Applied Time-frequency Analysis

应用时频分析

• 批准号: RGPIN-2014-05059
• 负责人: Zhu, Hongmei
• 金额: $ 0.8万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=611412
• 关键词: Applied; Time; frequency; Analysis

Abnormalities by their own nature have only extremely weak footprints hidden deeply underneath the vast majority of normal data. In many cases, they reveal themselves as unusual localized structures along a joint time and frequency domain of a large set of non-stationary data. Time-frequency analysis (TFA) by design aims to reveal local features of non-stationary signals with time-varying frequency content. It provides the ability to uncover hidden abnormalities if the original data can be intelligently transformed and represented along the time and frequency domains. For example, irregular heartbeats, abnormal brain activities, or abnormal airplane vibrations that have a sudden onset and occur at a distinct frequency range can all be identified by TFA. Early detection of critical abnormalities allows us to take appropriate action to prevent expensive and fatal damages. Despite of its usefulness, two main issues severely impede the effectiveness of the TFA-based diagnoses. First, as TFA represents a one-dimensional signal as a function of two variables, time and frequency, the computational efforts are often substantial. This is particularly problematic for processing ultra large data set and/or used in a real-time setting. However, in many cases, the intended application has unique features that can be exploited to considerably reduce the computational complexity. Second, many standard TFA techniques require simplifying assumptions or standard characteristics such as that the signals are deterministic, sampled evenly, or fit well to linear models of sinusoidal waveforms. However, in practice, the majority of important applications will violate these assumptions significantly. Nevertheless, current mathematical theories can be extended so that specific TFA techniques can be developed without the reliance of some of the simplifying assumptions. Furthermore, if the actual data has certain characteristics that can be usefully exploit, these “non-standard characteristics” can be incorporated in the theoretical development of the techniques to help increase the effectiveness. The objective of this research program is to fundamentally overcome the critical limitations of the existing TFA techniques, in order to release its full potential for practical applications. More specifically, we aim to generalize the rationale behind the time-frequency analysis 1) to first tackle ultra large data size and then real-time TFA-based signal processing; 2) to investigate a number of “non-standard characteristics” that are regularly presented in the actual data; 3) with the availability of efficient computational schemes and more refined theoretical framework established in 1) and 2), a much broader range of computer-aided diagnostic applications can be explored. This research proposal is interdisciplinary and practical. It integrates mathematics, statistics, computing, and applications development. I expect that the trainees in the program will work closely with engineers and scientists in medical science and industries and make significant original contributions relevant to real-world problems. The success of this program will advance time-frequency analysis field, create sophisticated time-frequency analysis techniques tailored for specific types of signals and lead to the R&D development of computer-assisted monitoring and diagnostic software for various purposes.

异常现象本身只有极其微弱的足迹隐藏在绝大多数正常数据之下。在许多情况下，它们表现为沿着大量非平稳数据的联合时频域的不寻常的局部化结构。时频分析旨在揭示具有时变频率成分的非平稳信号的局部特征。它提供了发现隐藏异常的能力，如果原始数据能够被智能地转换并沿着时间和频率域表示的话。例如，突然发作并以不同的频率范围发生的不规则心跳、异常大脑活动或异常飞机振动都可以通过TFA来识别。及早发现严重异常，使我们能够采取适当行动，防止代价高昂和致命的损害。 尽管有用，但有两个主要问题严重阻碍了基于TFA的诊断的有效性。首先，由于TFA将一维信号表示为时间和频率两个变量的函数，因此计算工作量往往很大。这对于处理超大数据集和/或在实时设置中使用尤其成问题。然而，在许多情况下，预期的应用程序具有独特的功能，可以利用这些功能来显著降低计算复杂性。其次，许多标准的TFA技术需要简化假设或标准特性，例如信号是确定性的、均匀采样的或与正弦波形的线性模型很好地匹配。然而，在实践中，大多数重要的应用程序都会严重违反这些假设。然而，当前的数学理论可以扩展，从而可以开发特定的TFA技术，而不依赖于一些简化的假设。此外，如果实际数据具有某些可以有效利用的特征，则可以将这些“非标准特征”结合到技术的理论开发中，以帮助提高有效性。 这项研究计划的目的是从根本上克服现有TFA技术的关键限制，以便充分释放其实际应用的潜力。更具体地说，我们的目标是概括时频分析背后的基本原理1)首先处理超大数据量，然后是基于TFA的实时信号处理；2)调查实际数据中经常出现的一些“非标准特征”；3)随着1)和2)中建立的有效计算方案和更精细的理论框架的可用，可以探索更广泛的计算机辅助诊断应用。 本研究方案具有跨学科、实用性强的特点。它集成了数学、统计、计算和应用程序开发。我期待该项目的学员将与医学科学和工业领域的工程师和科学家密切合作，并为现实世界的问题做出重大的原创性贡献。该项目的成功将推动时频分析领域的发展，创造出针对特定类型信号的复杂的时频分析技术，并导致各种用途的计算机辅助监测和诊断软件的研发。