AI 中文总结
该研究提出尖峰形状自适应模式分解（SSAMD）框架，针对非平稳尖峰信号分解，结合PCA参数化与熵正则化，在生物医学信号验证中实现去噪、波形跟踪等功能，克服现有模型局限。
AI 中文摘要
我们提出了一种用于分解非平稳尖峰信号的新框架。与将信号表示为调幅-调频（AM-FM）振荡的经典自适应非调和模型不同，该模型针对主导结构高度局域化、脉冲式或尖峰状且包含生理变异性的信号设计，这类信号难以用AM-FM表示建模，典型例子包括心电图（ECG）复合波、癫痫脑电图（EEG）瞬态及其他脉冲式生理信号。我们首先引入用于重复尖峰结构的固定波形模型，随后将其扩展以适应逐周期波形变异性。所得算法称为尖峰形状自适应模式分解（Spiky Shape-adaptive Mode Decomposition, SSAMD），在傅里叶系数域估计波形。傅里叶系数先通过局部回归估计，再利用其低维流形结构进行正则化。具体而言，我们将基于主成分分析（PCA）的参数化与作用于系数矩阵奇异值谱的熵正则化相结合，在保留结构化波形变异性的同时促进形态一致性。该框架具有灵活性，克服了现有模型的局限性。我们在合成信号及真实生物医学信号上验证了该方法，包括房颤心电图、癫痫脑电图和经腹母体心电图。实验结果表明，该方法可实现有效的去噪、波形跟踪、分解与分割，同时保留具有生理意义的形态变异性。
英文摘要
We propose a novel framework for decomposing nonstationary spiky signals. Unlike classical adaptive non-harmonic models, which represent signals as amplitude- and frequency-modulated (AM--FM) oscillations, the proposed model is designed for signals whose dominant structures are highly localized, impulsive, or spike-like, and contains physiological variability, which is challenging to be modeled as AM--FM representations. Representative examples include electrocardiogram (ECG) complexes, epileptic electroencephalogram (EEG) transients, and other pulse-like physiological signals. We first introduce a fixed-waveform model for repetitive spiky structures and then extend it to accommodate cycle-to-cycle waveform variability. The resulting algorithm, termed \emph{Spiky Shape-adaptive Mode Decomposition} (SSAMD), estimates waveforms in the Fourier coefficient domain. Fourier coefficients are first estimated via local regression and then regularized by exploiting their low-dimensional manifold structure. Specifically, we combine a PCA-based parametrization with an entropy regularization acting on the singular-value spectrum of the coefficient matrix, promoting morphological consistency while preserving structured waveform variability. The proposed framework is flexible and overcomes the limitations of existing models. We validate the method on synthetic and real biomedical signals, including ECG with atrial fibrillation, epileptic EEG, and trans-abdominal maternal ECG. Experimental results demonstrate effective denoising, waveform tracking, decomposition, and segmentation, while preserving physiologically meaningful morphological variations.
