Diffusion wavelet basis algorithm for sparse representation of sensory data in WSNs

Sparsity is a precondition for compressive data gathering in Wireless Sensor Networks. To solve the sparse representation problem of sensory data in temperature field, the paper puts forward a diffusion wavelet basis algorithm, which mainly includes the construction of diffusion operator and the filter of diffusion wavelet bases. The construction of diffusion operator takes spatial correlation between sensory data and the communication radius into account. Diffusion wavelet bases are generated from diffusion wavelet trees with different decomposition levels. The algorithm introduces numerical sparsity to evaluate the sparsity of approximately sparse data. Based on the measure of sparsity, diffusion wavelet basis with the better performance is extracted as the sparsifying basis. Synthetic data experiment and real data experiment are conducted to validate the performance of the sparsifying basis. The results of numerical experiments show that sensory data are approximately sparse, and the numerical sparsity in the proposed diffusion wavelet basis is less than that in the other types of the sparsifying bases. The recovery of sensory data considers the noiseless and noise cases. When BP and BPDN are used for data recovery, and the measurement matrix is sparse binary matrix, we observe that the proposed diffusion wavelet basis decreases relative error.