Applying weighted smoothed norm in sparse representation classification for face recognition

Document Type : Original Article

Authors

Faculty of Mathematical Sciences, University of K.N.T University, Teharn, Iran

Abstract

Classification and recognition is one of the most important methods of extracting information from images, and among them, facial image recognition as one of the most efficient biometric features for human identification has always been of interest, and extensive research has been conducted in this field in recent years. So far, various solutions for face recognition have been proposed by researchers, but among them, the use of Sparse representation classification has been considered as an effective and specific solution. One of the features of Sparse representation is to obtain features from input images without the need of feature extraction methods, therefore, in this article, the proposed method is aimed at applying weighted smoothed ℓ0 norm for face recognition using Sparse representation.
To check the performance of the proposed method, ORL and AR databases including images of different facial expressions have been used, and the simulated results show that the method performs very well compared to other well-known methods in the field of face recognition
.

Keywords


Smiley face

[1] K. R. Kakkirala, S. R. Chalamala, and S. Jami, “Thermal Infrared Face Recognition: A review,” UKSim-AMSS 19th International Conference on Modelling & Simulation, pp. 55–60, 2017, DOI:10.1109/UKSim.2017.38
[2] J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Yi Ma, “Robust face recognition via sparse representation,” IEEE Transaction on Pattern Analysis and Machine Intelligence, no. 2, pp. 210–227, February 2009, DOI: 10.1109/TPAMI.2008.79.
[3] K. Awedat, A. Essa, and V. Asari, “Sparse Representation Classification Based Linear Integration of  -norm and -norm for Robust Face Recognition,” presented at the Electro Information Technology (EIT), IEEE International Conference on, Lincoln, NE, USA, 2017, DOI:10.1109/EIT.2017.8053403.
[4] T. Liu, J. X. Mi, Y. Liu, and C. Li, “Robust face recognition via sparse boosting representation,” Neurocomputing, vol. 214, pp. 944–957, 2016, DOI:10.1016/j.neucom.2016.06.071.
[5] W. Jinming, and L. Haifeng, “Binary sparse signal recovery with binary matching pursuit,” Inverse Problems., vol. 37, no. 6, pp. 14–65, 2021, DOI: 10.1088/1361-6420/abf903.
[6] R. Liu, M. Shu, and C. Chen, “ECG Signal Denoising and Reconstruction Based on Basis Pursuit,” Applied Sciences 11, no. 4, 2021, DOI:10.3390/app11041591.
[7] A. Wan, “Uniform RIP Conditions for Recovery of Sparse Signals by Minimization,” in IEEE Transactions on Signal Processing, vol. 68, pp. 5379–5394, 2020, DOI:10.1109/TSP.2020.3022822.
[8] H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed  norm,” IEEE Trans. Signal Process., vol. 57, no. 1, pp. 289–301, 2009, DOI: 10.1109/TSP.2008.2007606.
[9] Babaie-Zadeh, M., B. Mehrdad, and G.B. Giannakis, “Weighted sparse signal decomposition. in Acoustics,” Speech and Signal Processing (ICASSP), IEEE International Conference on. 2012, DOI: 10.1109/ICASSP.2012.6288652.
[10] D. L. Donoho, “For most large underdetermined systems of linear equation the minimal  norm solution is also the sparsest solution,” Tech. Rep, 2004, DOI: 10.1002/cpa.20132.
[11] M. Malek-Mohammadi, M. Jansson, A. Owrang, A. Koochakzadeh, and M. Babaie-Zadeh, “DOA estimation in partially correlated noise using low-rank/sparse matrix decomposition,” in IEEE Sensor Array and Multichannel Signal Processing Workshop, pp. 373–376, 2014, DOI: 10.1109/SAM.2014.6882419.
[12] D. L. Donoho, and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via  minimization,” Proc of the National Acadmy of Sciences vol. 100, 2003, DOI: 10.1073/pnas.0437847100
[13] M. S. Alamdari, M. Fatemi and A. Ghaffari, “A Modified Sequential Quadratic Programming Method for Sparse Signal Recovery Problems,” Signal Processing, 2023, DOI: 10.1016/j.sigpro.2023.108955.
[14] M. S. Alamdari, M. Fatemi, A. Ghaffari, “The Recovery of Sparse Signals by Sequential Quadratic Programming Approach,” Journal of Operational Research and Its Applications, pp. 19–32, 2023, DOI: 10.21018/jamlu.2023.1932.21.
[15] M. Elad, “Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing,” Springer Science ans Business Media, 2010, DOI: 10.1007/978-1-4419.
 
[16] D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Info. Theory, vol. 52, no. 1, pp. 6–18, 2006, DOI: 10.1109/TIT.2005.860430.
 
[17] K. Huang, and S. Aviyente, “Sparse representation for signal classification,” in Advances in neural information processing systems. 2006.
[18] M. S. Alamdari and M. Fatemi, “Presenting a new method to separate fetal heart signals from the mother by using sequential quadratic programming,” Journal of Advanced Mathematical Modeling, pp. 153–167, 2023, DOI: 10.22055/jamm.2023.43652.2157.
 
[19] M. Shahrezaee and M. S. Alamdari, “The Application of Numerical Analysis Techniques to Pattern Recognition of Helicopters by Area Method, Journal of Mathematical Research,” pp. 51–60, 2015, DOI: 10.29252/mmr.1.2.51.
[20] M. S. Alamdari, “Providing an optimal mathematical model based on sparse display to improve image reconstruction,” Journal of New Researches in Mathematics, 2023, DOI: 10.30495/jnrm.2023.73817.2426.
[21] F. Samaria, and A. Harter, “Parameterisation of a stochastic model for human face identification,” In Second IEEE workshop on applications of computer vision, Sarasota ,1994.
[22] A. Martinez, and R. Benavente, “The AR face database. In: CVC technical report, no. 24, 1998.
[23] H. Khosravi, A. Ghaffari, and J. Vahidi, “Face recognition via weighted non-negative sparse representation,” International Journal of Nonlinear Analysis and Applications, vol. 12, no. 2, pp. 1141–1150, 2021.
[24] H.  Motameni, “Face recognition using sparce reprasentations and p-laplacian,” Journal of Advances in Computer Research, vol. 10, no. 4, pp. 37–49, 2019.