CAREER: Super-Resolution and Subwavelength Imaging

职业：超分辨率和亚波长成像

• 批准号: 1255203
• 负责人: Laurent Demanet
• 金额: $ 48万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-15 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1255203&HistoricalAwards=false
• 关键词: CAREER; Super; Resolution; Subwavelength; Imaging

Demanet1255203 The investigator aims to put the super-resolution phenomenon of signal estimation on a quantitative footing, and to explore the consequences of reliable super-resolution in tomographic imaging. The estimation of a signal from the knowledge of its Fourier transform in a band qualifies as super-resolved when the fine structure of the signal is recovered on a length scale smaller than the inverse of the band's width --- the so-called Shannon-Nyquist scaling. It is a poorly understood, yet real and decidedly nonlinear numerical phenomenon. Sparsity has been suggested as a principle according to which super-resolution reliably occurs. However, recent insights from analysis of convex programs indicate that a second principle, sign compatibility, is needed in tandem with sparsity to unlock positive results. Building on this, the investigator seeks quantitative guarantees of a new kind for successful signal recovery up to the ideal resolution level that no method can beat. Such results would generalize the theory of compressed sensing in the regime of very coherent dictionaries, where no restricted isometry-type property can be expected to hold. The investigator also studies algorithms based on translation-invariance such as the matrix pencil method, modified matching pursuits, precorrective filtering, and generalizations to higher dimensions. He explores implications, both positive and negative, for tomographic imaging modalities such as seismic and synthetic aperture radar in the subwavelength regime. The project aims to design advanced, nonlinear processing methods to deliver higher image resolution and interpretation levels in situations where the data come with poor frequency content, such as in the case of a blurring. A methodical understanding of the possibilities offered by super-resolution could eventually transform the methods by which information is extracted from data in a host of inverse problems, ranging from medical imaging (MRI, fluorescence microscopy) to geophysical imaging (exploration seismology) and defense applications. The project also offers an opportunity for students to acquire strong interdisciplinary training at the intersection of computational mathematics, modern data processing, and tomographic imaging. Graduate curricula typically fall short of covering this evolving material in a satisfactory way, even though there is a great demand in industry for quantitative-minded specialists who can operate as experts on all these fronts. The investigator is involved in several initiatives to introduce this new research area widely, through the organization of graduate summer schools, the administration of an internship program geared toward minorities, and remote teaching via MIT's online educational platforms OCW and EdX.

联系人：1255203 研究者的目的是把信号估计的超分辨率现象的定量基础上，并探讨可靠的超分辨率在断层成像的后果。 当信号的精细结构在小于频带宽度的倒数的长度尺度上恢复时，从频带中的傅里叶变换的知识中对信号的估计有资格作为超分辨--所谓的香农-奈奎斯特缩放。 这是一个很难理解的，但真实的和决定性的非线性数值现象。 稀疏性已被建议作为超分辨率可靠发生的原则。 然而，最近的凸规划分析的见解表明，第二个原则，符号兼容性，需要与稀疏解锁积极的结果。 在此基础上，研究人员寻求一种新的定量保证，以成功的信号恢复到理想的分辨率水平，没有任何方法可以击败。 这样的结果将在非常连贯的字典的制度中推广压缩感知理论，其中没有限制的等距型属性可以被期望保持。 调查员还研究算法的基础上，如矩阵束的方法，修改匹配的追求，precorrective过滤，并推广到更高的维度。 他探讨了影响，积极和消极的，断层成像方式，如地震和合成孔径雷达在亚波长制度。 该项目旨在设计先进的非线性处理方法，以便在数据频率含量较差的情况下（例如模糊情况下）提供更高的图像分辨率和解释水平。 对超分辨率所提供的可能性的系统理解最终可以改变从大量逆问题中从数据中提取信息的方法，从医学成像（MRI，荧光显微镜）到地球物理成像（勘探地震学）和国防应用。 该项目还为学生提供了一个机会，在计算数学，现代数据处理和断层成像的交叉点获得强大的跨学科培训。 研究生课程通常不能以令人满意的方式涵盖这种不断发展的材料，尽管工业界对能够在所有这些方面作为专家运作的定量思维专家有很大的需求。 调查员参与了几项举措，通过组织研究生暑期学校，管理面向少数民族的实习计划，以及通过麻省理工学院的在线教育平台OCW和EdX进行远程教学，广泛介绍这一新的研究领域。