Efficient reconstruction scheme with deep neural network for highly compressive sensing of fiber Bragg grating spectrum

Abstract

In this work, we propose an efficient reconstruction scheme for compressive sensing (CS) of fiber Bragg grating (FBG) spectrum. Taking advantage of the sparse reflection spectrum of the FBG array network, we have demonstrated the use of CS for compressing the spectrum at an excessively high compression factor up to 64. In addition to that, the spectral difference (SD) of the spectra is used to further enhance their sparsity for the CS model. In this investigation, four different configurations have been devised and tested to compare their performance and effectiveness. Configuration IV that is based on SD and deep neural network offers the best recovery performance. The proposed method is a potential tool for efficient data storage and transmission for FBG sensor network.

Keywords

Compressive sensing deep neural network reconstruction scheme fiber Bragg grating spectrum

Get full access to this article

View all access options for this article.

References

Asmara

Agustina

(2017) Discrete Fourier Transforms (DFT), and Discrete Wavelet Transforms (DWT) in Digital Image Watermarking. International Journal of Advanced Computer Science and Applications 8(2): 245–249.

Bai

, et al. (2015) Alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing. IEEE Transactions on Signal Processing 63(6): 1581–1594.

Baraniuk

(2007) Compressive sensing. IEEE Signal Processing Magazine 24(4): 118–124.

Baraniuk

Cevher

Duarte

, et al. (2010) Model-based compressive sensing. IEEE Transactions on Information Theory 56(4): 1982–2001.

Candès

Eldar

Needell

, et al. (2011) Compressed sensing with coherent and redundant dictionaries. Applied and Computational Harmonic Analysis 31(1): 59–73.

Cardoso

Debbah

Bianchi

, et al. (2008) Cooperative spectrum sensing using random matrix theory. In: 3rd international symposium on wireless pervasive computing (ISWPC), pp. 334–338. Available at: http://www-syscom.univ-mlv.fr/∼najim/Proceedings/cooperative.pdf

Chartrand

Yin

(2008) Iteratively reweighted algorithms for compressive sensing. In: ICASSP, IEEE international conference on acoustics, speech and signal processing, pp. 3869–3872. Available at: https://scholarship.rice.edu/bitstream/handle/1911/102083/TR08-01.pdf?sequence=1&isAllowed=y

Chen

Chi

, et al. (2014) Compressive sensing in a photonic link with optical integration. Optics Letters 39(8): 2222.

Gan

Nguyen

, et al. (2012) Fast and efficient compressive sensing using structurally random matrices. IEEE Transactions on Signal Processing 60(1): 139–154.

10.

Duan

Zhang

Wang

, et al. (2020) Fast peak-tracking method for FBG reflection spectrum and nonlinear error compensation. Optics Letters 45(2): 451–454.

11.

Eckle

Schmidt-Hieber

(2019) A comparison of deep networks with ReLU activation function and linear spline-type methods. Neural Networks 110: 232–242.

12.

Foucart

Rauhut

(2013) A Mathematical Introduction to Compressive Sensing. Available at: https://users.math.msu.edu/users/iwenmark/Teaching/MTH994/Holger_Simon_book.pdf

13.

Fred Agarap

(2018) Deep learning using rectified linear units (ReLU). Available at: https://arxiv.org/abs/1803.08375v2 (accessed 10 January 2022).

14.

Herrmann

(2012) Efficient least-squares imaging with sparsity promotion and compressive sensing. Geophysical Prospecting 60(4): 696–712.

15.

Hurley

Rickard

(2009) Comparing measures of sparsity. IEEE Transactions on Information Theory 55(10): 4723–4741.

16.

Jin

Zhang

, et al. (2006) An embedded FBG sensor for simultaneous measurement of stress and temperature. IEEE Photonics Technology Letters 18(1): 154–156.

17.

Kim

Park

Lee

(2020) Compressive sensing spectroscopy using a residual convolutional neural network. Sensors (Switzerland) 20(3): 594.

18.

Kitichotkul

Metzler

Ong

, et al. (2021) SUREMap: Predicting uncertainty in CNN-based image reconstructions using Stein’s unbiased risk estimate. In: Institute of Electrical and Electronics Engineers (IEEE), pp. 1385–1389. Available at: https://arxiv.org/abs/2010.13214#:∼:text=version%2C%20v2%5D-,SUREMap%3A%20Predicting%20Uncertainty%20in%20CNN%2Dbased%20Image%20Reconstruction,Using%20Stein’s%20Unbiased%20Risk%20Estimate&text=Convolutional%20neural%20networks%20(CNN)%20have,to%2Dunderstand%20black%2Dboxes

19.

