With the emergence of wireless sensor networks (WSNs), many traditional signal processing tasks are required to be computed in a distributed fashion, without transmissions of the raw data to a centralized processing unit, due to the limited energy and bandwidth resources available to the sensors. In this paper, we propose a distributed independent component analysis (ICA) algorithm, which aims at identifying the original signal sources based on observations of their mixtures measured at various sensor nodes. One of the most commonly used ICA algorithms is known as FastICA, which requires a spatial pre-whitening operation in the first step of the algorithm. Such a pre-whitening across all nodes of a WSN is impossible in a bandwidth-constrained distributed setting as it requires to correlate each channel with each other channel in the WSN. We show that an explicit network-wide pre-whitening step can be circumvented by leveraging the properties of the so-called Distributed Adaptive Signal Fusion (DASF) framework. Despite the lack of such a network-wide pre-whitening, we can still obtain the$Q$least Gaussian independent components of the centralized ICA solution, where$Q$scales linearly with the required communication load.

Various new brain-computer interface technologies or neuroscience applications require decoding stimulus-following neural responses to natural stimuli such as speech and video from, e.g., electroencephalography (EEG) signals. In this context, generalized canonical correlation analysis (GCCA) is often used as a group analysis technique, which allows the extraction of correlated signal components from the neural activity of multiple subjects attending to the same stimulus. GCCA can be used to improve the signal-to-noise ratio of the stimulus-following neural responses relative to all other irrelevant (non-)neural activity, or to quantify the correlated neural activity across multiple subjects in a group-wise coherence metric. However, the traditional GCCA technique is stimulus-unaware: no information about the stimulus is used to estimate the correlated components from the neural data of several subjects. Therefore, the GCCA technique might fail to extract relevant correlated signal components in practical situations where the amount of information is limited, for example, because of a limited amount of training data or group size. This motivates a new stimulus-informed GCCA (SI-GCCA) framework that allows taking the stimulus into account to extract the correlated components. We show that SI-GCCA outperforms GCCA in various practical settings, for both auditory and visual stimuli. Moreover, we showcase how SI-GCCA can be used to steer the estimation of the components towards the stimulus. As such, SI-GCCA substantially improves upon GCCA for various purposes, ranging from preprocessing to quantifying attention.

OBJECTIVE: Building large-scale data bases of biomedical signal recordings for training artificial-intelligence systems involves substantial human effort in data processing and annotation. In the case of event detection, experts need to exhaustively scroll through the recordings and highlight events of interest. METHODS: We propose an iterative annotation support algorithm with a human in the loop to improve the efficiency of the annotation process. Our algorithm generates proposal events based on an event detection model trained on incomplete annotations. The human only needs to verify candidate events proposed by the tool instead of scrolling through the entire data set. Our algorithm iterates between proposal generation and verification to leverage the human-in-the-loop feedback to obtain a growing set of event annotations. RESULTS: Our algorithm finds a substantial amount of events at a fraction of the human time spent when comparing with a benchmark method and the normal manual process, finding all events in one data set and 70% of events in another with the human-in-the-loop only viewing 20% of the data. CONCLUSION: Our results show that combining human and computer effort can substantially speed up the annotation process for events in biomedical signal processing. SIGNIFICANCE: Due to its simplicity and minimal reliance on task-specific information, our algorithm is broadly applicable, unlocking substantial improvements in the scalability and efficiency of biomedical signal annotation.

We propose a dynamic sensor selection approach for deep neural networks (DNNs), which is able to derive an optimal sensor subset selection for each specific input sample instead of a fixed selection for the entire dataset. This dynamic selection is jointly learned with the task model in an end-to-end way, using the Gumbel-Softmax trick to allow the discrete decisions to be learned through standard backpropagation. We then show how we can use this dynamic selection to increase the lifetime of a wireless sensor network (WSN) by imposing constraints on how often each node is allowed to transmit. We further improve performance by including a dynamic spatial filter that makes the task-DNN more robust against the fact that it now needs to be able to handle a multitude of possible node subsets. Finally, we explain how the selection of the optimal channels can be distributed across the different nodes in a WSN. We validate this method on a use case in the context of body-sensor networks, where we use real electroencephalography (EEG) sensor data to emulate an EEG sensor network for motor execution decoding. For this use case, we demonstrate that the distributed algorithm -with only a small amount of cooperation between the nodes- achieves a performance close to the upper bound defined by a fully centralized dynamic selection (maximum absolute decrease of 4% in accuracy). Furthermore, we observe that our dynamic sensor selection framework can achieve large reductions in transmission energy with a limited cost to the task accuracy, validating it as a practical tool for increasing the lifetime of body-sensor networks.

