Jalil Taghia

An evaluation of noise power spectral density estimation algorithms in adverse acoustic environments

Noise power spectral density estimation is an important component of speech enhancement systems due to its considerable effect on the quality and the intelligibility of the enhanced speech. Recently, many new algorithms have been proposed and significant progress in noise tracking has been made. In this paper, we present an evaluation framework for measuring the performance of some recently proposed and some well-known noise power spectral density estimators and compare their performance in adverse acoustic environments. In this investigation we do not only consider the performance in the mean of a spectral distance measure but also evaluate the variance of the estimators as the latter is related to undesirable fluctuations also known as musical noise. By providing a variety of different non-stationary noises, the robustness of noise estimators in adverse environments is examined.

Bayesian estimation of Dirichlet mixture model with variational inference

In statistical modeling, parameter estimation is an essential and challengeable task. Estimation of the parameters in the Dirichlet mixture model (DMM) is analytically intractable, due to the integral expressions of the gamma function and its corresponding derivatives. We introduce a Bayesian estimation strategy to estimate the posterior distribution of the parameters in DMM. By assuming the gamma distribution as the prior to each parameter, we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions. The extended factorized approximation method is applied to introduce a single lower-bound to the variational objective function and an analytically tractable estimation solution is derived. Moreover, there is only one function that is maximized during iterations and, therefore, the convergence of the proposed algorithm is theoretically guaranteed. With synthesized data, the proposed method shows the advantages over the EM-based method and the previously proposed Bayesian estimation method. With two important multimedia signal processing applications, the good performance of the proposed Bayesian estimation method is demonstrated.

Single channel speech enhancement using Bayesian NMF with recursive temporal updates of prior distributions

We present a speech enhancement algorithm which is based on a Bayesian Nonnegative Matrix Factorization (NMF). Both Minimum Mean Square Error (MMSE) and Maximum a-Posteriori (MAP) estimates of the magnitude of the clean speech DFT coefficients are derived. To exploit the temporal continuity of the speech and noise signals, a proper prior distribution is introduced by widening the posterior distribution of the NMF coefficients at the previous time frames. To do so, a recursive temporal update scheme is proposed to obtain the mean value of the prior distribution; also, the uncertainty of the prior information is governed by the shape parameter of the distribution which is learnt automatically based on the nonstationarity of the signals. Simulations show a considerable improvement compared to the maximum likelihood NMF based speech enhancement algorithm for different input SNRs.

A variational Bayes approach to the underdetermined blind source separation with automatic determination of the number of sources

In this paper, we propose a variational Bayes approach to the underdetermined blind source separation and show how a variational treatment can open up the possibility of determining the actual number of sources. The procedure is performed in a frequency bin-wise manner. In every frequency bin, we model the time-frequency mixture by a variational mixture of Gaussians with a circular-symmetric complex-Gaussian density function. In the Bayesian inference, we consider appropriate conjugate prior distributions for modeling the parameters of this distribution. The learning task consists of estimating the hyper-parameters characterizing the parameter distributions for the optimization of the variational posterior distribution. The proposed approach requires no prior knowledge on the number of sources in a mixture.

Bayesian Estimation of the von-Mises Fisher Mixture Model with Variational Inference

This paper addresses the Bayesian estimation of the von-Mises Fisher (vMF) mixture model with variational inference (VI). The learning task in VI consists of optimization of the variational posterior distribution. However, the exact solution by VI does not lead to an analytically tractable solution due to the evaluation of intractable moments involving functional forms of the Bessel function in their arguments. To derive a closed-form solution, we further lower bound the evidence lower bound where the bound is tight at one point in the parameter distribution. While having the value of the bound guaranteed to increase during maximization, we derive an analytically tractable approximation to the posterior distribution which has the same functional form as the assigned prior distribution. The proposed algorithm requires no iterative numerical calculation in the re-estimation procedure, and it can potentially determine the model complexity and avoid the over-fitting problem associated with conventional approaches based on the expectation maximization. Moreover, we derive an analytically tractable approximation to the predictive density of the Bayesian mixture model of vMF distributions. The performance of the proposed approach is verified by experiments with both synthetic and real data.

