RECNN: Restoration and extraction of incomplete brillouin gain spectrum based on CNN framework combined with SVAE and attention mechanism

Abstract

In this paper, we propose a novel method under convolutional neural network framework combined with a supervised variational autoencoder and an attention mechanism, named the Restoration and Extraction Convolutional Neural Network (RECNN), for the restoration and extraction of Incomplete Brillouin Gain Spectrum (IBGS). It is important to clarify that the IBGS discussed here does not encompass information around the Brillouin Frequency Shift (BFS). This omission complicates the task of reconstructing the original spectrum or determining the BFS value. The RECNN framework consists of two main components: Restoration Supervised Variational Autoencoder (RSVAE) with an attention module for IBGS restoration, and Residual Attention Convolutional Neural Network (RACNN) for BFS extraction. Different types of IBGS are discussed in detail. We define the K index to quantify the incompleteness of the IBGS and introduce the R-squared index to measure the restoration performance of RSVAE. Additionally, the Root Mean Square Error (RMSE) and uncertainty are used to evaluate the overall performance of RECNN. Both simulation and experimental results demonstrate that the R-squared index increases with increasing K and Signal-to-Noise Ratio (SNR), while both RMSE and uncertainty decrease with increasing K and SNR. In comparisons with various other methods including Linear Curve Fitting (LCF) and artificial neural networks, RECNN consistently outperforms them. Specifically, simulation results show that when K is 0.5 and SNR is 4 dB, the R-squared value for RSVAE reaches 0.82, significantly higher than the 0.31 achieved by LCF method. Experimental results indicate that for an SNR of 6.78 dB and K of 0.5, the RMSE and uncertainty of RECNN are 3.21 MHz and 2.68 MHz, respectively, representing reductions of 11.43 MHz and 11.17 MHz compared to LCF. It's noteworthy that the time consumption evaluation indicates that RECNN requires less than 7 ms to restore the complete BGS and obtain the BFS value. These results are consistently observed in both simulations and experimental studies, which bodes well for the future of extracting valuable latent information from outdated and corrupted data stored in databases of distributed fiber sensing applications.