Selective attention enables humans to efficiently process visual stimuli by enhancing important elements and filtering out irrelevant information. Locating visual attention is fundamental in neuroscience with potential applications in brain-computer interfaces. Conventional paradigms often use synthetic stimuli or static images, but visual stimuli in real life contain smooth and highly irregular dynamics. We show that these irregular dynamics can be decoded from electroencephalography (EEG) signals for selective visual attention decoding. To this end, we propose a free-viewing paradigm in which participants attend to one of two superimposed videos, each showing a center-aligned person performing a stage act. Superimposing ensures that the relative differences in the neural responses are not driven by differences in object locations. A stimulus-informed decoder is trained to extract EEG components correlated with the motion patterns of the attended object, and can detect the attended object in unseen data with significantly above-chance accuracy. This shows that the EEG responses to naturalistic motion are modulated by selective attention. Eye movements are also found to be correlated to the motion patterns in the attended video, despite the spatial overlap with the distractor. We further show that these eye movements do not dominantly drive the EEG-based decoding and that complementary information exists in EEG and gaze data. Moreover, our results indicate that EEG may also capture neural responses to unattended objects. To our knowledge, this study is the first to explore EEG-based selective visual attention decoding on natural videos, opening new possibilities for experiment design.

Change Point Detection (CPD) refers to the task of identifying abrupt changes in the characteristics or statistics of time series data. Recent advancements have led to a shift away from traditional model-based CPD approaches, which rely on predefined statistical distributions, toward neural network-based and distribution-free methods using autoencoders. However, many state-of-the-art methods in this category often neglect to explicitly leverage spatial information across multiple channels, making them less effective at detecting changes in cross-channel statistics. In this paper, we introduce an unsupervised, distribution-free CPD method that explicitly incorporates both temporal and spatial (cross-channel) information in multi-channel time series data based on the so-called Time-Invariant Representation (TIRE) autoencoder. Our evaluation, conducted on both simulated and real-life datasets, illustrates the significant advantages of our proposed multi-channel TIRE (MC-TIRE) method, which consistently delivers more accurate CPD results.

It is possible to decode auditory attention to speech from electrophysiological brain recordings such as electroencephalography (EEG). Such an auditory attention decoding (AAD) allows, e.g., to determine to which person a listener is attending in a multi-talker scenario. The vast majority of research has focused on developing supervised AAD algorithms in which the decoder is trained based on ground truth labels about the attention to each speaker. However, to work optimally, the trained decoders must be subject-specific and adapt over time to track sudden changes in signal statistics (e.g. electrode failures). Since it is often impractical to regularly retrain these decoders with a dedicated calibration session, an unsupervised algorithm has recently emerged as an alternative.In this paper, we show that the state-of-the-art unsupervised AAD algorithm is biased by its initialisation, which leads to a suboptimal convergence. This bias has the largest effect when only a limited amount of data is available to train it, e.g. to train an unsupervised decoder that can quickly adapt to sudden changes. We show that this bias can be easily removed, leading to a better classification accuracy. However, the gain in accuracy reduces as the number of classified segments increases.

Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive signal fusion (DASF) algorithm solves this problem by having the nodes collaboratively solve low-dimensional versions of the original optimization problem, relying solely on the exchange of compressed views of the sensor data between the nodes. However, the DASF algorithm has only been shown to converge for filtering problems that can be expressed as smooth optimization problems. In this paper, we explore an extension of the DASF algorithm to a family of non-smooth spatial filtering problems, allowing the addition of non-smooth regularizers to the optimization problem, which could for example be used to perform node selection, and eliminate nodes not contributing to the filter objective, therefore further reducing communication costs. We provide a convergence proof of the non-smooth DASF algorithm and validate its convergence via simulations in both a static and adaptive setting.

Spatial filtering procedures aim to optimally fuse the different signals collected in a sensor array, by exploiting their inter-channel correlations. If the sensors are physically distributed, as it is the case in a wireless sensor network, the inter-channel statistics cannot directly be measured or tracked, unless the data is transmitted to a central processor, which is not always possible due to energy or bandwidth constraints. The so-called distributed adaptive signal fusion (DASF) algorithm allows to solve such problems in a distributed fashion with a reduced communication burden. The DASF algorithm iterates over the different nodes of the network, each solving a local compressed version of the original (centralized) optimization problem. However, if the solver for these local optimization problems is in itself also iterative, the computational burden can become quite large as these iterations are nested within the DASF iterations. In this paper, we focus on Dinkelbach's iterative procedure to solve fractional programs, i.e., problems of which the objective function is a ratio of two continuous functions. We propose the fractional DASF (F-DASF) algorithm which interleaves the iterations of DASF with those of Dinkelbach's procedure, to reduce the computational burden without affecting the convergence properties of the original DASF algorithm.

