We propose the product-of-filters (PoF) model, a generative model that
decomposes audio spectra as sparse linear combinations of "filters" in the
log-spectral domain. PoF makes similar assumptions to those used in the classic
homomorphic filtering approach to signal processing, but replaces hand-designed
decompositions built of basic signal processing operations with a learned
decomposition based on statistical inference. This paper formulates the PoF
model and derives a mean-field method for posterior inference and a variational
EM algorithm to estimate the model's free parameters. We demonstrate PoF's
potential for audio processing on a bandwidth expansion task, and show that PoF
can serve as an effective unsupervised feature extractor for a speaker
identification task.

本文提出了一种基于统计推断的生成模型 —— 产品滤波器（PoF）模型，它将音频频谱分解为对数频谱领域中的 “过滤器” 的稀疏线性组合，然后借助平均场方法进行后验推断，并采用变分 EM 算法估计模型的自由参数，实验证明 PoF 模型在音频处理和说话人识别任务中具有很高的潜力，因为它可以作为有效的无监督特征提取器。