Method for Brillouin gain spectrum recovery based on compressed sensing with convex optimization

The traditional Brillouin optical fiber distributed sensors obtain the Brillouin gain spectrum (BGS) through frequency-by-frequency sweeping acquisition, which can be time-consuming and data intensive. These characteristics put a lot of pressure on data storage, especially on signal processing. Compressed sensing is a method represented by random sampling to reduce the number of acquisition frequencies, but the results obtained may be unstable. In this paper, we have proposed a reconstruction algorithm based on compressed sensing with convex optimization (COP), which can recover the whole BGS by collecting only 10% of the acquisition frequencies. The recovered BGS can attain a RMSE similar to the fully collected BGS. The proposed algorithm also provides more accurate and stable performances for different random sampling points compared to existing reconstruction methods. For example, for a 10% sampling percentage, with a reduction in error of 2.24 and 0.40 MHz, values are lower than those employing the orthogonal matching pursuit (OMP) and the regularized orthogonal matching pursuit (ROMP), respectively. Moreover, the reconstruction results of the proposed method are more stable for different random sampling points, with a reduction in standard deviation of 2.58 and 0.07 MHz.