Sparse Representation of Sensor Network Signals Based on the K-SVD Algorithm

The sparse basis of signals plays a key role in signals processing of wireless sensor networks (WSNs). However, the existing sparse bases, such as principal component analysis (PCA) and discrete cosine transform (DCT), do not support a good recovery effect in WSNs. In this paper, the general K-SVD (K-Means Singular Value Decomposition) is optimized and a new adaptive overcomplete dictionary (K-SVD-DCT) is constructed by extracting features of distributed WSN signals. First of all, we normalize the data and select the DCT matrix as the initial training dictionary D of the K-SVD algorithm, and then use the orthogonal matching pursuit (OMP) method to carry out sparse decomposition on signals, obtaining the sparse representation matrix. Then the dictionary atom is upgraded by iterating D. Eventually, K-SVD-DCT for sensor network signals' sparse representation is obtained after multiple iterations. We evaluate the performances of overcomplete dictionaries constructed by three initial training dictionaries. The experimental results show that the recovery errors of using the K-SVD-DCT are smaller than that of the PCA basis and are similar to that of the DCT basis. However, the successful recovery rate (8.0%) of the DCT basis is much lower than that of the K-SVD-DCT (82%).