Lecun

Bengio

Hinton

(2015) Deep learning. Nature 521(7553): 436–444.

20.

Dong

Wang

, et al. (2018) ConvCSNet: A convolutional compressive sensing framework based on deep learning. Available at: http://arxiv.org/abs/1801.10342 (accessed 17 June 2021).

21.

Yuan

Ping

(2015) Turbo compressed sensing with partial DFT sensing matrix. IEEE Signal Processing Letters 22(2): 158–161.

22.

Mizuno

Ishikawa

Lee

, et al. (2019) Potential of discriminative sensing of strain and temperature using perfluorinated polymer FBG. IEEE Sensors Journal 19(12): 4454–4462.

23.

Peng

Lin

Tseng

, et al. (2004) Intensity and wavelength-division multiplexing FBG sensor system using a tunable multiport fiber ring laser. IEEE Photonics Technology Letters 16(1): 230–232.

24.

Perdios

Vonlanthen

Martinez

, et al. (2020) CNN-based image reconstruction method for ultrafast ultrasound imaging. Available at: http://arxiv.org/abs/2008.12750 (accessed 17 June 2021).

25.

Pilastri

Tavares

JMRS

(2016) Reconstruction algorithms in compressive sensing: An overview. Proceedings of the Doctoral Symposium in Informatics Engineering16: 127–137.

26.

Qiao

Meng

, et al. (2020) Deep learning for video compressive sensing. APL Photonics 5(3): 30801.

27.

Rodrigues

Félix

Lage

, et al. (2010) Development of a long-term monitoring system based on FBG sensors applied to concrete bridges. Engineering Structures 32(8): 1993–2002.

28.

Romero

Ariananda

Tian

, et al. (2016) Compressive covariance sensing: Structure-based compressive sensing beyond sparsity. IEEE Signal Processing Magazine 33(1): 78–93.

29.

Saba

Alsayyh

MAMY

Mohamad

, et al. (2017) A novel fused image compression technique using DFT, DWT, and DCT. Journal of Information Hiding and Multimedia Signal Processing 8(2): 261–271.

30.

Sugavanam

Gbadebo

Kamalian-Kopae

, et al. (2021) Computational compressed sensing of Fiber Bragg gratings. Available at: https://arxiv.org/pdf/2106.09544.pdf

31.

Sun

, et al. (2020) A novel end-to-end 1D-ResCNN model to remove artifact from EEG signals. Neurocomputing 404: 108–121.

32.

Tosi

(2017) Review and analysis of peak tracking techniques for Fiber Bragg grating sensors. Sensors (Switzerland) 17(10): 2368.

33.

Tosi

Olivero

Perrone

(2012) Performance analysis of peak tracking techniques for fiber Bragg grating interrogation systems. Journal of Microwaves, Optoelectronics and Electromagnetic Applications 11(2): 252–262.

34.

Vella

Chadderdon

Selfridge

, et al. (2010) Full-spectrum interrogation of Fiber Bragg gratings at 100 kHz for detection of impact loading. Measurement Science and Technology 21(9): 094009.

35.

Wang

(2014) Spectral analysis based on compressive sensing in nanophotonic structures. Optics Express 22(21): 25608.

36.

Wei

Qiao

Jia

(2011) Simultaneous sensing of displacement and temperature with a single FBG. Optoelectronics Letters 7(1): 26–29.

37.

Yang

Zhang

(2011) Alternating direction algorithms for

ℓ_{1}

-problems in compressive sensing. Society for Industrial and Applied Mathematics 33(1): 250–278.

38.

Zanddizari

Rajan

Zarrabi

(2018) Increasing the quality of reconstructed signal in compressive sensing utilizing Kronecker technique. Biomedical Engineering Letters 8(2): 239–247.

39.

Zelnik-Manor

Rosenblum

Eldar

(2011) Sensing matrix optimization for block-sparse decoding. IEEE Transactions on Signal Processing 59(9): 4300–4312.

40.

Zhu

Chi

Jin

, et al. (2018) Photonics-enabled compressive sensing with spectral encoding using an incoherent broadband source. Optics Letters 43(2): 330.