Abstract
We consider the problem of distributed representation of signals in sensor networks, where sensors exchange quantized information with their neighbors. The signals of interest are assumed to have a sparse representation with spectral graph dictionaries. We further model the spectral dictionaries as polynomials of the graph Laplacian operator. We first study the impact of the quantization noise in the distributed computation of matrix-vector multiplications, such as the forward and the adjoint operator, which are used in many classical signal processing tasks. It occurs that the performance is clearly penalized by the quantization noise, whose impact directly depends on the structure of the spectral graph dictionary. Next, we focus on the problem of sparse signal representation and propose an algorithm to learn polynomial graph dictionaries that are both adapted to the graph signals of interest and robust to quantization noise. Simulation results show that the learned dictionaries are efficient in processing graph signals in sensor networks where bandwidth constraints impose quantization of the messages exchanged in the network.
Highlights
Wireless sensor networks have been widely used for applications such as surveillance, weather monitoring, or automatic control, that often involve distributed signal processing methods
We build on our previous work [15], and we study the effect of quantization in distributed graph signal representations
We study the quantization error that appears in the distributed computations with polynomial graph dictionaries in Section 3, and in Section 4, we analyze the specific case of the sparse approximation of graph signals
Summary
Wireless sensor networks have been widely used for applications such as surveillance, weather monitoring, or automatic control, that often involve distributed signal processing methods. Such methods are typically designed by assuming local inter-sensor communication, i.e., communication between neighbor sensors, in order to achieve a global objective over the network. The information exchanged by the sensors has to be quantized prior to transmission due to limited communication bandwidth and limited computational power. This quantization process may lead to significant performance degradation, if the system is not designed to handle it properly. A graph signal is defined as a function that assigns a real
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