Neural Source Coding (NSC) is a technique that exploits the modelling power of (deep) neural network for the purpose of source coding. Its goal is to transform the data into a space of low entropy, where they can be coded by classic entropy coding schemes. In this paper, our goal is to investigate the use of NSC in so-called neuro-sensor networks, i.e., a type of body-sensor network consisting of a collection of wireless sensor nodes that record brain activity at different scalp locations, e.g., via electroencephalography (EEG) sensors. All nodes wirelessly transmit their data to a fusion center, where inference is then performed on the joint sensor signals by a given deep neural network. The NSC parameters and inference network are learned jointly, optimizing the trade-off between accuracy and bitrate for a given application. We validate this method on a motor execution task in an emulated EEG sensor network and compare the resulting trade-offs with those obtained by directly quantizing the transmitted data to low-bit precision. We demonstrate that NSC yields more favorable trade-offs than straightforward quantization for very low bit depths and allows for large bandwidth gains at little loss in accuracy on the investigated brain-computer interface (BCI) task.

Change point detection (CPD) refers to the problem of detecting changes in the statistics of pseudo-stationary signals or time series. A recent trend in CPD research is to replace the traditional statistical tests with distribution-free autoencoder-based algorithms, which can automatically learn complex patterns in time series data. In particular, the so-called time-invariant representation (TIRE) models have gained traction, as these separately encode time-variant and time-invariant subfeatures, as opposed to traditional autoencoders. However, optimizing the trade-off between two loss terms, i.e., the reconstruction loss and the time-invariant loss, is challenging. To address this issue, we propose a novel loss function that elegantly combines both losses without the need for manually tuning a trade-off hyperparameter. We demonstrate that this new hyperparameter-free loss, in combination with a relatively simple convolutional neural network (CNN), consistently achieves superior or comparable performance compared to the manually-tuned baseline TIRE models across diverse benchmark datasets, both simulated and real-life. In addition, we present a representation analysis, demonstrating that the distribution of the time-invariant features extracted by our model is more concentrated within the same segment (more so than with previous TIRE models), which implies that these features can potentially be used for other applications, such as classification and clustering.

In this paper, we describe a design methodology to design distributed neural network architectures that can perform efficient inference within sensor networks with communication bandwidth constraints. The different sensor channels are distributed across multiple sensor devices, which have to exchange data over bandwidth-limited communication channels to solve a classification task. Our design methodology starts from a centralized neural network and transforms it into a distributed architecture in which the channels are distributed over different nodes. The distributed network consists of two parallel branches, whose outputs are fused at the fusion center. The first branch collects classification results from local, node-specific classifiers while the second branch compresses each node's signal and then reconstructs the multi-channel time series for classification at the fusion center. We further improve bandwidth gains by dynamically activating the compression path when the local classifications do not suffice. We validate this method on a motor execution task in an emulated EEG sensor network and analyze the resulting bandwidth-accuracy trade-offs. Our experiments show that the proposed framework enables up to a factor 20 in bandwidth reduction and factor 9 in power reduction with minimal loss (up to 2%) in classification accuracy compared to the centralized baseline on the demonstrated task. The proposed method offers a way to transform a centralized architecture to a distributed, bandwidth-efficient network amenable for low-power sensor networks. While the application focus of this paper is on wearable brain-computer interfaces, the proposed methodology can be applied in other sensor network-like applications as well.

The goal of auditory attention decoding (AAD) is to determine to which speaker out of multiple competing speakers a listener is attending based on the brain signals recorded via, e.g., electroencephalography (EEG). AAD algorithms are a fundamental building block of so-called neuro-steered hearing devices that would allow identifying the speaker that should be amplified based on the brain activity. A common approach is to train a subject-specific stimulus decoder that reconstructs the amplitude envelope of the attended speech signal. However, training this decoder requires a dedicated 'ground-truth' EEG recording of the subject under test, during which the attended speaker is known. Furthermore, this decoder remains fixed during operation and can thus not adapt to changing conditions and situations. Therefore, we propose an online time-adaptive unsupervised stimulus reconstruction method that continuously and automatically adapts over time when new EEG and audio data are streaming in. The adaptive decoder does not require ground-truth attention labels obtained from a training session with the end-user and instead can be initialized with a generic subject-independent decoder or even completely random values. We propose two different implementations: a sliding window and recursive implementation, which we extensively validate on three independent datasets based on multiple performance metrics. We show that the proposed time-adaptive unsupervised decoder outperforms a time-invariant supervised decoder, representing an important step toward practically applicable AAD algorithms for neuro-steered hearing devices.

Auditory attention decoding (AAD) algorithms decode the auditory attention from electroencephalography (EEG) signals that capture the listener’s neural activity. Such AAD methods are believed to be an important ingredient towards so-called neuro-steered assistive hearing devices. For example, traditional AAD decoders allow detecting to which of multiple speakers a listener is attending to by reconstructing the amplitude envelope of the attended speech signal from the EEG signals. Recently, an alternative paradigm to this stimulus reconstruction approach was proposed, in which the directional focus of auditory attention is determined instead, solely based on the EEG, using common spatial pattern filters (CSP). Here, we propose Riemannian geometry-based classification (RGC) as an alternative for this CSP approach, in which the covariance matrix of a new EEG segment is directly classified while taking its Riemannian structure into account. While the proposed RGC method performs similarly to the CSP method for short decision lengths (i.e., the amount of EEG samples used to make a decision), we show that it significantly outperforms it for longer decision window lengths.

