While deep neural networks have facilitated significant advancements in the field of speech enhancement, most existing methods are developed following either empirical or relatively blind criteria, lacking adequate guidelines in pipeline design. Inspired by Taylor's theorem, we propose a general unfolding framework for both single- and multi-channel speech enhancement tasks. Concretely, we formulate the complex spectrum recovery into the spectral magnitude mapping in the neighborhood space of the noisy mixture, in which an unknown sparse term is introduced and applied for phase modification in advance. Based on that, the mapping function is decomposed into the superimposition of the 0th-order and high-order polynomials in Taylor's series, where the former coarsely removes the interference in the magnitude domain and the latter progressively complements the remaining spectral detail in the complex spectrum domain. In addition, we study the relation between adjacent order terms and reveal that each high-order term can be recursively estimated with its lower-order term, and each high-order term is then proposed to evaluate using a surrogate function with trainable weights so that the whole system can be trained in an end-to-end manner. Given that the proposed framework is devised based on Taylor's theorem, it possesses improved internal flexibility. Extensive experiments are conducted on WSJ0-SI84, DNS-Challenge, Voicebank+Demand, spatialized Librispeech, and L3DAS22 multi-channel speech enhancement challenge datasets. Quantitative results show that the proposed approach yields competitive performance over existing top-performing approaches in terms of multiple objective metrics.

翻译：尽管深度神经网络已极大推动了语音增强领域的发展，但现有方法大多遵循经验性或相对盲目的准则，缺乏系统性的管线设计指导原则。受泰勒定理启发，我们提出了一种适用于单通道和多通道语音增强任务的通用展开式框架。具体而言，我们将复频谱恢复问题转化为含噪混合信号邻域空间内的谱幅度映射，其中引入未知稀疏项用于相位修正预处理。基于此，我们将映射函数分解为泰勒级数中零阶多项式与高阶多项式的叠加：前者在幅度域粗消除干扰，后者在复频谱域逐步补充残留谱细节。此外，我们研究了相邻阶项之间的关联性，揭示每个高阶项可通过其低阶项进行递归估计，继而提出利用具有可训练权重的替代函数来评估每个高阶项，使整个系统能够以端到端方式训练。由于所提框架基于泰勒定理构建，其具有增强的内部灵活性。我们在WSJ0-SI84、DNS-Challenge、Voicebank+Demand、空间化Librispeech及L3DAS22多通道语音增强挑战数据集上开展了大量实验。定量结果表明，在多个客观指标评估下，所提方法相较于现有顶级方法展现出具有竞争力的性能。