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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 7/2019

06.11.2017 | Original Article

KKT condition-based smoothing recurrent neural network for nonsmooth nonconvex optimization in compressed sensing

verfasst von: Dan Wang, Zhuhong Zhang

Erschienen in: Neural Computing and Applications | Ausgabe 7/2019

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Abstract

This work probes into a smoothing recurrent neural network (SRNN) in terms of a smoothing approximation technique and the equivalent version of the Karush–Kuhn–Tucker condition. Such a network is developed to handle the \(L_0\hbox {-norm}\) minimization model originated from compressed sensing, after replacing the model with a nonconvex nonsmooth approximation one. The existence, uniqueness and limit behavior of solutions of the network are well studied by means of some mathematical tools. Multiple kinds of nonconvex approximation functions are examined so as to decide which of them is most suitable for SRNN to address the problem of sparse signal recovery under different kinds of sensing matrices. Comparative experiments have validated that among the chosen approximation functions, transformed L1 function (TL1), logarithm function (Log) and arctangent penalty function are effective for sparse recovery; SRNN-TL1 is robust and insensitive to the coherence of sensing matrix, while it is competitive by comparison against several existing discrete numerical algorithms and neural network methods for compressed sensing problems.
Vorheriger Artikel Large-scale structural learning and predicting via hashing approximation
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Literatur
1.
2.
Candes EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509MathSciNetMATHCrossRef
3.
4.
5.
Gasso G, Rakotomamonjy A, Canu S (2009) Recovering sparse signals with a certain family of nonconvex penalties and DC programming. IEEE Trans Signal Process 57(12):4686–4698MathSciNetMATHCrossRef
6.
Foucart S, Lai MJ (2009) Sparsest solutions of underdetermined linear systems via \(l_q\)-minimization for \(0<q\le 1\). Appl Comput Harmon Anal 26(3):395–407MathSciNetMATHCrossRef
7.
Lai MJ, Xu Y, Yin W (2013) Improved iteratively reweighted least squares for unconstrained smoothed \(l_q\) minimization. SIAM J Numer Anal 51(2):927–957MathSciNetMATHCrossRef
8.
Geman D, Yang C (1995) Nonlinear image recovery with half-quadratic regularization. IEEE Trans Image Process 4(7):932–946CrossRef
9.
Trzasko J, Manduca A (2009) Relaxed conditions for sparse signal recovery with general concave priors. IEEE Trans Signal Process 57(11):4347–4354MathSciNetMATHCrossRef
10.
Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Amer Stat Assoc 96(456):1348–1360MathSciNetMATHCrossRef
11.
Friedman JH (2012) Fast sparse regression and classification. Int J Forecast 28(3):722–738CrossRef
12.
13.
Zhang S, Qian H, Chen W, Zhang Z (2013) A concave conjugate approach for nonconvex penalized regression with the MCP penalty. In: Proceedings of the 27th AAAI conference on artificial intelligence 2013, pp 1027–1033
14.
Zhang T (2010) Analysis of multi-stage convex relaxation for sparse regularization. J Mach Learn Res 11(2):1081–1107MathSciNetMATH
15.
Gao C, Wang N, Yu Q, Zhang Z (2011) A feasible nonconvex relaxation approach to feature selection. In: Proceedings of the 25th AAAI conference on artificial intelligence 2011, pp 356–361
16.
Soubies E, Blanc-Fraud L, Aubert G (2015) A continuous exact \(L_0\) penalty (CEL0) for least squares regularized problem. SIAM J Imaging Sci 8(3):1607–1639MathSciNetMATHCrossRef
17.
Malek-Mohammadi M, Koochakzadeh A, Babaie-Zadeh M, Jansson M, Rojas CR (2016) Successive concave sparsity approximation for compressed sensing. IEEE Trans Signal Process 64(21):5657–5671MathSciNetMATHCrossRef
18.
Selesnick IW, Bayram I (2014) Sparse signal estimation by maximally sparse convex optimization. IEEE Trans Signal Process 62(5):1078–1092MathSciNetMATHCrossRef
19.
Lou Y, Osher S, Xin J (2015) Computational aspects of constrained \(L_1-L_2\) minimization for compressive sensing. Modelling. Springer, Computation and optimization in information systems and management sciences, pp 169–180