When multiple speakers talk simultaneously, a hearing device cannot identify which of these speakers the listener intends to attend to. Auditory attention decoding (AAD) algorithms can provide this information by, for example, reconstructing the attended speech envelope from electroencephalography (EEG) signals. However, these stimulus reconstruction decoders are traditionally trained in a supervised manner, requiring a dedicated training stage during which the attended speaker is known. Pre-trained subject-independent decoders alleviate the need of having such a per-user training stage but perform substantially worse than supervised subject-specific decoders that are tailored to the user. This motivates the development of a new unsupervised self-adapting training/updating procedure for a subject-specific decoder, which iteratively improves itself on unlabeled EEG data using its own predicted labels. This iterative updating procedure enables a self-leveraging effect, of which we provide a mathematical analysis that reveals the underlying mechanics. The proposed unsupervised algorithm, starting from a random decoder, results in a decoder that outperforms a supervised subject-independent decoder. Starting from a subject-independent decoder, the unsupervised algorithm even closely approximates the performance of a supervised subject-specific decoder. The developed unsupervised AAD algorithm thus combines the two advantages of a supervised subject-specific and subject-independent decoder: it approximates the performance of the former while retaining the 'plug-and-play' character of the latter. As the proposed algorithm can be used to automatically adapt to new users, as well as over time when new EEG data is being recorded, it contributes to more practical neuro-steered hearing devices.

In sensor arrays or sensor networks, tracking each sensors utility helps in excluding those which do not sufficiently contribute to the task at hand, thereby reducing energy consumption or avoiding model overfitting. In a linearly-constrained minimum variance (LCMV) beamformer, the utility of a sensor is defined as the increase in the beamformer's output noise power when the sensor would be removed and the beamformer coefficients re-optimized. An expression to efficiently compute this utility metric has been found for the case where each sensor removal corresponds to a single beamformer coefficient. However, in a filter-and-sum implementation, a single sensor is filtered by a group of beamformer coefficients. Furthermore, sometimes one wants to track the joint utility of a group of sensors. In this paper we derive a generalized expression to efficiently calculate the utility of such groups as a whole, called the group-utility. We show that the computational complexity of this generalized expression is negligible if the number of groups is larger than the group sizes, leading to a very efficient group-utility computation compared to the straightforward implementation. Furthermore, an efficient updating equation re-optimizing the LCMV beamformer when a group of G beamformer inputs is removed is found as a by-product.

When inserting an electrode array in the brain, its electrodes will record so-called 'spikes' which are generated by the neurons in the neighbourhood of the array. Spike sorting is the process of detecting and assigning these recorded spikes to their putative neurons. Many spike sorting pipelines rely on a clustering algorithm that groups the spikes coming from the same neuron in a pre-defined feature space. However, classical spike sorting algorithms fail when spike overlap, i.e., the near-simultaneous occurrence of two or more spikes from different neurons, is present in the recording. In such cases, the overlapping spikes segment ends up in a seemingly random position in the feature space and is not assigned to the correct cluster. This problem has been addressed before by extending the sorting algorithm with a template matching post-processor. In this work, a novel approach is presented to resolve spike overlap directly in the feature space. To this end, a neural network feature map is presented, that generates spike embeddings (feature vectors) that behave as a linear superposition in the feature space in the case of spike overlap. Its performance is quantified on semi-synthetic data obtained through a data augmentation procedure applied to real neural recordings.

Advances in electroencephalography (EEG) equipment now allow monitoring of people with epilepsy in their daily-life environment. The large volumes of data that can be collected from long-term out-of-clinic monitoring require novel algorithms to process the recordings on board of the device to identify and log or transmit only relevant data epochs. Existing seizure-detection algorithms are generally designed for post-processing purposes, so that memory and computing power are rarely considered as constraints. We propose a novel multi-channel EEG signal processing method for automated absence seizure detection which is specifically designed to run on a microcontroller with minimal memory and processing power. It is based on a linear multi-channel filter that is precomputed offline in a data-driven fashion based on the spatial-temporal signature of the seizure and peak interference statistics. At run-time, the algorithm requires only standard linear filtering operations, which are cheap and efficient to compute, in particular on microcontrollers with a multiply-accumulate unit (MAC). For validation, a dataset of eight patients with juvenile absence epilepsy was collected. Patients were equipped with a 20-channel mobile EEG unit and discharged for a day-long recording. The algorithm achieves a median of 0.5 false detections per day at 95% sensitivity. We compare our algorithm with state-of-the-art absence seizure detection algorithms and conclude it performs on par with these at a much lower computational cost.

