Abstract
In compressed sensing applications, self-learning generative models have attracted increasing attention because they provide guarantees that are similar to those of standard compressed sensing without employing sparsity. However, improving the performances of a generative model is challenging. In this paper, we improve the recovery performances of generative models (generative adversarial networks) by making use of prior knowledge about the support of the vector of the original signal in the relevant domain. We demonstrate the advantage of using a parametric model with the Fisher distance metric for the exploitation of a distribution over the support when constraints on the distribution have been specified. We combine the generative model with the Fisher distance to study the recovery of sparse signals that satisfy a distribution for the purpose of improving the recovery performance of the model when there are some constraints on the distribution. Finally, we present the results of extensive experiments conducted on simulated signals and imaging signals.
Similar content being viewed by others
References
Abdur RM, Simon D (2014) Energy-efficient sensing in wireless sensor networks using compressed sensing. Sensors 14(2):2822–2859
Wang DX, Mackie TR, Tome WA (2009) Proton computed tomography reconstruction using compressed sensing and prior image constrained compressed sensing. Med Phys 36(6):2443
Bo K, Gengxin Z, Wei Z, Dongming B, Zhidong X (2016) Data persistence in planetary surface network using raptor codes and probabilistic broadcasting Int. J Distrib Sens Netw 12(8):51–65
Candes EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Proc Mag 25(2):21–30
Muthukrishnan S (2003) Data streams: algorithms and applications. Found Trends Theor Comput Sci 1(2):413–413
Candes EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203–4215
Blumensath T, Davies ME (2009) Iterative hard thresholding for compressed sensing. Appl Comput Harmon Anal 27(3):265–274
Baron D, Sarvotham S, Baraniuk RG (2010) Bayesian compressive sensing via belief propagation. IEEE Signal Proc 58(3):269–280
Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20(1):33–61
Gilbert A, Guha S, Indyk P, Muthukrishnan S, Strauss M (2000) Near-optimal sparse Fourier representations via sampling.In: Proceedings of the 34th annual ACM symposium on theory of computing, pp 152−161
Cai TT, Wang L (2011) Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans Inf Theory 57(7):4680–4688
Li S, Fang L (2011) Signal denoising with random refined orthogonal matching pursuit. IEEE Instrum Meas Soc 23:26–34
Chen SS, Donoho DL, Saunders MA (2001) Atomic decomposition by basis pursuit. SIAM Rev 43(1):129–159
Bazerque JA, Giannakis GB (2013) Nonparametric basis pursuit via sparse kernel-based learning: a unifying view with advances in blind methods. IEEE Signal Process Mag 30(4):112–125
Baron D, Sarvotham S, Baraniuk RG (2010) Bayesian compressive sensing via belief propagation. IEEE Trans Signal Process 58(1):269–280
He L, Carin L (2009) Exploiting structure in wavelet-based bayesian compressive sensing. IEEE Trans Signal Process 57(9):3488–3497
LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444
Palangi H, Ward R, Deng Li (2017) Convolutional deep stacking networks for distributed compressive sensing. Signal Process 131:181–189
Wang M, Xiao CB, Ning ZH, Li T, Gong B (2019) Neural networks for compressed sensing based on information geometry. Circuits Syst Signal Process 38(2):569–589
Merhej D et al (2011) Embedding prior knowledge within compressed sensing by neural networks. IEEE Trans Neural Netw 22(10):1638–1649
Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. Adv Neural Inf Process Syst vol 2, pp 2672–2680
Bora A, Jalal A, Price E, Dimakis AG (2018) Compressed sensing using generative models. In: Proceedings of the 34th international conference on machine learning, PMLR, vol 70, pp 537–546
Mardani M, Gong E, Cheng JY, Vasanawala S, Xing L, Pauly JM (2017) Deep generative adversarial networks for compressed sensing (GANCS) automates MRI. In: 31st Conference on neural information processing systems (NIPS 2017), Long Beach, CA, USA
Quan TM, Nguyen-Duc T, Jeong W-K (2018) Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss. IEEE Trans Med Imaging 37(6):1488–1497
Yang G, Yu S, Dong H, Slabaugh G, Dragotti PL, Ye X, Liu F, Arridge S, Keegan J, Guo Y, Firmin D (2018) DAGAN: deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction. IEEE Trans Med Imaging 37(6):1310–1321
Hao L, Dawei X, Xingwu Y, Xinyu Z (2019) Compressed sensing method for IGBT high-speed switching time on-line monitoring. IEEE Trans Ind Electron 66(4):3185–3195
Razzaque MA, Simon D (2014) Energy-efficient sensing in wireless sensor networks using compressed sensing. Sensors 14:2822–2859
Hong-An L, Zhan-Li L, Zhuo-Ming D (2017) A reconstruction method of compressed sensing 3D medical models based on the weighted 0-norm. J Med Imaging Health Inform 7(2):416–420
Majumdar A, Ward RK (2010) Compressive color imaging with group-sparsity on analysis prior. In: Proc. 17th IEEE Int. Conf. Image Process. (ICIP), Sep. 26–29, pp 1337–1340
Yu L et al (2011) Bayesian compressive sensing for clustered sparse signals. In: Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), May 22–27, pp 3948–3951
Vera E et al (2009) Bayesian compressive sensing of wavelet coefficients using multiscale Laplacian priors. In: Proc. IEEE/Signal Process. 15th Workshop Statist. Signal Process. (SSP), Aug. 31–Sep. 3, pp 229–232
Amari S (1985) Differential-geometrical methods in statistics. Lect Notes Stat 28(5):168–178
Duong TV, Phung DQ, Bui HH, Venkatesh S (2006) Human behavior recognition with generic exponential family duration modeling in the hidden semi-Markov model. In: International conference on pattern recognition, pp 202–208
Ravanbakhsh S, Poczos B, Schneider J (2016) Stochastic neural networks with monotonic activation functions. In: Appearing in Proceedings of the 19th international conference on artificial intelligence and statistics (AISTATS) 2016, Cadiz, Spain. JMLR: W&CP vol 41
Rao CR (1945) Information and accuracy attainable in the estimation of statistical parameters. Bull Calcutta Math Soc 37:81–91
Costa SIR, Santos SA, Strapasson JE (2014) Fisher information distance: a geometrical reading. Discrete Appl Math S0166218X14004211
Arwini K, Dodson CTJ (2008) Information geometry: near randomness and near independence. Lecture Notes in Mathematics, Springer
Hazewinkel M (ed) (2001) Jensen inequality. In: Encyclopedia of mathematics. Springer Science + Business Media B.V./Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Candès EJ, Romberg JK, Tao T (2006) Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math 59(8):1207–1223
Slavche P, Venceslav K (2015) Asymptotic capacity lower bound for an OFDM system with lasso compressed sensing channel estimation for Bernoulli-Gaussian channel. IEEE Commun Soc 19(3):379–382
Candes EJ, Tao T (2006) Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Trans Inf Theory 52(12):5406–5425
LeCun M, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324
Liu Z, Luo P, Wang X et al (2015) Deep learning face attributes in the wild. In: Proceedings of the IEEE international conference on computer vision, pp 3730–3738
Acknowledgements
This research was funded by the Beijing Science and Technology Planning Program of China (Z171100004717001), Beijing Natural Science Foundation (4172002), and Natural Science Foundation of China (61701009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, M., Yu, J., Ning, ZH. et al. Compressed sensing using generative models based on fisher information. Int. J. Mach. Learn. & Cyber. 12, 2747–2759 (2021). https://doi.org/10.1007/s13042-021-01337-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-021-01337-1