A Survey on Probabilistic Models in Human Perception and Machines

Extracting information from noisy signals is of fundamental importance for both biological and artificial perceptual systems. To provide tractable solutions to this challenge, the fields of human perception and machine signal processing (SP) have developed powerful computational models, including Bayesian probabilistic models. However, little true integration between these fields exists in their applications of the probabilistic models for solving analogous problems, such as noise reduction, signal enhancement, and source separation. In this mini review, we briefly introduce and compare selective applications of probabilistic models in machine SP and human psychophysics. We focus on audio and audio-visual processing, using examples of speech enhancement, automatic speech recognition, audio-visual cue integration, source separation, and causal inference to illustrate the basic principles of the probabilistic approach. Our goal is to identify commonalities between probabilistic models addressing brain processes and those aiming at building intelligent machines. These commonalities could constitute the closest points for interdisciplinary convergence.

Learning time-frequency mask for noisy speech enhancement using gaussian-bernoulli pre-trained deep neural networks

Speech enhancement is a very important problem in various speech processing applications. Recently, supervised speech enhancement using deep learning approaches to estimate a time-frequency mask have proved remarkable performance gain. In this paper, we have proposed time-frequency masking-based supervised speech enhancement method for improving intelligibility and quality of the noisy speech. We believe that a large performance gain can be achieved if deep neural networks (DNNs) are layer-wise pre-trained by stacking Gaussian-Bernoulli Restricted Boltzmann Machine (GB-RBM). The proposed DNN is called as Gaussian-Bernoulli Deep Belief Network (GB-DBN) and are optimized by minimizing errors between the estimated and pre-defined masks. Non-linear Mel-Scale weighted mean square error (LMW-MSE) loss function is used as training criterion. We have examined the performance of the proposed pre-training scheme using different DNNs which are established on three time-frequency masks comprised of the ideal amplitude mask (IAM), ideal ratio mask (IRM), and phase sensitive mask (PSM). The results in different noisy conditions demonstrated that when DNNs are pre-trained by the proposed scheme provided a persistent performance gain in terms of the perceived speech intelligibility and quality. Also, the proposed pre-training scheme is effective and robust in noisy training data.

Speech Enhancement Using Gaussian Scale Mixture Models

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress.

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback-Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation-maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion.