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题名	信号的系数表示与处理技术在关联成像及超分辨中的应用
作者	王慧
学位类别	博士
答辩日期	2013
授予单位	中国科学院上海光学精密机械研究所
导师	韩申生
关键词	稀疏表象 关联成像 超分辨 量子涨落
其他题名	Applications of signal processing in sparse representations in Ghost Imaging and Super-resolution
中文摘要	关联成像，又称鬼成像，是上世纪 90 年代发展起来的一种利用二阶强度关联获取物体信息的成像技术。由于关联成像的特殊成像结构和机理，这种技术在X射线成像，遥感，生物医学成像等方面都有应用前景。然而基于关联算法的传统关联成像需要大量的采样数据，成像效率很低，这就需要我们通过一些先验知识来提高成像速度和成像质量。 物体的稀疏性是信号处理中常用的一类先验知识。在本论文中，我们将重点讨论这种稀疏性先验知识在关联成像中的应用，及其对成像效率和成像质量的影响。目前，关于稀疏表象及信号处理技术的讨论都是基于经典理论分析的。本论文将首次讨论该技术在成像结构中的物理极限问题。论文内容安排如下： 第 1章， 首先从光的量子理论的发展介绍关联成像的早期双光子实现以及量子涨落的背景知识，继而引入目前经典关联成像结构的发展应用和实用限制，并概述了稀疏表象下信号获取与处理技术的发展背景。 第 2章，详细介绍稀疏与冗余表象下信号获取与处理技术。由信号的稀疏表达引入了稀疏与冗余表象以及凸优化问题的概念，继而介绍凸优化问题应用在稀疏信号恢复过程中以及保证信号恢复的条件，为后续章节的算法应用奠定数学理论基础。 第 3章，回顾了传统关联成像的结构和算法，并介绍了本人在博士期间将稀疏表象下信号恢复算法在关联成像中应用的研究。分别以相干关联成像和非相干关联成像两种结构讨论了稀疏信号恢复方法的应用，并给出了模拟和实验结果。 第 4章， 主要介绍了本人在博士期间关于弱光场照明下的稀疏信号恢复问题。首先介绍了电磁场的表象并以几种常用光源为例给出弱光场的模型，在该模型下讨论并模拟了不同光源模型下，在传统双臂关联成像以及单臂 DMD调制关联成像结构中稀疏物体的恢复结果。 第 5章，以经典超分辨的概念为标准，介绍了传统超分辨的方法，并在此基础上介绍了本人在博士期间的一些重要研究结果——物体稀疏性先验知识对超分辨的贡献及其量子极限问题。 第 6章，简单介绍了对本论文研究内容的应用展望。
英文摘要	Ghost Imaging (GI), which was developed from 1980s, is a novel and promising imaging technique based on the classical or quantum correlation of the light field fluctuations. Because of the typical imaging scheme advantages, GI benefits lots of practical applications, such as X-ray diffraction imaging, remote sensing, biomedical imaging and so on. However, the traditional GI calculation, which is based on the correlation of the light field, is of low efficiency and massive measurements are necessary for good visibility. To improve the imaging efficiency and the image quality, it requires priori information about the object or imaging scheme. Sparsity of the objects has been taken as popular a priori information in signal processing. In this thesis, we will introduce the sparsity priori information of the object into the GI scheme to study the improvement of such imaging processing. Till now, all the discussion about sparse representations is based on classical analysis, while in this thesis, we will make the first step to introduce quantum mechanics into this theory and discuss the corresponding quantum limit. The thesis is arranged as follows: In Chapter 1, we will give a short introduction of three important aspects related to this thesis: Quantum theory of the light field—the history of quantum imaging and quantum fluctuations; Ghost imaging—the background of such technique and the existing development; signal processing in sparse and redundant representations—the background of the mathematical algorithms. The relevant theory of signal processing in sparse and redundant representations is presented in Chapter 2. Firstly, we introduce the concept of “Sparse representation”, followed by the optimization problem, which is the mathematical groundwork of the sparse signal processing. Finally, we give the form of optimization problem in sparse signal reconstructions and the conditions that guarantee the successful recovery. All of these will help to understand the optical design and imaging results in the following chapters. In Chapter 3, we give a historical retrospect to the scheme and calculation of the traditional GI system. A brief introduction of the experimental realization of GI is given for the feasibility of taking advantage of the sparse image reconstruction. The application of the sparse signal processing and acquirement is demonstrated in two different GI schemes: incoherent and coherent schemes. The simulated and experimental results are also presented. In view of the practical requirements, the GI of sparse object in weak light field is discussed in Chapter 4. We introduce several presentations of the electromagnetic field, based on which we establish the model of weak light field and simulated the GI results in two imaging schemes: the single arm GI scheme with DMD modulation and the double arms GI scheme. The applications of the sparse signal processing and acquirement in super-resolution is given in Chapter 5. Given the concept of classical diffraction limit and methods of super-resolution, we also introduce the quantum theory of super-resolution for both continuous and discrete objects. When taking into account the sparsity priori information of the object, the super-resolution reconstruction is studied in both classical and quantum theories with simulations. In Chapter 6, we take a brief discussion of the applications of this thesis in three domains: X-ray diffraction imaging, remote sensing and biomedical imaging.
语种	中文
内容类型	学位论文
源URL	[http://ir.siom.ac.cn/handle/181231/15738]
专题	上海光学精密机械研究所_学位论文
推荐引用方式 GB/T 7714	王慧. 信号的系数表示与处理技术在关联成像及超分辨中的应用[D]. 中国科学院上海光学精密机械研究所. 2013.

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