The issue of how to efficiently represent the data collected by a network of microphones recording spatio-temporal acoustic wave fields is addressed. Each sensor node in the network samples the sound field, quantizes the samples and transmits the encoded samples to some central unit, which computes an estimate of the original sound field based on the information received from all the microphones. Our analysis is based on the spectral properties of the sound field, which are induced by the physics of wave propagation and have a significant impact on the efficiency of the chosen sampling lattice and coding scheme. As field acquisition by a sensor network typically implies spatio-temporal sampling of the field, a multidimensional sampling theorem for homogeneous random fields with compactly supported spectral measures is proved. To assess the loss of information implied by source coding, rate distortion functions for various coding schemes and sampling lattices are determined. In particular, centralized coding, independent coding and some multiterminal schemes are compared. Under the assumption of spectral whiteness of the sound field, it is shown that sampling with a quincunx lattice followed by independent coding is optimal as it achieves the lower bound given by centralized coding.

We study the source coding problem in sensor networks deployed to monitor the evolution of spatio-temporal temperature distributions. The sensors sample the temperature field, quantize the samples and transmit the encoded samples through digital channels to some central unit, which computes an estimate of the original temperature field. Our analysis is based on the heat kernel's spectral properties, which are induced by the physics of heat diffusion. We determine rate distortion functions for various source coding schemes. In particular, we compare centralized coding, independent coding, Berger-Tung coding, and predictive quantization.

We consider the rate-distortion problem for recording a Gaussian acoustic field with an array of sensors equipped with microphones. Our analysis is based on the field's spatio-temporal correlation structure, which is induced by the physics of sound propagation. Under certain assumptions about the spectrum of the wave kernel, we determine the rate-distortion functions for various distributed source coding schemes and sampling lattices. Our results also include an answer to the multiterminal rate-distortion problem for the setup considered in the paper

We consider the rate-distortion problem for sensing the continuous space-time physical temperature in a circular ring on which a heat source is applied over space and time, and which is allowed to cool by radiation or convection. The heat source is modelled as a continuous space-time stochastic process which is bandlimited over space and time. The temperature field is the result of a certain continuous space-time convolution of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors and it has to be reconstructed at a base station. The goal is to minimize the mean-square-error per second, for a given number of nats per second, assuming ideal communication channels between sensors and base station. We find a) the centralized R/sup c/(D) function of the temperature field, where the base station can optimally encode all the space-time samples jointly. Then, we obtain b) the R/sup s-i/(D) function, where each sensor, independently, encodes its samples optimally over time, and c) the R/sup st-i/(D) function, where each sensor is constrained to encode also independently over time. We also study two distributed prediction-based approaches: a) with perfect feedback from the base station, where temporal prediction is performed at the base station and each sensor performs differential encoding; and b) without feedback, where each sensor locally performs temporal prediction.

We consider the rate-distortion problem for sensing the continuous space-time physical temperature in a circular ring on which a heat source is applied over space and time, and which is also allowed to cool by radiation or convection to its surrounding medium. The heat source is modelled as a continuous space-time stochastic process which is bandlimited over space and time. The temperature field is the result of a circular convolution over space and a continuous-time causal filtering over time of the heat source with the Green's function corresponding to the heat equation, which is space and time invariant. The temperature field is sampled at uniform spatial locations by a set of sensors and it has to be reconstructed at a base station. The goal is to minimize the mean-square-error per second, for a given number of nats per second, assuming ideal communication channels between sensors and base station. We find a) the centralized Rc (D) function of the temperature field, where all the space-time samples can be observed and encoded jointly. Then, we obtain b) the Rs-i (D) function, where each sensor, independently, encodes its samples optimally over time and c) the Rst-i (D) function, where each sensor is constrained to encode also independently over time. We also study two distributed prediction-based approaches: a) with perfect feedback from the base station, where temporal prediction is performed at the base station and each sensor performs differential encoding, and b) without feedback, where each sensor locally performs temporal prediction.