Energy efficiency is crucial for a wireless sensor network (WSN) since its nodes are generally powered by energy sources of limited capacity, such as batteries. The bit depth used to quantize the sensor signal samples heavily influences energy consumption, as it strongly impacts the amount of information to be transmitted between the sensor nodes. Bit depth allocation problems seek to assign a certain bit depth to each sensor signal such that energy consumption is minimized while respecting a performance constraint. For multi-channel signal estimation tasks these problems are generally non-convex, and they are often solved through simplifying assumptions or through convex relaxation. However, for linear minimum mean squared error (MMSE) estimation, we show how the matrix inversion lemma allows to transform the MMSE constraint into a convex constraint, which can then be interpreted as a constraint on the excess MMSE due to quantization. As a result, as long as the cost function representing energy consumption is convex, this class of bit depth allocation problems is convex, i.e., if the bit depth variable is relaxed to a real-valued variable. This guarantees global optimality up to discretization of the obtained solution.

Spike sorting is the process of assigning each detected neuronal spike in an extracellular recording to its putative source neuron. A linear filter design is proposed where the filter output allows for threshold-based spike sorting of high-density neural probe data. The proposed filter design is based on optimizing the signal-to-peak-interference ratio for each detectable neuron in a data-driven way. Threshold-based spike sorting using linear filters is particularly interesting for real-time spike sorting because of the low computational complexity and predictable delay of those filters, enabling closed-loop neuroscience with unit-activity controlled brain stimulation. We validate our method on both paired and hybrid in-vivo recorded high-density data.

In this demonstration, we aim at presenting our recent implementation results and provide an evaluation testbed through which users can experiment and compare the outputs of the distributed speech enhancement algorithms in [1-3]. The system allows a user to assess the merits of these algorithms in any acoustic setup. The multi-channel Wiener filter (MWF) is a well-known noise reduction algorithm for multi-microphone speech processing applications. In general, the noise reduction improves as the number of available microphones increases, since a better spatial sampling or diversity can be exploited. Motivated by this, wireless acoustic sensor networks (WASNs), consisting of a multitude of collaborating nodes with an embedded signal processing unit and microphone array, have been proposed to increase the spatial diversity of multi-microphone systems. However, due to the limited per-node computational power and communication bandwidth, reduced-bandwidth distributed processing is more favorable than a centralized processing where all the microphone signals are transmitted to a fusion center. In this demo, we evaluate the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm [1] which is essentially a distributed realization of the MWFs of the individual nodes of a WASN and allows the nodes to cooperate by exchanging pre-filtered and compressed signals, while eventually converging to the same centralized MWF solutions as if each node would have access to all the microphone signals in theWASN [1,2]. In the original version of DANSE in [1], the required speech correlation matrices are estimated using a straightforward subtraction-based method. This method, however, has been shown to deliver an unsatisfying performance in the presence of second-order statistics error (e.g., due to low-SNR conditions, highly non-stationary noise or erroneous voice activity detections (VADs)) [4]. An alternative version of DANSE, called generalized eigenvalue decomposition (GEVD)-based DANSE, has been developed in [3] in which each node incorporates a GEVD-based low-rank approximation of the speech correlation matrix in its local MWF. An in-depth theoretical study of the underlying principals of the GEVD-based DANSE algorithm has been presented in [3]. In order to also evaluate the merits of the GEVD-based DANSE algortihm in a practical realistic environment, a real-time experimental setup has been developed which will be explained in the next section.

Microphone arrays allow to exploit the spatial coherence between simultaneously recorded microphone signals, e.g., to perform speech enhancement, i.e., to extract a speech signal and reduce background noise. However, in systems where the microphones are not sampled in a synchronous fashion, as it is often the case in wireless acoustic sensor networks, a sampling rate offset (SRO) exists between signals recorded in different nodes, which severely affects the speech enhancement performance. To avoid this performance reduction, the SRO should be estimated and compensated for. In this paper, we propose a new approach to blind SRO estimation for an asynchronous wireless acoustic sensor network, which exploits the phase drift of the coherence between the asynchronous microphones signals. We utilize the fact that the SRO causes a linearly increasing time delay between two signals and hence a linearly increasing phase-shift in the short-time Fourier transform domain. The increasing phase shift, observed as a phase drift of the coherence between the signals, is used in a weighted least-squares framework to estimate the SRO. This method is referred to as least-squares coherence drift (LCD). Experimental results in different real-world recording and simulated scenarios show the effectiveness of LCD compared to different benchmark methods. The LCD is effective even for short signal segments. We finally demonstrate that the use of the LCD within a conventional compensation approach eliminates the performance loss due to SRO in a speech enhancement algorithm based on the multichannel Wiener filter.

