Adel Zahedi

Audio coding in wireless acoustic sensor networks

In this paper, we consider the problem of source coding for a wireless acoustic sensor network where each node in the network makes its own noisy measurement of the sound field, and communicates with other nodes in the network by sending and receiving encoded versions of the measurements. To make use of the correlation between the sources available at the nodes, we consider the possibility of combining the measurement and the received messages into one single message at each node instead of forwarding the received messages and separate encoding of the measurement. Moreover, to exploit the correlation between the messages received by a node and the node?s measurement of the source, we propose to use the measurement as side information and thereby form a distributed source coding (DSC) problem. Assuming that the sources are Gaussian, we then derive the rate-distortion function (RDF) for the resulting remote DSC problem under covariance matrix distortion constraints. We further show that for this problem, the Gaussian source is the worst to code. Thus, the Gaussian RDF provides an upper bound to other sources such as audio signals. We then turn our attention to audio signals. We consider an acoustical model based on the room impulse response (RIR) and provide simulation results for the rate-distortion performance in a practical setup where a set of microphones record the sound in a standard listening room. Since our reconstruction scheme and distortion measure are defined over the direct sound source, coding and dereverberation are performed in a joint manner. HighlightsWe treat the problem of source coding for wireless acoustic sensor networks.We consider vector sources to make use of the time correlation in the audio sequences.We use the measurements at the receiving nodes as side information using distributed source coding.We derive local rate-distortion functions to be used for rate allocation for an optimal sum-rate.Our encoding/decoding process is joint with dereverberation.

Distributed Remote Vector Gaussian Source Coding for Wireless Acoustic Sensor Networks

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 nodes 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.

Distributed Remote Vector Gaussian Source Coding with 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.

Coding and Enhancement in Wireless Acoustic Sensor Networks

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.

On Perceptual Audio Compression with Side Information at the Decoder

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.

Source Coding in Networks with Covariance Distortion Constraints

We first present an explicit formula R(D) for the rate-distortion function (RDF) of the vector Gaussian re- mote Wyner-Ziv problem with covariance matrix distortion constraints. To prove the lower bound, we use a particular variant of joint matrix diagonalization to establish a notion of the minimum of two symmetric positive-definite matrices. We then show that from the resulting RDF, it is possible to derive RDFs with different distortion constraints. Specifically, we rederive the RDF for the vector Gaussian remote Wyner-Ziv problem with the mean-squared error distortion constraint, and a rate-mutual information function. This is done by minimizing R(D) subject to appropriate constraints on the distortion matrix D. The key idea to solve the resulting minimization problems is to lower- bound them with simpler optimization problems and show that they lead to identical solutions. We thus illustrate the generality of the covariance matrix distortion constraint in the Wyner-Ziv setup.We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function. We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e., remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.