Signal reconstruction of compressed sensing based on recurrent neural networks

Abstract In this paper, neural network approach is addressed for signal reconstruction under the frame of compressed sensing. By introducing implicit variables, we convert the basis pursuit denoising model into a quadratic programming problem. Based on a class of generalized Fischer–Burmeister complementarity functions, we establish a neural network method for the signal reconstruction of compressed sensing. A projection neural network is also presented to recover the original signals. These two neural networks can be implemented using integrated circuits and two block diagrams of the neural networks are presented. Based on our proposed method, some potential applications of the compressed sensing are discussed.

[1]  Kun Liu,et al.  Fleet algorithm for X-ray pulsar profile construction and TOA solution based on compressed sensing , 2014 .

[2]  Yang Li,et al.  Optical image encryption technique based on compressed sensing and Arnold transformation , 2013 .

[3]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[4]  Kun Liu,et al.  Joint L1/Lp-regularized minimization in video recovery of remote sensing based on compressed sensing , 2014 .

[5]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[6]  Bin Song,et al.  An Adaptive-ADMM Algorithm With Support and Signal Value Detection for Compressed Sensing , 2013, IEEE Signal Processing Letters.

[7]  P. Shearer,et al.  Compressive sensing of the Tohoku‐Oki Mw 9.0 earthquake: Frequency‐dependent rupture modes , 2011 .

[8]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[9]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[10]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[11]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[12]  舒适,et al.  First-order optimality condition of basis pursuit denoise problem , 2014 .

[13]  Zhanjie Song,et al.  An improved IRLS algorithm for sparse recovery with intra-block correlation , 2015 .

[14]  Xiaolin Hu,et al.  A Recurrent Neural Network for Solving a Class of General Variational Inequalities , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Yang Shuyuan,et al.  Block-Based Adaptive Compressed Sensing of Image Using Texture Information , 2013 .

[16]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[17]  Wei Wang,et al.  An adaptive sampling method of compressed sensing based on texture feature , 2016 .

[18]  Lu Gan.  Block Compressed Sensing of Natural Images , 2007, 2007 15th International Conference on Digital Signal Processing.

[19]  Jun Wang,et al.  A recurrent neural network for solving nonlinear convex programs subject to linear constraints , 2005, IEEE Transactions on Neural Networks.

[20]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[21]  Ke Wei,et al.  Fast Iterative Hard Thresholding for Compressed Sensing , 2015, IEEE Signal Processing Letters.

[22]  Richard G. Baraniuk,et al.  Compressive Sensing DNA Microarrays , 2008, EURASIP J. Bioinform. Syst. Biol..

[23]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[24]  James E. Fowler,et al.  Block compressed sensing of images using directional transforms , 2009, ICIP.

[25]  James E. Fowler,et al.  Multiscale block compressed sensing with smoothed projected Landweber reconstruction , 2011, 2011 19th European Signal Processing Conference.

[26]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[27]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[28]  Entao Liu,et al.  Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing ∗ , 2010 .

[29]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[30]  Jein-Shan Chen,et al.  Recurrent neural networks for solving second-order cone programs , 2011, Neurocomputing.

[31]  Haixia Long,et al.  Remote sensing image noise reduction using wavelet coefficients based on OMP , 2015 .