Image Reconstruction In Diffuse Optical Tomography With Sparsity Constraints

具有稀疏性约束的漫射光学层析成像中的图像重建

• 批准号: 0915214
• 负责人: Taufiquar Khan
• 金额: $ 16.23万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915214&HistoricalAwards=false
• 关键词: Image; Reconstruction; Diffuse; Optical; Tomography

In this project, the PI will investigate Sparsity Constrained Regularization (SCR) for solving the Diffuse Optical Tomography (DOT) inverse problem. Two recent algorithms are available for the implementation of SCR in DOT: the Generalized Conditional Gradient Method with Sparsity Constraint (GCGM-SC) and the Generalized Semi-smooth Newton's Method with Sparsity Constraint (GSNM-SC). The efficacy of GCGM-SC has been demonstrated with both theoretical and numerical results for linear and some non-linear problems. GCGM-SC, which has also been derived for linear problems, minimizes a given functional, not necessarily convex, with sparsity constraint with respect to a given basis. In this project, the computational aspect of the DOT inverse problem will be investigated to (i) develop a reconstruction algorithm for DOT using GCGM-SC, (ii) devise a strategy for computing adaptive basis such as finite elements to take full advantage of the sparsity constraint idea, (iii) extend GSNM-SC to nonlinear problems and compare GSNM-SC to Tikhonov regularization, and (iv) perform convergence analysis of the proposed GSNM-SC and GCGM-SC in DOT. The interdisciplinary research project seeks to integrate education and research and foster an international exchange of students. The educational activities in the project will include: (i) international research experience for students, (ii) student exchange between Clemson University and the University of Bremen, Germany, (iii) the incorporation of much of the research activities into teaching activities to help students bridge course materials with research, (iv) exposure of high school students to applied mathematics research, and (v) attraction of underrepresented groups to pursue appliedmathematics.Diffuse Optical Tomography (DOT) is a method for imaging a highly scattering medium using near infrared and visible light. For example, optical tomography of biological tissue has potential applications for the early detection of breast cancer. One major advantage of DOT is that it is less expensive and non-invasive as compared with x-ray mammography. DOT imaging technology also shows great promise as a tool for initiating discoveries in physics, biology, and medicine. However, despite its great potential, it has yet to be commercially or medically successful as the instability in image reconstruction results in the blurring of any resulting image. To overcome these difficulties, we will investigate novel mathematical techniques for image reconstruction. Research applications will vary from cancer detection in biomedical imaging to land mine detection in remote sensing to imaging objects in the ocean. Research results are also expected to contribute to scientific knowledge in neutron transport, transport in atmospheric science, photothermal spectroscopies and microscopies, laser pump probes, diffuse photon density waves and new tomography technologies, such as optical, electronic and thermal imaging, and biomedical diagnostics.

在该项目中，PI 将研究稀疏约束正则化 (SCR)，以解决漫反射光学断层扫描 (DOT) 逆问题。最近有两种算法可用于在 DOT 中实现 SCR：具有稀疏性约束的广义条件梯度法 (GCGM-SC) 和具有稀疏性约束的广义半光滑牛顿法 (GSNM-SC)。 GCGM-SC 的有效性已通过针对线性和一些非线性问题的理论和数值结果得到证明。 GCGM-SC 也是针对线性问题而导出的，它通过相对于给定基的稀疏性约束来最小化给定函数（不一定是凸函数）。在该项目中，将研究 DOT 反问题的计算方面，以 (i) 使用 GCGM-SC 开发 DOT 重建算法，(ii) 设计计算自适应基础（例如有限元）的策略，以充分利用稀疏约束思想，(iii) 将 GSNM-SC 扩展到非线性问题，并将 GSNM-SC 与 Tikhonov 正则化进行比较，以及 (iv) 在 DOT 中对所提出的 GSNM-SC 和 GCGM-SC 进行收敛分析。该跨学科研究项目旨在整合教育和研究，并促进学生的国际交流。该项目的教育活动将包括：（i）为学生提供国际研究经验，（ii）克莱姆森大学和德国不来梅大学之间的学生交流，（iii）将大部分研究活动纳入教学活动以帮助学生将课程材料与研究联系起来，(iv) 让高中生接触应用数学研究，以及 (v) 吸引代表性不足的群体追求应用数学。漫反射光学断层扫描 (DOT) 是一种使用近红外对高散射介质进行成像的方法和可见光。例如，生物组织的光学断层扫描对于乳腺癌的早期检测具有潜在的应用。与 X 射线乳房 X 光检查相比，DOT 的一大优点是成本较低且无创。 DOT 成像技术还显示出作为物理、生物学和医学领域新发现的工具的巨大前景。然而，尽管其潜力巨大，但它尚未在商业或医学上取得成功，因为图像重建的不稳定性会导致任何生成的图像模糊。为了克服这些困难，我们将研究用于图像重建的新颖数学技术。研究应用范围广泛，从生物医学成像中的癌症检测到遥感中的地雷检测再到海洋中的物体成像。研究成果预计还将有助于中子输运、大气科学输运、光热光谱和显微镜、激光泵浦探针、漫射光子密度波和新断层扫描技术（例如光学、电子和热成像以及生物医学诊断）方面的科学知识。