Speech enhancement in wireless acoustic sensor networks requires the exchange of audio signals. Since the wireless communication often dominates the nodes’ energy budget, techniques for data exchange reduction are crucial. Adaptive quantization aims to optimize the bit depth of each exchanged signal according to its contribution to the speech enhancement performance. This enables the network to scale its energy and communication bandwidth requirements according to the current operating environment. The impact metric was previously proposed to predict the effect of quantization in linear minimum mean squared error (MMSE) estimation. We provide new insights into greedy adaptive quantization based on this impact metric. We achieve this by expanding the mathematical framework to include a new metric based on the gradient of the MMSE as a function of the quantization noise power. Using these tools, we show how the MMSE gradient naturally leads to a greedy algorithm and how the impact metric is a generalization of the gradient metric and a previously proposed metric. Besides, we validate the impact metric for adaptive quantization both in a simulated and in a real wireless acoustic sensor network deployed in a home environment, showing the energy savings achievable through greedy adaptive quantization.

The linearly constrained minimum variance (LCMV) beamformer has been widely employed to extract (a mixture of) multiple desired speech signals from a collection of microphone signals, which are also polluted by other interfering speech signals and noise components. In many practical applications, the LCMV beamformer requires that the subspace corresponding to the desired and interferer signals is either known, or estimated by means of a data-driven procedure, e.g., using a generalized eigenvalue decomposition (GEVD). In practice, however, it often occurs that insufficient relevant samples are available to accurately estimate these subspaces, leading to a beamformer with poor output performance. In this paper we propose a subspace projection-based approach to improve the performance of the LCMV beamformer by exploiting the available data more efficiently. The improved performance achieved by this approach is demonstrated by means of simulation results.

We study a distributed node-specific parameter estimation problem where each node in a wireless sensor network is interested in the simultaneous estimation of different vectors of parameters that can be of local interest, of common interest to a subset of nodes, or of global interest to the whole network. We assume a setting where the nodes do not know which other nodes share the same estimation interests. First, we conduct a theoretical analysis on the asymptotic bias that results in case the nodes blindly process all the local estimates of all their neighbors to solve their own node-specific parameter estimation problem. Next, we propose an unsupervised diffusion-based LMS algorithm that allows each node to obtain unbiased estimates of its node-specific vector of parameters by continuously identifying which of the neighboring local estimates correspond to each of its own estimation tasks. Finally, simulation experiments illustrate the efficiency of the proposed strategy.

The ability to efficiently assess and track the utility of each sensor signal is crucial to reduce the energy consumption in a wireless sensor network (WSN), e.g., by putting the sensors with low utility to sleep. Methods to track the sensor signal utility have been described for several multichannel signal estimation methods. For linear minimum mean squared error (LMMSE) estimation, the utility of a sensor signal is defined as the predicted increase in the minimum mean squared error when the sensor would be shut down. However, rather than making such a binary decision, more flexible energy-saving methods could be considered where a sensor changes internal parameters such as, e.g., the number of bits per sample, which results in noise injection in the transmitted sensor signal. We propose a generalization of the original definition of sensor signal utility to include this effect, and we show that it can be efficiently computed and tracked at hardly any computational cost compared to the already available LMMSE estimator. In addition, we illustrate how it can be used to assign a number of bits to each sensor with a greedy approach. Simulation results show that a greedy assignment based on the proposed generalized utility leads to improved results compared to the original utility measure.

A general binaural noise reduction system is considered that employs the multichannel Wiener filter with partial noise estimation (MWFη) allowing for an explicit tradeoff between noise reduction and binaural noise cue preservation. In this paper, it is assumed that along with the general binaural system, a remote microphone signal with a high input signal-to-noise ratio (SNR) is available for inclusion in the MWFη. The use of this remote microphone signal with a high input SNR allows for a simultaneous increase in both noise reduction performance and preservation of the binaural noise cues. To further increase the performance, a modification to the partial noise estimation (PNE) variable, η, is proposed which relies on exploiting the aforementioned trade-off by either constraining the output SNR or binaural noise cues to the same level before and after the addition of the remote microphone signal. The validity of the theoretical results are supplemented via simulations using a binaural setup with a single speech and noise source.

Using periodic auditory stimuli, it is possible to evoke so-called auditory steady-state responses (ASSRs) in the brain, which can be measured using electroencephalography (EEG). They can be used to objectively estimate frequency-specific hearing thresholds, which is especially useful for early hearing assessment in newborns. The main problem is the extremely low signal-to-noise ratio (SNR), necessitating long measurements of up to an hour for a full audiometric assessment. To speed up the detection, we apply a linear spatial filter to the multi-channel EEG measurements, resulting in a new 'virtual' channel with optimal SNR. To ensure robustness, we then consider a hybrid ASSR detection method in which the original EEG channels are complemented with this virtual channel. The addition of this virtual channel successfully speeds up the detection of ASSRs by over 15 %. Furthermore our method not only speeds up the detection, but also greatly improves its sensitivity, in particular in the (clinically most relevant) lowest SNR scenarios. This could help reduce the gap that still exists between behaviourally and objectively obtained hearing thresholds.

