You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In this study, we propose a modulation decoupling based single channel speech enhancement subspace framework, in which the spectrogram of noisy speech is decoupled as the product of a spectral envelop subspace and a spectral details subspace. This decoupling approach provides a method to specifically work on elimination of those noises that greatly affect the intelligibility. Two supervised low-rank and sparse decomposition schemes are developed in the spectral envelop subspace to obtain a robust recovery of speech components. A Bayesian formulation of non-negative factorization is used to learn the speech dictionary from the spectral envelop subspace of clean speech samples. In the spectral details subspace, a standard robust principal component analysis is implemented to extract the speech components. The validation results show that compared with four speech enhancement algorithms, including MMSE-SPP, NMF-RPCA, RPCA, and LARC, the proposed MS based algorithms achieve satisfactory performance on improving perceptual quality, and especially speech intelligibility.

Cited Abstract(s):
[1]: We systematically determined which spectrotemporal modulations in speech are necessary for comprehension by human listeners. Speech comprehension has been shown to be robust to spectral and temporal degradations, but the specific relevance of particular degradations is arguable due to the complexity of the joint spectral and temporal information in the speech signal. We applied a novel modulation filtering technique to recorded sentences to restrict acoustic information quantitatively and to obtain a joint spectrotemporal modulation transfer function for speech comprehension, the speech MTF. For American English, the speech MTF showed the criticality of low modulation frequencies in both time and frequency. Comprehension was significantly impaired when temporal modulations <12 Hz or spectral modulations <4 cycles kHz were removed. More specifically, the MTF was bandpass in temporal modulations and low-pass in spectral modulations: temporal modulations from 1 to 7 Hz and spectral modulations <1 cycles kHz were the most important. We evaluated the importance of spectrotemporal modulations for vocal gender identification and found a different region of interest: removing spectral modulations between 3 and 7 cycles kHz significantly increases gender misidentifications of female speakers. The determination of the speech MTF furnishes an additional method for producing speech signals with reduced bandwidth but high intelligibility. Such compression could be used for audio applications such as file compression or noise removal and for clinical applications such as signal processing for cochlear implants.
In this study, our proposed speech enhancement algorithm can be categorized as modulation subspace based semi-supervised LSD. Modulation domain based source separation technologies are mainly developed according to the knowledge that the spectrogram of speech can be described as a time-varying weighted sum of component modulations [1] . By exploiting intrinsic decomposition through well convex optimization, low-rank and sparse analysis overcomes the high sensitive of the conventional principle component analysis (PCA) when subjecting to large corruptions.