computed tomography Filtered back projection algorithm New Filter Partial reconstruction Symmetric block iterative algorithm Compton backscatter imaging Multi-objective optimization reconstruction Neural Networks Laplace equation boundary value problem
CLC: R310
Type: PhD thesis
Year: 2004
Downloads: 242
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Abstract


Computed tomography (CT) is not only a milestone in the field of diagnostic radiology medical, but also an important research tool in the field of modern industrial non-destructive testing and exploration. Filtered back projection and Algebraic Reconstruction Technique is the most common CT algorithm, based on in-depth analysis of these two algorithms, proposed improvements on the key, making the speed and accuracy of the algorithm has improved. Filtered back projection algorithm key filter function, this paper proposes a novel filtering function, the main part of the operator for the functional analysis of polished. As a filter function, it has many excellent properties, the analysis of the time-frequency characteristics given for CT reconstruction error estimates. Not compactly supported, but can be rapidly decay, it is this feature of the new filtering function makes it especially beneficial for the local reconstruction, and this method and Quasidifferential the operator noticed the Fourier transform of the compactly supported function and wavelet method is different. This paper describes the principle of a partial reconstruction of the CT image with new filtering function and this reconstruction is given secondary error estimates. The new filtering function for the global as well as local reconstruction experimental simulation and test data, and results show that the new filtering function in image spatial resolution better able to overcome the Gibbs effect. Local reconstruction method is also simple and efficient, if the partial reconstruction of the area is about one-tenth of the global zone, the reconstruction time is about global reconstruction tenth time, and the image quality of global reconstruction image quality. Algebraic reconstruction method of calculation of a large amount of storage space is well-known, is that one of the root causes of non-zero coefficients calculated projection matrix. In this regard, we find a geometric symmetry of nature, you can simplify the calculation of the non-zero coefficients of the projection matrix. This symmetry has nothing to do with the distribution of the reconstructed image function, it is applied to the reconstruction problem. Combined with the the Classic ART and SIRT algorithm and the use of symmetry, symmetrical block image reconstruction fast iterative algorithm. Reconstitution experiments on the computer simulation and experimental data for comparison with other algorithms, error indicators to analyze. The results show that, the symmetric block iterative algorithm compared to the conventional iterative algorithm not only rebuild speed and high accuracy of the reconstructed images. Relative to CT imaging technology, Compton scattering imaging technique has a high sensitivity, the degree of freedom in the arrangement of the experimental apparatus, three-dimensional imaging, etc. directly; However, it is facing as a result of incident light and scattered light attenuation problem the nonlinear nature \Focus here on the previous problem. People usually transmission and scattering imaging study, the imaging system-based model into a unified mathematical framework, analyzed and compared. And starting from the physical processes of Compton scattering, Zhejiang University Doctoral Dissertation Norton backscatter imaging resolution reconstruction formula rederived the detector response function has a clear physical meaning, easy-depth understanding of the problem and further research . Elaborate scattered energy spectrum the line scan Compton backscatter imaging principle, the imaging equation boils down to a large non-linear equations, and then use a neural network based on multi-objective optimization to find the solution of the reconstruction problem. By the digital-to-analog under different experimental conditions, the results show that: scattering imaging technique suitable for light material reconstruction; multi-criteria neural network algorithm is feasible and suitable for dealing with such ill-posed reconstruction problem. As a side study, using filtered back projection algorithm gives expression the LaPlace equation general boundary value problem solution provides a fast algorithm for solving potential function.

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