Sparse representation of Brillouin spectrum using dictionary learning

Distributed optical fiber Brillouin sensors can monitor the temperature and strain along a fiber by estimating the Brillouin frequency shift (BFS) according to the measured Brillouin spectrum. The system performance is highly dependent on the algorithm of BFS extraction. The well-established Lorentz curve fitting (LCF) method is generally employed because the Brillouin spectrum theoretically satisfies a Lorentz shape. Recently, machine-learning methods have been proposed for more effective BFS extraction, but they have some drawbacks and limitations. The machine-learning algorithms require a large amount of data and high computing power to find suitable extraction methods. However, with prior knowledge, Brillouin spectrum can be treated as a regular signal that requires only three degrees of freedom to define. The unique sparsity characteristics of Brillouin spectrum have not been well studied or exploited. In this paper, we propose a sparse representation method for Brillouin spectrum that extracts three sparse features of the Brillouin spectrum through the dictionary-learning algorithm (K-means singular value decomposition). The correlation between the sparse coefficient and the BFS is experimentally calibrated and verified. The accuracy of the proposed algorithm is comparable to that of LCF, and its processing is six times faster. This sparse representation method for Brillouin spectra is promising as an alternative universal BFS extraction method for distributed Brillouin sensors.