An Image Watermarking Method Based on Bidimensional Empirical Mode Decomposition

In this paper, we propose a blind image watermarking scheme based on bidimensional empirical mode decomposition (BEMD). BEMD is a possible 2D extension of empirical mode decomposition (EMD). We employ BEMD in watermark embedding and watermark extraction. In watermark embedding scheme at first, the original image is divided into K sub-images then in order to obtain a set of 2D-IMFs BEMD is applied to each sub-image and watermark. For watermark embedding each 2D-IMF, which is extracted from watermark, is placed instead of one of the 2D-IMFs which are extracted from each sub-image in a special procedure. On the other hand the proposed method in watermark extraction is based on BEMD and clustering method with metric, local linear structure and affine symmetry to extract watermark blindly. We perform two classes of tests in our experiments: First, we measure imperceptibility of watermark and then we examine the performance against different kinds of attacks.

A Variational Bayesian Inference Framework for Multiview Depth Image Enhancement

In this paper, a general model-based framework for multiview depth image enhancement is proposed. Depth imagery plays a pivotal role in emerging free-viewpoint television. This technology requires high quality virtual view synthesis to enable viewers to move freely in a dynamic real world scene. Depth imagery of different viewpoints is used to synthesize an arbitrary number of novel views. Usually, the depth imagery is estimated individually by stereo-matching algorithms and, hence, shows lack of inter-view consistency. This inconsistency affects the quality of view synthesis negatively. This paper enhances the inter-view consistency of multiview depth imagery by using a variational Bayesian inference framework. First, our approach classifies the color information in the multiview color imagery. Second, using the resulting color clusters, we classify the corresponding depth values in the multiview depth imagery. Each clustered depth image is subject to further sub clustering. Finally, the resulting mean of the sub-clusters is used to enhance the depth imagery at multiple viewpoints. Experiments show that our approach improves the quality of virtual views by up to 0.25 dB.

Probabilistic Multiview Depth Image Enhancement Using Variational Inference

An inference-based multiview depth image enhancement algorithm is introduced and investigated in this paper. Multiview depth imagery plays a pivotal role in free-viewpoint television. This technology requires high-quality virtual view synthesis to enable viewers to move freely in a dynamic real world scene. Depth imagery of different viewpoints is used to synthesize an arbitrary number of novel views. Usually, the depth imagery is estimated individually by stereo-matching algorithms and, hence, shows inter-view inconsistency. This inconsistency affects the quality of view synthesis negatively. This paper enhances the multiview depth imagery at multiple viewpoints by probabilistic weighting of each depth pixel. First, our approach classifies the color pixels in the multiview color imagery. Second, using the resulting color clusters, we classify the corresponding depth values in the multiview depth imagery. Each clustered depth image is subject to further subclustering. Clustering based on generative models is used for assigning probabilistic weights to each depth pixel. Finally, these probabilistic weights are used to enhance the depth imagery at multiple viewpoints. Experiments show that our approach consistently improves the quality of virtual views by 0.2 dB to 1.6 dB, depending on the quality of the input multiview depth imagery.

Multiview depth map enhancement by variational bayes inference estimation of Dirichlet mixture models

High quality view synthesis is a prerequisite for future free-viewpoint television. It will enable viewers to move freely in a dynamic real world scene. Depth image based rendering algorithms will play a pivotal role when synthesizing an arbitrary number of novel views by using a subset of captured views and corresponding depth maps only. Usually, each depth map is estimated individually by stereo-matching algorithms and, hence, shows lack of inter-view consistency. This inconsistency affects the quality of view synthesis negatively. This paper enhances the inter-view consistency of multiview depth imagery. First, our approach classifies the color information in the multiview color imagery by modeling color with a mixture of Dirichlet distributions where the model parameters are estimated in a Bayesian framework with variational inference. Second, using the resulting color clusters, we classify the corresponding depth values in the multiview depth imagery. Each clustered depth image is subject to further sub-clustering. Finally, the resulting mean of each sub-cluster is used to enhance the depth imagery at multiple viewpoints. Experiments show that our approach improves the average quality of virtual views by up to 0.8 dB when compared to views synthesized by using conventionally estimated depth maps.

Variational Inference for Watson Mixture Model

This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets.