Mixed-Norm Projection-Based Iterative Algorithm for Face Recognition

In this paper, the mixed-norm optimization is investigated for sparse signal reconstruction. Furthermore, an iterative optimization algorithm based on the projection method is presented for face recognition. From the theoretical point of view, the optimality and convergence of the proposed algorithm is strictly proved. And from the application point of view, the mixed norm combines the \(L_1\) and \(L_2\) norms to give a sparse and collaborative representation for pattern recognition, which has higher recognition rate than sparse representation algorithms. The algorithm is designed by combining the projection operator onto a box set with the projection matrix, which is effective to guarantee the feasibility of the optimal solution. Moreover, numerical experiments on randomly generated signals and three face image data sets are presented to show that the mixed-norm minimization is a combination of sparse representation and collaborative representation for pattern classification.

[1]  Terence Sim,et al.  The CMU Pose, Illumination, and Expression Database , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Lei Zhang,et al.  Sparse representation or collaborative representation: Which helps face recognition? , 2011, 2011 International Conference on Computer Vision.

[3]  Lie Wang,et al.  Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise , 2011, IEEE Transactions on Information Theory.

[4]  J. P. Lasalle.  The stability of dynamical systems , 1976 .

[5]  Qingshan Liu,et al.  $L_{1}$ -Minimization Algorithms for Sparse Signal Reconstruction Based on a Projection Neural Network , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Jun Wang,et al.  A dual neural network for bi-criteria kinematic control of redundant manipulators , 2002, IEEE Trans. Robotics Autom..

[7]  Qingshan Liu,et al.  Iterative projection based sparse reconstruction for face recognition , 2018, Neurocomputing.

[8]  Qingshan Liu,et al.  A One-Layer Projection Neural Network for Nonsmooth Optimization Subject to Linear Equalities and Bound Constraints , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[10]  Andy Harter,et al.  Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.

[11]  Qingshan Liu,et al.  A Collective Neurodynamic Approach to Distributed Constrained Optimization , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Mohamed S. Kamel,et al.  Novel Cooperative Neural Fusion Algorithms for Image Restoration and Image Fusion , 2007, IEEE Transactions on Image Processing.

[13]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Haim Brezis.  Review: David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications , 1982 .

[15]  Yiguang Hong,et al.  Constrained Consensus Algorithms With Fixed Step Size for Distributed Convex Optimization Over Multiagent Networks , 2017, IEEE Transactions on Automatic Control.

[16]  Jun Wang,et al.  A general projection neural network for solving monotone variational inequalities and related optimization problems , 2004, IEEE Transactions on Neural Networks.

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

[18]  D. Donoho,et al.  Atomic Decomposition by Basis Pursuit , 2001 .

[19]  Jun Wang,et al.  A one-layer recurrent neural network for support vector machine learning , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  René Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications , 2012, IEEE transactions on pattern analysis and machine intelligence.

[21]  Qingshan Liu,et al.  A Discrete-Time Projection Neural Network for Sparse Signal Reconstruction With Application to Face Recognition , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Jun Wang.  Analysis and design of a recurrent neural network for linear programming , 1993 .

[23]  Yihong Gong,et al.  Locality-constrained Linear Coding for image classification , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[24]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Michael Elad,et al.  Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.