Graph-Based Regularization Techniques and Their Applications

基于图的正则化技术及其应用

基本信息

  • 批准号:
    1818374
  • 负责人:
  • 金额:
    $ 18.6万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2018
  • 资助国家:
    美国
  • 起止时间:
    2018-07-01 至 2019-08-31
  • 项目状态:
    已结题

项目摘要

The rapid development of science and technology ushers in a new era of big data that requires developing specialized algorithms to process a large amount of data. Signal processing and other related techniques aim to recover signals of interest or some of their properties; this goal can be reduced to an optimization question. Due to physical limitations of hardware, the size of the acquired data is in general much smaller than that of the underlying signal, resulting in an ill-posed problem for signal recovery with infinitely many solutions. Regularization techniques have been developed to address this inherent ill-posedness. Despite being widely applied in low-dimensional signal processing, regularization has seen limited use in processing high-dimensional data sets, especially those best represented by graphs, that is, networks with sophisticated connections. This project aims to further develop graph-based regularization techniques, with potential to revolutionize imaging and data analysis technologies in many areas of data science.This project aims to develop a useful graph-based regularization framework for various signal processing problems, to address major theoretical and computational challenges for its applications, to provide new interpretations of low-dimensional regularization techniques, and to demonstrate its capability for handling large-scale data sets. The research has three objectives: (1) Develop novel graph-based regularization techniques along with rigorous theoretical guarantees to handle the more challenging signal processing problems and related inverse problems; (2) Develop efficient numerical algorithms to solve the corresponding optimization problems; and (3) Conduct numerical experiments in imaging applications to demonstrate the advantages of the proposed approaches in terms of accuracy and efficiency. The research aims to improve data processing techniques and to infuse new insights into mathematical signal and image processing, with a variety of applications such as medical imaging and remote sensing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
科学技术的快速发展开启了大数据的新时代,需要开发专门的算法来处理海量数据。信号处理和其他相关技术旨在恢复感兴趣的信号或其某些特性;这一目标可以归结为优化问题。由于硬件的物理限制,采集的数据通常比底层信号的大小要小得多,这导致了一个具有无限多个解的信号恢复的不适定问题。正则化技术已经被开发出来,以解决这种固有的不适定性。尽管正则化在低维信号处理中得到了广泛的应用,但它在处理高维数据集方面的应用有限,特别是那些由图最好地表示的数据集,即具有复杂连接的网络。该项目旨在进一步开发基于图形的正则化技术,具有在数据科学的许多领域中革新成像和数据分析技术的潜力。该项目旨在为各种信号处理问题开发一个有用的基于图形的正则化框架,解决其应用中的主要理论和计算挑战,对低维正则化技术提供新的解释,并展示其处理大规模数据集的能力。这项研究有三个目标:(1)开发新的基于图的正则化技术,并提供严格的理论保证来处理更具挑战性的信号处理问题和相关的逆问题;(2)开发有效的数值算法来解决相应的优化问题;(3)在成像应用中进行数值实验,以验证所提出的方法在精度和效率方面的优势。这项研究旨在改进数据处理技术,为数学信号和图像处理注入新的见解,并应用于医学成像和遥感。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Current Design with Minimum Error in Transcranial Direct Current Stimulation
经颅直流电刺激误差最小的电流设计
  • DOI:
    10.1007/978-3-030-05587-5_6
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Qin, J.;Wang, Y.;Liu, W.
  • 通讯作者:
    Liu, W.
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Jing Qin其他文献

Synthetic, Non-Natural Analogs of Ceramide Elevate Cellular Ceramide, Inducing Apoptotic Death to Prostate Cancer Cells and Eradicating Tumors in Mice
神经酰胺的合成非天然类似物可提升细胞神经酰胺水平,诱导前列腺癌细胞凋亡并根除小鼠肿瘤
  • DOI:
    10.3109/07357900903478915
  • 发表时间:
    2010
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Jing Qin;L. Weiss;S. Slavin;S. Gatt;A. Dagan
  • 通讯作者:
    A. Dagan
Warm deformation and dynamic strain aging behavior of Nb-Cr micro-alloyed low-carbon steel
Nb-Cr微合金化低碳钢的温变形及动态应变时效行为
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Zhigang Wang;Xin Liu;Qiangqiang Yuan;Rongchun Chen;Jianguo He;Jing Qin;Yao Huang;Hongjin Zhao
  • 通讯作者:
    Hongjin Zhao
Privacy-Preserving and Publicly Verifiable Protocol for Outsourcing Polynomials Evaluation to a Malicious Cloud
用于将多项式评估外包到恶意云的隐私保护和可公开验证的协议
The effectiveness of China#39;s RMB exchange rate reforms: An insight from multifractal detrended fluctuation analysis
中国的有效性
A Verifiable Symmetric Searchable Encryption Scheme Based on the AVL Tree
一种基于AVL树的可验证对称可搜索加密方案
  • DOI:
    10.1093/comjnl/bxab152
  • 发表时间:
    2021-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Qing Wang;Xi Zhang;Jing Qin;Jixin Ma;Xinyi Huang
  • 通讯作者:
    Xinyi Huang

Jing Qin的其他文献

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{{ truncateString('Jing Qin', 18)}}的其他基金

Graph-Based Regularization Techniques and Their Applications
基于图的正则化技术及其应用
  • 批准号:
    1941197
  • 财政年份:
    2019
  • 资助金额:
    $ 18.6万
  • 项目类别:
    Standard Grant

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