In this paper we present a novel Hierarchical Bayesian approach to estimate Relative Impulse Response (ReIR) using short, noisy and reverberant microphone recordings. The information contained in ReIRs between two microphones is useful for a wide range of multichannel speech processing applications such as speaker localization, speech enhancement, etc. It has been shown in several previous works that the Relative Transfer Function (RTF) corresponding to a given ReIR is dynamic and depends on the environment, microphone positions and target position. This acts as the main motivation of this work, as we develop a structured sparse Bayesian learning algorithm to estimate ReIR using very short recordings, which will be robust to changes in the environment. An extensive experimental study with real-world recordings has also been conducted to show the efficacy of our proposed approach over other competing approaches.

In this letter, some results involving a form of least-squares beamformer are derived based only on directional criteria. In far-field assumptions (i.e., plane wave propagation model for the signals captured), we show that certain factors appearing in the beamformer coefficients calculation, which are usually formulated using complicated integrals, can be computed using closed-form expressions involving familiar, physically meaningful quantities. Next, by resorting to a limiting case, we demonstrate a clear theoretical link between the resulting solution and MVDR beamforming in cylindrically isotropic noise fields. We then discuss a solution to preserve spatial cues if desired which also allows to easily control and modulate the enhancement strength of the beamformer. Some experimental results are finally given in a challenging real-world environment, showing the merits of the approach.

In this correspondence, a unified approach to the autoregressive (AR) modeling of power spectral densities is described. We show that by introducing auxiliary sequences, the minimization of several customary spectral distances can be performed with the exact same convenient approach, whether a gradient-descent or a Newton/quasi-Newton descent is chosen. Moreover, we extend the usual optimization of unnormalized AR coefficients to a two-step optimization of normalized AR coefficients, and provide evidence that this alternative approach can accelerate convergence and provide robustness to erroneous initializations. Convergence and modeling results are also given.

We propose a neural architecture for the perceptual sparse coding of audio signals based on a previously proposed technique called Local Competitive Algorithm (LCA) that was originally applied to image and video coding. LCAs are designed to be implemented in a dynamical system composed of many neuron-like elements operating in parallel. For the processing of audio signals, we here use gamma-tone filters that mimic the behavior of the auditory pathway as the receptive field of our neurons. We also adapted LCA to time-varying audio signals. Given the fact that LCA does not take into account the difference between perceived coding error and mathematical Mean-Squared Error (MSE), we propose in this article the Perceptual Local Competitive Algorithm (PLCA) and derive a convergence formula, as well as a corresponding neural architecture for it.We show that our proposed PLCA minimizes the perceptual coding error and can model phenomena such as absolute threshold of hearing and masking. Our sparse audio coder based on PLCA compares with the more conventional greedy (i.e., matching pursuit) algorithms for sparse coding in terms of quality and can be implemented in a much faster way, especially when parallel processing units (i.e., embedded circuits) can be afforded. We also show that our proposed PLCA is much more robust to quantization error than the conventional matching pursuit for audio coding.

Motivated by the reportedly strong performance of particle filters (PFs) for noise reduction on essentially linear speech production models, and the mounting evidence that the introduction of nonlinearities can lead to a refined speech model, this paper presents a study of PF solutions to the problem of speech enhancement in the context of nonlinear, neural-type speech models. Several variations of a global model are presented (single/multiple neurons; bias/no bias), and corresponding PF solutions are derived. Different importance functions are given when beneficial, Rao-Blackwellization is proposed when possible, and dual/nondual versions of each algorithms are presented. The method shown can handle both white and colored noise. Using a variety of speech and noise signals and different objective quality measures, the performance of these algorithms are evaluated against other PF solutions running on linear models, as well as some traditional enhancement algorithms. A certain hierarchy in performance is established between each algorithm in the paper. Depending on the experimental conditions, the best-performing algorithms are a classical Rao-Blackwellized particle filter (RBPF) running on a linear model, and a proposed PF employing a nondual, nonlinear model with multiple neurons and no biases. With consistence, the neural-network-based PF outperforms RBPF at low signal-to-noise ratio (SNR).

Among the various types of existing speech enhancement algorithms, respective advantages are usually well-known and well-studied, making it possible to choose the right algorithm given a certain type of audio quality requirement (e.g. background noise intrusiveness, naturalness of the speech, etc.). Very little has however been said so far on the quality of speech enhanced by particle filters (PFs). In this paper, we show the detailed results of the analysis of PF-enhanced speech signals. This analysis is conducted using several objective measures, and is based on the comparison with other enhancement algorithms. We find that in general, PF-based algorithms yield speech signals which are among the most natural-sounding, with a residual noise that can be seen as a white noise with its variance "modulated" by the resulting speech.

Rao-Blackwellised Particle Filters (RBPFs) are a class of Particle Filters (PFs) that exploit conditional dependencies between parts of the state to estimate. By doing so, RBPFs can improve the estimation quality while also reducing the over-all computational load in comparison to original PFs. However, the computational complexity is still too high for many real-time applications. In this paper, we propose a modified RBPF that requires a single Kalman Filter (KF) iteration per input sample. Comparative experiments show that while good convergence can still be obtained, computational efficiency is always drastically increased, making this algorithm an option to consider for real-time implementations.