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# The Method of Solving Mathematical Model of the Image Restoration about X-ray Diffraction Association Imaging

Author: YangLing
Tutor: GuoHua
School: Jilin University
Course: Applied Mathematics
Keywords: X-ray diffraction association imaging signal recovery compressive sampling spar-sity gradient projection
CLC: TP391.41
Type: Master's thesis
Year: 2011
Downloads: 32
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### Abstract

 With the development of information science, people continue to turn inside informa-tion of opaque objects that the human eye can not directly see or the information of small objects into the image information that people can intuitive with scientific method. X-ray be-cause of its strong penetration, three-dimensional imaging capabilities and a rich source of imaging contrast is becoming an important method to achieve scientific imaging. Therefore X-ray imaging and image restoration are hot topics in the field of optical information, they have important applications in medicine, biology, environmental science, materials science and industrial non-destructive testing and other fields.Compression sampling theory plays an important role in image restoration. It can ef-fectively handle large amounts of data, reduce sampling rate in the process that bandwidth analog signal digital, make it possible to restore the image and signal, and sometimes can effectively restore the image and signal using small samples.Gradient projection method can effectively solve compression sampling model of the image restoration model, mainly BB gradient projection method, which recover the signal by using minimum lI norm to solve a convex programming problem, then transformed this problem into the bound-constrained quadratic programming.Based on the study of mathematics model of X-ray diffraction association imaging,this paper gave mathematical model of image restoration, proposed the way in which using com-pression sampling theory and BB gradient projection method to solve this restoration math-ematical model, established compression sampling model of the image restoration about X ray diffraction association imaging. and used BB gradient projection method to solve com-pression sampling model. The results show that this method is feasible and effective. This paper includes the following aspects:1. It introduced prepare knowledge of the image restoration about the X-ray diffraction associated imaging. This paper introduced the compression sampling theory,the gradient projection method,the important role in field of image restoration and compressed sampling history and status quo.2. It established and solved the mathematical model of the image restoration about X-ray diffraction association imaging.Based on the mathematical model of X-ray diffraction association imaging,this paper put forward that the mathematical model of image restora-tion was an integral equations, discretized this integral equation by using numerical integral method, established its compression sampling model by using the compression sampling theory,and finally solved the compression sampling model with BB gradient projection.3. Theoretical calculation example. This paper cited the example of the methods of solving mathematical model of the image restoration about X-ray diffraction association imaging. The results show that gradient projection method benefited from a good starting point, and needed appropriate factor t, the number of iterations depended on the closeness of the solution. The calculation results show that this method with high precision and high efficiency, is a good method of solving compression sampling model.

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