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

A General Unfolding Speech Enhancement Method Motivated by Taylor's Theorem