Collaborative Research: New perspectives from applied and computational time-frequency analysis

合作研究：应用和计算时频分析的新视角

• 批准号: 2309651
• 负责人: Christina Frederick
• 金额: $ 12.43万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309651&HistoricalAwards=false
• 关键词: Collaborative; Research; New; perspectives; applied

The project explores new theories and algorithms that address fundamental challenges in time-frequency analysis with significant societal implications, including those in industrial and scientific sectors, medical technology, and big data analytics where the outcomes have far-reaching effects. The primary objective is to develop mathematical insights that enable the design of algorithms capable of efficiently handling the increasing demands of modern technologies which generate extensive and intricate datasets. Specifically, the project emphasizes the investigation of data sparsity of complex wave signals aiming to identify the optimal mathematical components, or "building blocks," for expressing and simplifying the data. By uncovering the underlying patterns and structures within the data, the project aims to enable more accurate and insightful analysis. At an institutional level this project offers a valuable opportunity to train undergraduate students and graduate students, integrate research activities into teaching and course development, and widely disseminate and divulge findings through academic and public channels. This project enables STEM leadership development, enhancements in educational curricula, and advancements in equity and inclusion in scientific pursuits.This three-year project aims to develop computational methods that reduce the cost and improve the accuracy of capturing wave phenomena. The project seeks to discover sparsity in multi-scale representations, computational time-frequency analysis, and robust, high-dimensional sampling strategies. By combining frame theory, linear algebra, information theory, and insights from computational science, the project aims to develop numerical algorithms that enhance speed, precision, and cost-efficiency in computation and storage. The research objectives include constructing sparse time-frequency representations, developing optimal sampling strategies for high-dimensional signals, demonstrating the potential of these ideas for numerical approximation and signal recovery, and investigating unresolved problems in applied harmonic analysis.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.

该项目探讨了新的理论和算法，这些理论和算法在时间频率分析中具有重大的社会影响，包括工业和科学领域，医疗技术以及结果具有深远影响的大数据分析。主要目的是开发数学见解，以使能够有效地处理现代技术的需求不断增长的算法设计，从而产生广泛而复杂的数据集。具体而言，该项目强调了旨在确定最佳数学组件或“构建块”的复杂波信号的数据稀疏性的研究，以表达和简化数据。通过揭示数据中的基本模式和结构，该项目旨在实现更准确和有见地的分析。在机构层面上，该项目提供了一个宝贵的机会，可以培训本科生和研究生，将研究活动整合到教学和课程发展中，并通过学术和公共渠道广泛传播和泄露发现。该项目使STEM领导力发展，教育课程的增强以及在科学追求中的公平和包容性方面的进步。这三年项目旨在开发降低成本并提高捕获波浪现象准确性的计算方法。该项目旨在发现多尺度表示，计算时频分析和稳健，高维抽样策略的稀疏性。通过结合框架理论，线性代数，信息理论以及计算科学的见解，该项目旨在开发数值算法，从而增强计算和存储中速度，精度和成本效益。研究目的包括构建稀疏的时频表示，为高维信号制定最佳抽样策略，证明这些思想对数值近似和信号恢复的潜力，以及在应用谐波分析中调查未解决的问题。该奖项反映了NSF的法定任务，并通过评估范围来进行评估，并使用基金会的范围进行了评估。