An Improved Recognition Approach for Noisy Multispectral Palmprint by Robust L2 Sparse Representation with a TensorBased Extreme Learning Machine
Abstract
:1. Introduction
2. Acquisition Device of Multispectral Palmprint Images
3. Proposed Algorithm
3.1. Robust L2 Sparse Representation Method
3.1.1. SRC Model
3.1.2. Robust L2 Sparse Representation Method
3.2. Image Fusion Based on Adaptive Weighted Method
3.3. Principle of Tensor Based ELM
3.3.1. ELM
3.3.2. Tensor Based ELM
4. Experiments
4.1. The PolyU Multispectral Palmprint Database
4.2. Parameter Selection
4.2.1. Selection of $\mu $ and $\delta $ for Residual Function
4.2.2. Selection of the Hidden Node Numbers Along the Directions of TELM
4.3. Experiment Results and Analysis
5. Conclusions
Author Contributions
Funding
Acknowledgements
Conflicts of Interest
References
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Input: testing sample ${y}^{l},(l=1,2,\dots ,s)$, training sample matrix $X=[{X}_{1},\dots ,{X}_{i},\dots ,{X}_{C}]$, initiate the residual function matrix ${W}^{l,1}=diag(1,1,\dots ,1)$. Output: linear representation coefficient ${A}^{l}$$,(l=1,2,\dots ,s)$. 
While $error$ not convergent, do 1. Calculate the collaborative representation code ${\gamma}^{l}$ by solving
$${\gamma}^{l,t+1}=\mathrm{arg}\underset{{\gamma}^{l}}{\mathrm{min}}{\Vert {W}^{l,t}({y}^{l}X{\gamma}^{l})\Vert}_{2}^{2}+\xi {\Vert {\gamma}^{l}\Vert}_{2}^{2}.$$
2. Calculate the residual by employing
$${e}_{k}^{l,t+1}=\left{y}_{k}^{l}{X}_{k}{\gamma}^{l,t+1}\right,(k=1,\dots ,d).$$
3. Calculate the residual function by using
$$\omega ({e}_{k}^{l,t+1})=\frac{\mathrm{exp}(\mu {({e}_{k}^{l,t+1})}^{2}+\mu \delta )}{1+\mathrm{exp}(\mu {({e}_{k}^{l,t+1})}^{2}+\mu \delta )},(k=1,\dots ,d).$$
4. Update ${W}^{l}$ by utilizing
$${W}^{l,t+1}=diag(\omega ({e}_{1}^{l,t+1}),\omega ({e}_{2}^{l,t+1}),\dots ,\omega ({e}_{d}^{l,t+1})).$$
5. Calculate $error={\Vert {W}^{l,t+1}{W}^{l,t}\Vert}_{F}/{\Vert {W}^{l,t}\Vert}_{F}.$ End while 6. For each spectral testing sample ${y}^{l},(l=1,2,\dots ,s)$, calculate ${A}^{l},(l=1,2,\dots ,s)$ by using
$${A}^{l}={(2\lambda CM+2\lambda {X}^{T}X+{X}^{T}{W}^{l}X)}^{1}{X}^{T}{W}^{l}{y}^{l}$$

Representation Method  Recognition Rate (%)  

NoiseFree  White Gaussian Noise  Salt & Pepper Noise  
SRC  99.64  97.84  94.28 
CRC  99.44  98.76  96.68 
DSRM  97.96  96.68  96.28 
RL2SR  99.68  99.20  97.24 
Fusion Method  Noise Contamination Case  Recognition Rate (%)  

2  3  4  
Sum fusion  Noisefree  97.50  99.56  99.90 
White Gaussian noise  96.70  99.44  99.65  
Salt & pepper noise  89.63  96.56  98.55  
Minmax fusion  Noisefree  92.83  97.68  99.25 
White Gaussian noise  92.67  97.44  99.20  
Salt & pepper noise  72.53  82.16  85.85  
Our adaptive fusion  Noisefree  97.73  99.68  100.00 
White Gaussian noise  97.47  99.20  99.95  
Salt & pepper noise  92.27  97.24  99.05 
Classifiers  Recognition Rate (%)  

NoiseFree  White Gaussian Noise  Salt & Pepper Noise  
NN  99.24  96.48  44.24 
KNN  97.12  93.32  38.92 
ELM  99.18  99.16  95.55 
MPELM  99.00  98.80  95.60 
RELM  99.41  98.96  96.07 
TELM  99.68  99.20  97.24 
Classifiers  Classify Time (s) 

NN  7.76 
KNN  5.17 
ELM  1.51 
MPELM  1.82 
RELM  1.67 
TELM  1.59 
Spectral Combination  Recognition Rate (%)  

NoiseFree  White Gaussian Noise  Salt & Pepper Noise  
Blue  99.55  98.65  80.90 
Green  99.50  99.25  87.65 
Red  99.45  99.15  83.10 
NIR  98.65  94.50  76.75 
Blue, Green  100.00  99.80  95.80 
Blue, Red  99.95  99.80  93.30 
Blue, NIR  100.00  99.85  90.70 
Green, Red  99.75  99.50  96.15 
Green, NIR  100.00  99.80  95.80 
Red, NIR  99.90  99.90  96.60 
Blue, Green, Red  100.00  99.85  98.65 
Blue, Green, NIR  100.00  99.90  97.60 
Blue, Red, NIR  100.00  99.90  97.15 
Green, Red, NIR  99.95  99.85  98.35 
Blue, Green, Red, NIR  100.00  99.95  99.05 
Algorithm  Recognition Rate (%) for Different Training Sample Number  

3  4  5  6  
Deep scattering network method [18]  100  100  100  100 
Texture feature based method [42]    99.96  99.99  100 
DCTbased features method [43]    99.97  100  100 
Our proposed RL2SRTELM  99.68  100  100  100 
Algorithm  Recognition Rate (%)  

NoiseFree  White Gaussian Noise  Salt & Pepper Noise  
Matching scorelevel fusion by LOC [41]  99.43  99.23  96.48 
DSTMPELM [39]  99.47  98.30  89.98 
AERELM [38]  99.16  98.48  95.76 
QPCA + QDWT [37]  98.83  93.33  90.16 
Imagelevel fusion by DWT [32]  99.03  96.23  82.75 
Our proposed RL2SRTELM  99.68  99.20  97.24 
Procedure  RL2SR and Adaptive Fusion  TELM  Total Time 

Average time (s)  0.10892  0.00053  0.10945 
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Cheng, D.; Zhang, X.; Xu, X. An Improved Recognition Approach for Noisy Multispectral Palmprint by Robust L2 Sparse Representation with a TensorBased Extreme Learning Machine. Sensors 2019, 19, 235. https://doi.org/10.3390/s19020235
Cheng D, Zhang X, Xu X. An Improved Recognition Approach for Noisy Multispectral Palmprint by Robust L2 Sparse Representation with a TensorBased Extreme Learning Machine. Sensors. 2019; 19(2):235. https://doi.org/10.3390/s19020235
Chicago/Turabian StyleCheng, Dongxu, Xinman Zhang, and Xuebin Xu. 2019. "An Improved Recognition Approach for Noisy Multispectral Palmprint by Robust L2 Sparse Representation with a TensorBased Extreme Learning Machine" Sensors 19, no. 2: 235. https://doi.org/10.3390/s19020235