Speech Enhancement Using a-Minimum Mean-Square Error Short-Time Spectral Amplitude Estimator

By Y. Ephraim, D. Malah

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Deliang Wang
2. Dong Yu
3. Jinyu Li
4. Wei-Ning Hsu
5. Li Deng
6. Shinji Watanabe
7. Xu Tan
8. Jonathan Le Roux

Citations in the corpus

• Icassp 2022 Deep Noise Suppression Challenge (2022, background): “Real-time noise suppression for improving the perceptual quality of speech is a classical problem and researchers have proposed numerous solutions [1].”
• Real Time Speech Enhancement in the Waveform Domain (2020, methodology): “Traditionally speech enhancement methods generate either an enhanced version of the magnitude spectrum or produce an estimate of the ideal binary mask (IBM) that is then used to enhance the magnitude spectrum [5, 33].”
• Speech Enhancement in Multiple-Noise Conditions Using Deep Neural Networks (2016, background): “MMSE estimator [5] which performs non-linear estimation of short time spectral amplitude (STSA) of speech signal is another important work.”
• Gait recognition using wifi signals (2016, methodology): “Second, we apply frequency domain denoising method by subtracting the noise floor from the spectrogram [7].”
• The importance of phase in speech enhancement (2011, methodology): “MMSE STSA spectrum (Ephraim and Malah, 1984) and oracle phase spectrum”
• An Algorithm for Intelligibility Prediction of Time–Frequency Weighted Noisy Speech (2011, methodology): “That is, 1) the standard MMSE- STSA algorithm by Ephraim-Malah (EM) [22] which was developed under the assumption that speech and noise DFT coefficients are Gaussian, and 2) an improved version by Erkelens et al. (SG) [23], which assumes the speech and noise DFT coefficients to be super-Gaussian…”
• Conditional Generative Adversarial Networks for Speech Enhancement and Noise-Robust Speaker Verification (2017, methodology): “STSA-MMSE is a statistical-based SE technique, where the a priori signal to noise ratio (SNR) is estimated with the Decision-Directed approach [30] and the noise Power Spectral Density (PSD) is estimated with the noise PSD tracker in [31].”
• Subjective Comparison of Speech Enhancement Algorithms (2006, unknown): “KLT Eq. 14,48 [8] pKLT Eq. 34, =0.08 [9] MMSE-SPU Eq. 7,51, q=0.3 [10] logMMSE Eq. 20 [11] logMMSE-ne Eq. 20 [ 11 ] logMMSE-SPU Eq. 2,8,10,16 [12] pMMSE Eq. 12 [13] RDC Eq. 6,7,10,14,15 [14] RDC-ne Eq. 6,7,10,14,15 [14] MB Eq. 4-7 [15] WavThr Eq. 11,25 [16] Wiener as Eq. 3-7 [4] AudSup Eq. 26,38, b(”
• Speech enhancement for non-stationary noise environments (2001, background): “Substituting (6) and (8) into (7), we have p(k; ') = 1 + q(k; ') 1 − q(k; ') (1 + (k; ')) × exp(−(k; ')) −1 ; (9) where (k; ') , x (k; ') d (k; ') ; ;(k; ') , |Y (k; ')| 2 d (k; ') ; (k; ') , (k; ')(k; ') 1 + (k; ') ; (10) (k; ') and (k; ' ) represent the a priori and a posteriori SNRs [7] [18].”
• Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging (2003, methodology): “…theth frame, and assuming a complex Gaussian distribution of the STFT coefficients for both speech and noise [6], the conditional probability density functions (PDFs) of the observed signal are given by (1) (2) where and denote respectively the short-term spectrum of the speech and noise signals.”
• DeepMMSE: A Deep Learning Approach to MMSE-Based Noise Power Spectral Density Estimation (2020, methodology): “In [20], a limited maximum likelihood (ML) estimator [1] was used to estimate the a priori SNR.”
• Reasons why current speech-enhancement algorithms do not improve speech intelligibility and suggested solutions (2011, methodology): “Both distortions are treated equally in most SE algorithms, since the MSE metric is used in the derivation of most suppression functions (e.g., [7]).”
• Robust Speech Recognition Using a Cepstral Minimum-Mean-Square-Error-Motivated Noise Suppressor (2008, background): “Digital Object Identifier 10.1109/TASL.2008.921761 traditionally applied in the spectral domain (e.g., spectral subtraction, Wiener filtering, and Ephraim/Malah spectral amplitude MMSE suppressor [7], [13]).”
• Convolutional Neural Networks to Enhance Coded Speech (2018, background): “where the first-step a priori SNR estimate ξ̂1( , k) from the decision-direction approach [46] is”