Most of the well-known classic beamformers have resulted from optimization problems that minimize a cost function such as the mean-square error (MSE) between the noisy speech and a reference clean speech. The rationale behind these formulations involves a speech-versus-noise dichotomy, where anything branded as noise shall be suppressed as much as possible. While leading to simple closed-form solutions and reasonably practical beamformers, this rationale has its own limitations, for instance, when the ambient noise provides context and is therefore not entirely undesirable. In this article, we offer a new rationale, where the output of the beamformer is minimally processed with respect to a certain reference signal, as long as a given performance criterion is fulfilled. We provide a case study where the performance criterion is inspired by the Speech Intelligibility Index (SII), and the processing penalty is MSE. Regarding the reference signal, we consider two cases. In the first case, the reference signal is set to the unprocessed recording from a reference microphone, giving rise to a beamformer that limits the processing of the noisy signal to a minimum necessary for fulfilling the intelligibility requirement. For the second case, the reference signal is the output of an aggressive beamformer, yielding a beamformer that essentially eliminates the noise unless the concomitant distortion of the clean speech violates the intelligibility requirement. Through simulation studies, we demonstrate some of the benefits that each of the two cases offer in relevant contexts.

One of the challenges with the implementation of multi-microphone noise reduction systems in practical applications lies in the need for the knowledge of the speech and noise covariance matrices. Recently, a method based on Maximum Likelihood (ML) estimation addressed this problem. Despite its relative success in practical setups, this method may suggest negative spectral components for the clean speech due to noise influences. In this paper, we suggest a new estimation technique that tackles this issue by enforcing a power constraint on the estimation problem. We compare the proposed method with the ML method both in synthetic and real-life scenarios using objective measures. The results suggest that the proposed method can improve speech quality without a loss of intelligibility.

From the eardrum to the auditory cortex, where acoustic stimuli are decoded, there are several stages of auditory processing and transmission where information may potentially be lost. In this paper, we aim at quantifying the total information loss in the human auditory system by using information theoretic tools. To do so, we consider a speech communication model, where words are uttered and sent through a noisy channel, and then received and processed by a human listener. We define a notion of information loss that is related to the human word recognition rate. To assess the word recognition rate of humans, we conduct a closed-vocabulary intelligibility test. We derive upper and lower bounds on the information loss. Simulations reveal that the bounds are tight and we observe that the information loss in the human auditory system increases as the signal to noise ratio (SNR) decreases. Our framework also allows us to study whether humans are optimal in terms of speech perception in a noisy environment. Toward that end, we derive optimal classifiers and compare the human and machine performance in terms of information loss and word recognition rate. We observe a higher information loss and lower word recognition rate for humans compared to the optimal classifiers. In fact, depending on the SNR, the machine classifier may outperform humans by as much as 8 dB. This implies that for the speech-in-stationary-noise setup considered here, the human auditory system is suboptimal for recognizing noisy words.

Due to the distributed structure of many modern audio transmission setups, it is likely to have an observation at the receiver which is correlated with the desired source at the transmitter. This observation could be used as side information to reduce the transmission rate using distributed source coding. How to integrate distributed source coding into the perceptual audio compression procedure is thus a fundamental question. In this paper, we take a completely analytical approach to this problem, in particular to the rate-distortion trade-off and the corresponding coding schemes. We then interpret the results from an audio coding perspective. The main result is that, to upgrade a regular perceptual audio coder to a distributed coder, one needs to revise the perceptual masking curve. The revised masking curve models the availability of the side information as an extra masking effect, yielding lower rates. Interestingly, this means that at least conceptually, the distributed coding scenario could be integrated into the audio coder with minor changes, and without destructing the original coder.

We formulate a new problem which bridges between source coding and enhancement in wireless acoustic sensor networks. We consider a network of wireless microphones, each of which encoding its own measurement under a covariance matrix distortion constraint and sending it to a fusion center. To process the data at the center, we use a recent spatio-temporal prediction filter. We assume that a weighted sum-rate for the network is specified. The problem is to allocate optimal distortion matrices to the nodes in order to achieve a maximum output SNR at the fusion center after processing the received data, while the weighted sum-rate for the network is no more than the specified value. We formulate this problem as an optimization problem for which we derive a set of equalities imposed on the solution by studying the KKT conditions. In particular, for the special case of scalar sources with two microphones and a sum-rate constraint, we derive the distortion allocation in closed form and will show that if the given sum-rate is higher than a critical value, the stationary points from the KKT conditions lead to distortion allocations which maximize the output SNR of the filter.

In this paper, we consider the problem of remote vector Gaussian source coding for a wireless acoustic sensor network. Each node receives messages from multiple nodes in the network and decodes these messages using its own measurement of the sound field as side information. The node's measurement and the estimates of the source resulting from decoding the received messages are then jointly encoded and transmitted to a neighbouring node in the network. We show that for this distributed source coding scenario, one can encode a so-called conditional sufficient statistic of the sources instead of jointly encoding multiple sources. We focus on the case where node measurements are in form of noisy linearly mixed combinations of the sources and the acoustic channel mixing matrices are invertible. For this problem, we derive the rate-distortion function for vector Gaussian sources and under covariance distortion constraints.

In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide some cases, where the RDF can be derived exactly. We also show that previous results on specific instances of this problem can be generalized using our results. We finally show that if the distortion measure is the mean squared error, or if it is replaced by a certain mutual information constraint, the optimal rate can be derived from our main result.