Abstract Sparse representation of signals based on a redundant dictionary is a new signal representation theory. Recent research activities in this field have concentrated mainly on the study of dictionary design and sparse decomposition algorithms. Currently, the application of sparse representation on an Automatic Identification System (AIS) signal still requires further investigations. In this paper, a novel sparse representation of the AIS signal is proposed based on an adaptive redundant dictionary. Considering the characteristics of the AIS signal, an adaptive redundant dictionary is constructed using the K singular value decomposition (K-SVD) algorithm. Furthermore, an effective pursuit algorithm is proposed to obtain the sparse representation of AIS signal using the adaptive dictionary. The binary AIS message is demodulated from the sparse representation of AIS signal. The experimental results indicate that the sparse representation of the AIS signal has high accuracy and the reconstructive error rate can be under 10%; thus, the reconstructive precision is simultaneously guaranteed. The processing time of the proposed sparse representation algorithm is less than 26.7 ms which satisfies the requirements of AIS real-time signal processing. It shows that introducing the signal sparse representation in a real-time signal system obtains a satisfactory result.
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