Research On Sparse Representation Of Brillouin Gain Spectrum Based On Dictionary Learning

In recent years,distributed Brillouin optical fiber sensors have been widely used in the field of infrastructure safety monitoring such as bridge monitoring,geological disaster sensing,and oil and gas pipeline leak detection.For Brillouin sensing technology,the extraction of Brillouin frequency shift is important.The introduction of image processing and machine learning algorithms can effectively improve the system's signal-to-noise ratio and achieve efficient extraction of the Brillouin frequency shift.Therefore,advanced signal processing algorithms are of great significance to the rapid development of Brillouin sensing systems.As a new signal processing method,sparse representation plays an important role in the fields of feature extraction,signal dimensionality reduction,and image compression.By selecting a small number of atoms in the super-complete dictionary to represent the original signal,sparse representation can obtain main features in the sparse domain.In this paper,the sparse representation theory is introduced into the Brillouin sensing system,the sparse representation of the Brillouin gain spectrum is obtained through the dictionary learning K-means singular value decomposition(K-SVD)algorithm,and the unique sparseness is used to complete the Brillouin Noise filtering and Brillouin frequency shift extraction of gain spectrum.The main research content of this paper is as follows:(1)Apply the fixed discrete cosine basis and the dictionary obtained by the K-SVD algorithm to the three-dimensional Brillouin gain spectrum and obtain the corresponding sparse representation.Under the over-complete dictionary representation,the sparsity of each Brillouin gain spectrum can be unified to 3,and the three sparse representation coefficients are correlated with peak gain,Brillouin frequency shift and spectrum width.(2)Brillouin gain spectrum has sparseness under the over-complete dictionary,while noise does not have the same characteristics of sparseness.Therefore,the noise can be filtered while obtaining sparse representation of the gain spectrum.After using the K-SVD algorithm to obtain local sparse representation,a global prior condition is added to establish a global sparse model of the three-dimensional Brillouin gain spectrum.Solving the model can achieve signal-to-noise separation and obtain a clean Brillouin gain spectrum.The uncertainty of Brillouin frequency shift is 1.4 MHz and 0.6314 MHz,and the uncertainty of frequency shift measurement is reduced after denoising.Compared with classic image denoising algorithms,this denoising algorithm will not cause significant deterioration of spatial resolution,and can improve the measurement accuracy of the system.(3)Through further analysis of the K-SVD-based sparse representation theory and the Lorentz distribution of the Brillouin gain spectrum,the mathematical connection between the sparse representation coefficient and the three physical parameters of the Brillouin gain spectrum is established.A Brillouin frequency shift extraction method based on a two-step dictionary learning process is proposed.Experiments have proved that the linear correlation between the sparse coefficient obtained by the dictionary learning and the Brillouin frequency shift is above 0.97.The algorithm can obtain the same measurement accuracy as the Lorentz fitting method.At the optical fiber sensing distance of 10 km,the average processing time of is 34 s,and the temperature measurement uncertainty is 0.3211?.