20.
Yin P, Lou Y, He Q, Xin J (2015) Minimization of \(l_{1-2}\) for compressed sensing. SIAM J Sci Comput 37(1):A536–A563MATHCrossRef
21.
Zhang H, Li J, Ji Y, Yue H (2017) Understanding subtitles by character-level sequence-to-sequence learning. IEEE Trans Ind Inform 13(2):616–624CrossRef
22.
Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117CrossRef
23.
Bian W, Chen X (2014) Neural network for nonsmooth, nonconvex constrained minimization via smooth approximation. IEEE Trans Neural Netw Learn Syst 25(3):545–556CrossRef
24.
Qin S, Bian W, Xue X (2013) A new one-layer recurrent neural network for nonsmooth pseudoconvex optimization. Neurocomputing 120:655–662CrossRef
25.
Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52(3):141–152MATH
26.
Bian W, Chen X (2012) Smoothing neural network for constrained non-Lipschitz optimization with applications. IEEE Trans Neural Netw Learn Syst 23(3):399–411MathSciNetCrossRef
27.
Rozell CJ, Garrigues P (2010) Analog sparse approximation for compressed sensing recovery. In: Proceedings of the ASILOMAR conference on signals, systems and computers 2010, pp 822–826
28.
Charles AS, Garrigues P, Rozell CJ (2011) Analog sparse approximation with applications to compressed sensing. arXiv preprint arXiv:​1111.​4118
29.
Leung CS, Sum J, Constantinides AG (2014) Recurrent networks for compressive sampling. Neurocomputing 129:298–305CrossRef
30.
Feng R, Leung CS, Constantinides AG, Zeng WJ (2017) Lagrange programming neural network for nondifferentiable optimization problems in sparse approximation. IEEE Trans Neural Netw Learn Syst 28(10):2395–2407MathSciNetCrossRef
31.
32.
Liu Y, Hu J (2016) A neural network for \(l_1\)-\(l_2\) minimization based on scaled gradient projection: application to compressed sensing. Neurocomputing 173(3):988–993CrossRef
33.
Liu Q, Wang J (2016) \(L_1\)-minimization algorithms for sparse signal reconstruction based on a projection neural network. IEEE Trans Neural Netw Learn Syst 27(3):698–707MathSciNetCrossRef
34.
Guo Z, Wang J (2010) A neurodynamic optimization approach to constrained sparsity maximization based on alternative objective functions. In: Proceedings of the 2010 international joint conference on neural networks (IJCNN) 2010, pp 18–23
35.
Guo C, Yang Q (2015) A neurodynamic optimization method for recovery of compressive sensed signals with globally converged solution approximating to minimization \(L_0\). IEEE Trans Neural Netw Learn Syst 26(7):1363–1374MathSciNetCrossRef
36.
Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley, New YorkMATH
37.
38.
Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666MathSciNetMATHCrossRef
39.
Needell D, Tropp JA (2009) CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Anal 26(3):301–321MathSciNetMATHCrossRef
40.
41.
42.
Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122MATHCrossRef
43.
Hale E, Yin W, Zhang Y (2008) Fixed-point continuation for \(l_1\)-minimization: methodology and convergence. SIAM J Optim 19(3):1107–1130MathSciNetMATHCrossRef
44.
Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183–202MathSciNetMATHCrossRef
45.
Rozell CJ, Johnson DH, Baraniuk RG, Olshausen BA (2008) Sparse coding via thresholding and local competition in neural circuits. Neural Comput 20(10):2526–2563MathSciNetCrossRef
46.
47.
Gribonval R, Nielsen M (2007) Highly sparse representations from dictionaries are unique and independent of the sparseness measure. Appl Comput Harmon Anal 22(3):335–355MathSciNetMATHCrossRef
48.
Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New YorkMATH
49.
Bandeira A, Dobriban E, Mixon D, Sawin W (2013) Certifying the restricted isometry property is hard. IEEE Trans Inform Theory 59(6):3448–3450MathSciNetMATHCrossRef
50.
Slotine JJE, Li W (1991) Applied nonlinear control. Englewood Cliffs, Prentice-HallMATH
Metadaten
Titel
KKT condition-based smoothing recurrent neural network for nonsmooth nonconvex optimization in compressed sensing
verfasst von
Dan Wang
Zhuhong Zhang
Publikationsdatum
06.11.2017
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 7/2019
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-017-3239-6

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