Rake, Peel, Sketch:The Signal Processing Pipeline Revisited

The prototypical signal processing pipeline can be divided into four blocks. Representation of the signal in a basis suitable for processing. Enhancement of the meaningful part of the signal and noise reduction. Estimation of important statistical properties of the signal. Adaptive processing to track and adapt to changes in the signal statistics. This thesis revisits each of these blocks and proposes new algorithms, borrowing ideas from information theory, theoretical computer science, or communications. First, we revisit the Walsh-Hadamard transform (WHT) for the case of a signal sparse in the transformed domain, namely that has only K †N non-zero coefficients. We show that an efficient algorithm exists that can compute these coefficients in O(K log2(K) log2(N/K)) and using only O(K log2(N/K)) samples. This algorithm relies on a fast hashing procedure that computes small linear combinations of transformed domain coefficients. A bipartite graph is formed with linear combinations on one side, and non-zero coefficients on the other. A peeling decoder is then used to recover the non-zero coefficients one by one. A detailed analysis of the algorithm based on error correcting codes over the binary erasure channel is given. The second chapter is about beamforming. Inspired by the rake receiver from wireless communications, we recognize that echoes in a room are an important source of extra signal diversity. We extend several classic beamforming algorithms to take advantage of echoes and also propose new optimal formulations. We explore formulations both in time and frequency domains. We show theoretically and in numerical simulations that the signal-to-interference-and-noise ratio increases proportionally to the number of echoes used. Finally, beyond objective measures, we show that echoes also directly improve speech intelligibility as measured by the perceptual evaluation of speech quality (PESQ) metric. Next, we attack the problem of direction of arrival of acoustic sources, to which we apply a robust finite rate of innovation reconstruction framework. FRIDA â the resulting algorithm â exploits wideband information coherently, works at very low signal-to-noise ratio, and can resolve very close sources. The algorithm can use either raw microphone signals or their cross- correlations. While the former lets us work with correlated sources, the latter creates a quadratic number of measurements that allows to locate many sources with few microphones. Thorough experiments on simulated and recorded data shows that FRIDA compares favorably with the state-of-the-art. We continue by revisiting the classic recursive least squares (RLS) adaptive filter with ideas borrowed from recent results on sketching least squares problems. The exact update of RLS is replaced by a few steps of conjugate gradient descent. We propose then two different precondi- tioners, obtained by sketching the data, to accelerate the convergence of the gradient descent. Experiments on artificial as well as natural signals show that the proposed algorithm has a performance very close to that of RLS at a lower computational burden. The fifth and final chapter is dedicated to the software and hardware tools developed for this thesis. We describe the pyroomacoustics Python package that contains routines for the evaluation of audio processing algorithms and reference implementations of popular algorithms. We then give an overview of the microphone arrays developed

Robust Distributed Multi-Source Detection and Labeling in Wireless Acoustic Sensor Networks

The growing demand in complex signal processing methods associated with low-energy large scale wireless acoustic sensor networks (WASNs) urges the shift to a new information and communication technologies (ICT) paradigm. The emerging research perception aspires for an appealing wireless network communication where multiple heterogeneous devices with different interests can cooperate in various signal processing tasks (MDMT). Contributions in this doctoral thesis focus on distributed multi-source detection and labeling applied to audio enhancement scenarios pursuing an MDMT fashioned node-specific source-of-interest signal enhancement in WASNs. In fact, an accurate detection and labeling is a pre-requisite to pursue the MDMT paradigm where nodes in the WASN communicate effectively their sources-of-interest and, therefore, multiple signal processing tasks can be enhanced via cooperation. First, a novel framework based on a dominant source model in distributed WASNs for resolving the activity detection of multiple speech sources in a reverberant and noisy environment is introduced. A preliminary rank-one multiplicative non-negative independent component analysis (M-NICA) for unique dominant energy source extraction given associated node clusters is presented. Partitional algorithms that minimize the within-cluster mean absolute deviation (MAD) and weighted MAD objectives are proposed to determine the cluster membership of the unmixed energies, and thus establish a source specific voice activity recognition. In a second study, improving the energy signal separation to alleviate the multiple source activity discrimination task is targeted. Sparsity inducing penalties are enforced on iterative rank-one singular value decomposition layers to extract sparse right rotations. Then, sparse non-negative blind energy separation is realized using multiplicative updates. Hence, the multiple source detection problem is converted into a sparse non-negative source energy decorrelation. Sparsity tunes the supposedly non-active energy signatures to exactly zero-valued energies so that it is easier to identify active energies and an activity detector can be constructed in a straightforward manner. In a centralized scenario, the activity decision is controlled by a fusion center that delivers the binary source activity detection for every participating energy source. This strategy gives precise detection results for small source numbers. With a growing number of interfering sources, the distributed detection approach is more promising. Conjointly, a robust distributed energy separation algorithm for multiple competing sources is proposed. A robust and regularized $t_{\nu}M$-estimation of the covariance matrix of the mixed energies is employed. This approach yields a simple activity decision using only the robustly unmixed energy signatures of the sources in the WASN. The performance of the robust activity detector is validated with a distributed adaptive node-specific signal estimation method for speech enhancement. The latter enhances the quality and intelligibility of the signal while exploiting the accurately estimated multi-source voice decision patterns. In contrast to the original M-NICA for source separation, the extracted binary activity patterns with the robust energy separation significantly improve the node-specific signal estimation. Due to the increased computational complexity caused by the additional step of energy signal separation, a new approach to solving the detection question of multi-device multi-source networks is presented. Stability selection for iterative extraction of robust right singular vectors is considered. The sub-sampling selection technique provides transparency in properly choosing the regularization variable in the Lasso optimization problem. In this way, the strongest sparse right singular vectors using a robust $\ell_1$-norm and stability selection are the set of basis vectors that describe the input data efficiently. Active/non-active source classification is achieved based on a robust Mahalanobis classifier. For this, a robust $M$-estimator of the covariance matrix in the Mahalanobis distance is utilized. Extensive evaluation in centralized and distributed settings is performed to assess the effectiveness of the proposed approach. Thus, overcoming the computationally demanding source separation scheme is possible via exploiting robust stability selection for sparse multi-energy feature extraction. With respect to the labeling problem of various sources in a WASN, a robust approach is introduced that exploits the direction-of-arrival of the impinging source signals. A short-time Fourier transform-based subspace method estimates the angles of locally stationary wide band signals using a uniform linear array. The median of angles estimated at every frequency bin is utilized to obtain the overall angle for each participating source. The features, in this case, exploit the similarity across devices in the particular frequency bins that produce reliable direction-of-arrival estimates for each source. Reliability is defined with respect to the median across frequencies. All source-specific frequency bands that contribute to correct estimated angles are selected. A feature vector is formed for every source at each device by storing the frequency bin indices that lie within the upper and lower interval of the median absolute deviation scale of the estimated angle. Labeling is accomplished by a distributed clustering of the extracted angle-based feature vectors using consensus averaging