Flávio R. Avila

Bayesian Restoration of Audio Signals Degraded by Impulsive Noise Modeled as Individual Pulses

Impulsive noise, also known as clicks, is a very common type of distortion in old gramophone recordings. Existing methods (both heuristic and statistical) for removal of this type of defect usually do not exploit its underlying physical generation. This work proposes a model in which each click is individually modeled, which is more physically meaningful. A Bayesian method based on the reversible-jump Metropolis-Hastings algorithm for joint detection and removal of impulsive noise in audio signals is devised. Simulations with artificial and real audio signals as well as comparisons with competing approaches are presented to illustrate and validate the proposed method.

ML ESTIMATION OF MEMORYLESS NONLINEAR DISTORTIONS IN AUDIO SIGNALS

Many real-world signals are subjected to nonlinear distortions that can be approximately modeled as memoryless and invertible. In Audio applications, they are typical of magnetic recordings but can also result of dynamic compression employed in vinyl recordings etc. Such an effect can be disturbing to a modern audience which is used to higher quality material. This paper proposes an iterative algorithm to maximize the likelihood function of the distortion function parameters, based solely on samples of the degraded signal, and then recover the original signal. The method assumes the original signal to be autoregressive and Gaussian in short sections - a standard model for audio - and the nonlinearity to be time-invariant throughout the signal, thus allowing the use of all samples in the model estimation. Additionally, a simple and time-efficient alternative technique to estimate the nonlinear function is proposed; it can be used either as a fast and reliable stand-alone procedure or as a initialization routine for the more sophisticated maximum likelihood approach. The robustness of the proposed techniques is verified through application to artificial and real signals nonlinearly distorted.

Bayesian Blind Identification of Nonlinear Distortion with Memory for Audio Applications

Whenever an audio device introduces unwanted nonlinear distortions into the manipulated signal, finding a tractable system to approximately model and estimate such degradations can be instrumental to recover the undistorted audio. This paper approaches such blind estimation task (for which classical identification tools are unsuitable) by bringing into the Bayesian framework a Hammerstein system model: the cascade of a static memoryless nonlinearity with a memory-inducing linear filter, which has been shown to be effective in describing many real systems. By assuming the underlying clean audio signal is autoregressive in short sections, the proposed method identifies the distorting system by simulating, in a Markov-Chain Monte Carlo context, the posterior distribution of the model parameters conditioned on the distorted signal. To deal with the resulting non-standard posterior distribution, a combination of the Metropolis-Hastings (MH) algorithm and the Gibbs Sampling is adopted. MH proposals are based on the Laplace approximation of the posterior distribution thanks to its almost Gaussian shape around modes. A heuristic that forces a broad region of the parameter space to be visited on an occasional basis prevents the Markov Chain from getting stuck around local maxima. A series of experiments with artificially distorted music recordings attests the effectiveness of the proposed algorithm.

A Parametric Objective Quality Assessment Tool for Speech Signals Degraded by Acoustic Echo

This paper discusses the automatic quality assessment of echo-degraded speech in the context of teleconference systems. Subjective listening tests conducted over a carefully designed database of signals degraded by acoustic echo have been used to assess how this impairment is perceived and to determine which parameters have a significant impact on speech quality. The results have shown that, similarly to electric transmission line echo, acoustic echo is mainly influenced by echo delay and echo gain. Based on this observation, a mapping between these two parameters and the mean subjective score is devised. Moreover, a signal-based algorithm for the estimation of these parameters is described, and its performance is evaluated. The complete system comprising both the parameter estimators and the mapping function achieves a correlation of 94% between predicted and actual subjective scores, and can be employed as a non-intrusive monitoring tool for in-service quality evaluation of teleconference systems. Further validation indicates the operating range of the proposed quality assessment tool can be extended by proper retraining.

Bayesian suppression of memoryless nonlinear audio distortion

Even if nonlinear distortion may be deliberately applied to audio signals for esthetic or technical reasons, it is common to hear annoying defects in accidentally saturated or amateurishly processed audio - which calls for some means to automatically undo the impairment. This paper proposes an algorithm to blindly identify the nonlinear distortion suffered by an audio signal and reconstruct its original form. Designed to deal with memoryless impairments, the model adopted for the nonlinear distortion is a curve composed of an invertible sequence of linear segments, capable of following the typical shape of compressed audio, and whose parameters are easily interpretable and thus constrainable. The solution builds on the posterior statistical distribution of the curve parameters given the degraded signal, and yields perceptually impressive results for real signals distorted by arbitrary curves.

On the Sparsity-Based Identification and Compensation of Hammerstein Systems

This letter investigates blind identification and compensation of Hammerstein systems, whose inputs are sparse in the frequency domain. In our analysis, the Hammerstein system comprises an antisymmetric invertible polynomial nonlinear curve followed by a minimum-phase linear system. We show analytically in a simple scenario and empirically in more complex situations that the Hammerstein system is identifiable with high probability, provided that the nonlinear component of the system reduces the sparsity of the input by a sufficiently large amount. Moreover, we propose a practical compensation procedure in the form of the Wiener system that provides a maximally sparse output when cascaded with the given Hammerstein system. Monte Carlo experiments show that the procedure is effective for Hammerstein systems with sufficiently strong nonlinearities submitted to inputs within a wide range of sparsity levels.

Objective quality assessment of echo-impaired full-band speech signals

This paper describes a double-ended objective quality assessment method for evaluating full-band (sampled at 48 kHz) speech signals impaired by acoustic echo and background noise. The proposed method is based on a single metric of the ITU-T standard PEAQ (originally developed for audio signals) that, along with an appropriate mapping function, is shown to be able to reliably predict the overall quality of speech signals concurrently degraded by acoustic echo and background noise. In order to train and validate the proposed method, three speech signal databases were developed and subjectively assessed. One database is used only for training and testing purposes whereas the other two are employed in validation. Using the validation databases, it has been shown that the proposed method can predict the quality of signals degraded with a wider scope of acoustic echo and noise characteristics than those considered in its development.

Unsupervised time domain nonlinear post-equalization for ACO-OFDM visible light communication systems

LED nonlinearity is an important issue limiting the performance of Visible Light Communication (VLC) systems. This form of distortion is particularly problematic when the system employs Optical-OFDM because of the high Peak-to-Average Power Ratio (PAPR) of its time domain symbol. This paper proposes using ancillary statistical properties of the O-OFDM signal in order to mitigate LED nonlinearities in an unsupervised fashion. By exploring the Gaussianity of the time domain OFDM signal and the idea of distribution equalization, we propose a semi-parametric approach to blind nonlinear post-equalization for asymmetrically clipped O-OFDM (ACO-OFDM) VLC systems. In addition to not requiring training data, the equalizer is robust to different LED types and it is adaptive to time-varying nonlinearities. Simulations with a realistic LED model show that the developed tool is capable of substantially mitigating the effects of nonlinear distortion on system performance.

Audio Soft Declipping Based on Constrained Weighted Least Squares

This letter presents a novel approach to blind recovery of audio signals that have been distorted by a memoryless, invertible, and smooth nonlinear function. We introduce a cost function consisting of a weighted sum of squared discrete cosine transform coefficients of the recovered signal, whose weights are obtained from the distorted signal itself and, thus, can adapt to different signal characteristics. In order to prevent undesired trivial solutions, we impose an either quadratic or linear equality constraint, the latter case with closed-form solution. Despite its simplicity, our method outperforms a recent sparsity-based solution for memoryless nonlinearity compensation, in audio and speech databases.