In this paper, we consider the problem of distributed estimation of node-specific signals in a fully-connected wireless sensor network with multi-sensor nodes. The estimation relies on a data-driven design of a spatial filter, referred to as the generalized eigenvalue decomposition (GEVD)-based multi-channel Wiener filter (MWF). In non-stationary or low-SNR conditions, this GEVD-based MWF has been demonstrated to be more robust than the original MWF due to an inherent GEVD-based low-rank approximation of the sensor signal correlation matrix. In a centralized realization where a fusion center has access to all the nodes' sensor signal observations, the network-wide sensor signal correlation matrix and its low-rank approximation can be directly estimated from the sensor signals. However, in this paper we aim to avoid centralizing the sensor signal observations, in which case this network-wide correlation matrix cannot be estimated. We introduce a distributed algorithm which is able to significantly compress the broadcast signals while still converging to the centralized GEVD-based MWF as if each node would have access to all sensor signal observations.

We study a distributed node-specific signal estimation problem where the node-specific desired signals and/or the sensor observations can have partially-overlapping latent signal subspaces. First, we provide the minimum number of linear combinations of observed sensor signals that each node can broadcast to still let all other nodes achieve the network-wide Linear Minimum Mean-Square Error (LMMSE) estimate of their node-specific desired signals. Later, for a fully-connected wireless sensor network, we derive a distributed algorithm that, under some settings, allows each node to achieve the LMMSE estimate of its node-specific desired signals by broadcasting the smallest number of signals. Unlike the existing algorithms, the proposed algorithm deals with the problem of partially-overlapping node-specific interests and incomplete observability of all latent sources at the nodes. Finally, the effectiveness of the proposed technique is shown through numerical simulations.

In this paper, we present a distributed algorithm to remove eye blink artifacts from electroencephalography (EEG) signals recorded in a modular high-density EEG system, referred to as a wireless EEG sensor network (WESN). A WESN is a particular instance of a wireless body area network for long-term non-invasive neuromonitoring, which is amenable to extreme miniaturization and low-power system design. We first propose a centralized algorithm for eye blink artifact removal (EBAR) based on the multi-channel Wiener filter (MWF). We then show how this MWF-based EBAR algorithm can be implemented in a distributed fashion to remove the eye blink artifacts in each EEG node without centralizing all the raw EEG data. Instead, the EEG nodes share fused EEG signals with each other. Nevertheless, it can be shown that the estimation performance of the distributed algorithm is equivalent to the performance of the centralized MWF, as if each EEG node had access to all the EEG channels of the WESN. This is also experimentally validated by means of recorded EEG data.

We envisage a wireless sensor network (WSN) where each node is tasked with estimating a set of node-specific desired signals that has been corrupted by additive noise. The nodes accomplish this estimation by means of the distributed adaptive node-specific estimation (DANSE) algorithm in a tree topology (T-DANSE). In this paper, we consider a network where there is at least one node with a large (virtually infinite) energy budget, which we select as the root node. We propose a modification to the signal flow of the T-DANSE algorithm where instead of each node having two-way signal communication, there is a single signal flow toward the root node of the tree topology which then broadcasts a single signal to all other nodes. We demonstrate that the modified algorithm is equivalent to the original T-DANSE algorithm in terms of the signal estimation performance, shifts a large part of the communication burden toward the highpower root node to reduce the energy consumption in the low-power nodes and reduces the input-output delay.

In this paper, we describe a distributed adaptive (time-recursive) algorithm to estimate and track the eigenvectors corresponding to the Q largest or smallest eigenvalues of the global sensor signal covariance matrix in a wireless sensor network (WSN). We only address the case of fully connected (broadcast) networks, in which the nodes broadcast compressed Q-dimensional sensor observations. It can be shown that the algorithm converges to the desired eigenvectors without explicitely constructing the global covariance matrix that actually defines them, i.e., without the need to centralize all the raw sensor observations. The algorithm allows each node to estimate (a) the node-specific entries of the global covariance matrix eigenvectors, and (b) Q-dimensional observations of the full set of sensor observations projected onto the Q estimated eigenvectors. The theoretical results are validated by means of numerical simulations.

A wireless acoustic sensor network is envisaged that is composed of distributed nodes each with several microphones. The goal of each node is to perform signal enhancement, by means of a multi-channel Wiener filter (MWF), in particular to produce an estimate of a desired speech signal. In order to reduce the number of broadcast signals between the nodes, the distributed adaptive node-specific signal estimation (DANSE) algorithm is employed. When each node broadcasts only linearly compressed versions of its microphone signals, the DANSE algorithm still converges as if all uncompressed microphone signals were broadcast. Due to the iterative and statistical nature of the DANSE algorithm several blocks of data are needed before a node can update its node-specific parameters leading to poor tracking performance. In this paper a sub-layer algorithm is presented, that operates under the primary layer DANSE algorithm, which allows nodes to update their parameters during every new block of data and is shown to improve the tracking performance in time-varying environments.

