CIF: Small: Resonance-Based Signal Analysis: Algorithms and Applications

CIF：小型：基于共振的信号分析：算法和应用

• 批准号: 1018020
• 负责人: Ivan Selesnick
• 金额: $ 24.55万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-01 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018020&HistoricalAwards=false
• 关键词: CIF; Small; Resonance; Based; Signal

Resonance-Based Signal Analysis: Algorithms and Applications Ivan SelesnickMany signals arising from physiological and physical processes are not only non-stationary but also posses a mixture of sustained oscillations and non-oscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geophysical signals. For example, EEG signals contain rhythmic oscillations (alpha waves, etc) but they also contain transients due to measurement artifacts and non-rhythmic brain activity. This research program involves the development and application of new algorithms designed to decompose such signals into 'resonance' components - a high-resonance component being a signal consisting of multiple simultaneous sustained oscillations; a low-resonance component being a signal consisting of non-oscillatory transients of unspecified shape and duration. While frequency components are straightforwardly defined and can be obtained by linear filtering, resonance components are more difficult to define and procedures to obtain resonance components are necessarily nonlinear. It is envisioned that the decomposition of a non-stationary multi-resonance signal into resonance components will enable the more effective utilization of existing processing methods specialized to each component. For example, sinusoidal modeling of speech is most efficient and effective for signals consisting primarily of sustained oscillations (high-resonance signals). On the other hand, time-domain and wavelet-domain methods are most effective for piecewise smooth signals that are defined primarily by their transients or singularities (low-resonance signals). This research utilizes recent developments in signal processing, including sparse signal representations, morphological component analysis, constant-Q (wavelet) transforms with varying Q-factors, fast algorithms for L1-norm regularized linear inverse problems, and related algorithms. The research consists of developing algorithms for resonance-based signal decomposition and generalizations, and assessing their effectiveness for the processing of signals arising from several physical and physiological processes.

基于共振的信号分析：算法和应用Ivan Selesnick生理和物理过程中产生的许多信号不仅是非平稳的，而且是持续振荡和非振荡瞬变的混合物，难以用线性方法解开。这样的信号的示例包括语音、生物医学和地球物理信号。例如，EEG信号包含有节奏的振荡（α波等），但它们也包含由于测量伪影和非节奏的大脑活动而引起的瞬变。该研究计划涉及新算法的开发和应用，该算法旨在将此类信号分解为“共振”分量-高共振分量是由多个同时持续振荡组成的信号;低共振分量是由未指定形状和持续时间的非振荡瞬态组成的信号。虽然频率分量被直接定义并且可以通过线性滤波获得，但是谐振分量更难以定义，并且获得谐振分量的过程必然是非线性的。 可以设想，将非平稳多谐振信号分解成谐振分量将使得能够更有效地利用专用于每个分量的现有处理方法。例如，语音的正弦建模对于主要由持续振荡组成的信号（高共振信号）是最有效的。另一方面，时域和小波域的方法是最有效的分段平滑信号，主要是由他们的瞬态或奇异性（低共振信号）。本研究利用信号处理的最新发展，包括稀疏信号表示，形态成分分析，恒定Q（小波）变换与不同的Q因子，L1范数正则化线性逆问题的快速算法，以及相关算法。 该研究包括开发基于共振的信号分解和概括算法，并评估其对处理来自几个物理和生理过程的信号的有效性。