Widely linear (WL) filtering has been shown to improve performance compared to linear filtering due to its ability to incorporate the non-circularity of the signal statistics. However there has been some inconsistency in its application, specifically when constructing complex signals from real signals, which has recently been considered in the context of speech enhancement in binaural or stereo systems. This letter shows that the corresponding WL filtered output contains exactly the same information as the linear filter output while increasing the computational complexity and memory requirements.

In this paper, we revisit the distributed total least squares (D-TLS) algorithm, which operates in an ad hoc sensor network where each node has access to a subset of the equations of an overdetermined set of linear equations. The D-TLS algorithm computes the total least squares (TLS) solution of the full set of equations in a fully distributed fashion (without fusion center). We modify the D-TLS algorithm to eliminate the large computational complexity due to an eigenvalue decomposition (EVD) at every node and in each iteration. In the modified algorithm, a single power iteration (PI) is performed instead of a full EVD computation, which significantly reduces the computational complexity. Since the nodes then do not exchange their true eigenvectors, the theoretical convergence results of the original D-TLS algorithm do not hold anymore. Nevertheless, we find that this PI-based D-TLS algorithm still converges to the network-wide TLS solution, under certain assumptions, which are often satisfied in practice. We provide simulation results to demonstrate the convergence of the algorithm, even when some of these assumptions are not satisfied.

A wireless acoustic sensor network is considered with spatially distributed microphones which observe a desired speech signal that has been corrupted by noise. In order to reduce the noise the signals are sent to a fusion center where they are processed with a centralized rank-1 multi-channel Wiener filter (R1-MWF). The goal of this work is to efficiently compute an assessment of the contribution of each individual microphone with respect to either signal-to-noise ratio (SNR), signal-to-distortion ratio (SDR) or the minimized cost function referred to as the utility. These performance measures are derived by exploiting unique properties of the R1-MWF which can be computed efficiently from values that are known from the current signal estimation process. The performance measures may be used in unison or individually to determine the contributions of each microphone and help facilitate in selecting only a subset of the available signals in order to meet the bandwidth and power constraints of the system.

We consider distributed linearly constrained minimum variance (LCMV) beamforming in a wireless sensor network. Each node computes an LCMV beamformer with node-specific constraints, based on all sensor signals available in the network. A node has a local sensor array, and compresses its sensor signals to a signal with fewer channels, which is then shared with other nodes in the network. The compression rate depends inversely on the total number of linear constraints. Even though a significant compression is obtained, each node is able to generate the same outputs as a centralized LCMV beamformer, as if all sensor signals are available to every node. Since the distributed LCMV algorithm exploits a similar parametrization as previously developed distributed unconstrained MMSE signal estimation algorithms, it has similar dynamics and convergence properties. We provide simulation results to demonstrate the optimality and convergence of the algorithm.

In this paper, we propose an energy-based technique to track the power of multiple simultaneous speakers using an ad hoc microphone array with unknown microphone positions. By considering the short-term power of the microphone signals, the problem can be converted into a non-negative blind source separation (NBSS) problem. By exploiting the prior knowledge that the source signals are non-negative and well-grounded, very efficient algorithms can be used to solve this NBSS problem, based only on second order statistics. We provide simulation results that demonstrate the effectiveness of the presented algorithm.

We introduce a distributed adaptive estimation algorithm operating in an ideal fully connected sensor network. The algorithm estimates node-specific signals at each node based on reduced-dimensionality sensor measurements of other nodes in the network. If the node-specific signals to be estimated are linearly dependent on a common latent process with a low dimension compared to the dimension of the sensor measurements, the algorithm can significantly reduce the required communication bandwidth and still provide the optimal linear estimator at each node as if all sensor measurements were available in every node. Because of its adaptive nature and fast convergence properties, the algorithm is suited for real-time applications in dynamic environments, such as speech enhancement in acoustic sensor networks.

Non-negative matrix factorisation (NMF) is an unsupervised learning technique that decomposes a non-negative data matrix into a product of two lower rank non-negative matrices. The non-negativity constraint results in a parts-based and often sparse representation of the data. We use NMF to factorise a matrix with spectral slices of continuous speech to automatically find a feature set for speech recognition. The resulting decomposition yields a filter bank design with remarkable similarities to perceptually motivated designs, supporting the hypothesis that human hearing and speech production are well matched to each other. We point out that the divergence cost criterion used by NMF is linearly dependent on energy, which may influence the design. We will however argue that this does not significantly affect the interpretation of our results. Furthermore, we compare our filter bank with several hearing models found in literature. Evaluating the filter bank for speech recognition shows that the same recognition performance is achieved as with classical MEL-based features.