Improving hyperspectral sub-pixel target detection in multiple target signatures using a revised replacement signal model

Figures & data

Figure 1. Cooke City dataset with target locations identified by the color squares (left). Plots showing the reference spectra of targets (right). The greyscale image (a), and the targets (b-h)

Figure 2. Overview of the proposed method

Figure 3. Examples of the greyscale images for bad band 63 (a), and 64 (b)

Table 1. The evaluation results for the predicted spectral signature based on the proposed strategy in the Cook City dataset. Good values for R² and RMSE are 100%, and 0, respectively

	V1	V2 (cabin)	V2 (back)	V3	F1	F2	F3	F4
R^2 [%]	74.0	85.0	60.0	71.7	91.9	67.5	74.0	76.9
RMSE	0.05	0.08	0.02	0.08	0.04	0.02	0.1	0.6

Figure 4. Plots showing the reflectance spectra of targets. Blue spectra denote the reference signature, and red spectra denote the prediction signature of V1 (a), V2-cabin (b), V2-back (c), and V3 (d)

Figure 5. Plots showing the reflectance spectra of targets. Blue spectra denote the reference signature, and red spectra denote the prediction signature of F1 (a), F2 (b), F3 (c), and F4 (d)

Table 2. Area under the ROC curve for vehicles. The bold values denote the best result

	Winner-take-all CEM (%)	ACE (%)	MF (%)	The proposed method (%)
V1	50.1	99.1	50.5	99.2
V2	50.1	99.0	50.8	99.1
V3	50.8	99.0	50.7	99.1
Average	50.3	99.0	50.6	99.1

Table 3. Area under the ROC curve for fabric panels. The bold values denote the best result

	Winner-take-all CEM (%)	ACE (%)	MF (%)	The proposed method (%)
F1	50.0	99.0	50.3	99.1
F2	50.5	98.9	50.9	98.9
F3	50.0	98.9	50.4	98.9
F4	50.6	99.0	50.7	99.0
Average	50.2	98.9	50.6	98.9

Figure 6. Results of the first target (V1). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 7. Results of the second target (V2). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 8. Results of the third target (V3). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 9. Results of the fourth target (F1). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 10. Results of the fifth target (F2). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 11. Results of the sixth target (F3). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Figure 12. Results of the seventh target (F4). The Probability prediction values for target pixels are defined in a range from 0% to 100%

Table 4. A comparison between probability prediction values in the proposed approach and the state-of-the-art methods for different targets. The bold values denote the best result

	Winner-take-all CEM (%)		ACE (%)		MF (%)		The proposed method (%)
	Pure	Mixed	Pure	Mixed	Pure	Mixed	Pure	Mixed
V1	3.0	2.3	16	8.1	3.3	2.6	30	9.3
V2	0.0	0.0	0.0	1.5	0.0	0.0	5.5	4.0
V3	0.0	0.0	3.0	4.0	0.0	0.5	6.0	4.3
F1	0.0	0.0	42.9	40.9	3.9	3.1	44.0	40.9
F2	5.4	1.3	35.7	6.9	5.4	1.5	35.6	6.9
F3	0.0	0.0	1.2	0.3	0.1	0.1	1.2	0.3
F4	0.0	0.0	29.2	14.6	0.0	0.0	29.2	14.6
Average	1.2	0.5	18.3	10.9	1.8	1.1	21.6	11.5

Table

Pf	False alarm probability
P0(z)	Gaussian distribution with mean zero and variance ${\sigma }_{z_l}^2$
G	Background covariance matrix
M	Total number of pixels
q	Virtual dimensionality determined by the HFC approach
x	Observed pixel spectrum
s	Spectrum of the target
v	Spectrum of the background
ε	An error threshold
ACE	Adaptive cosine estimator
ATGP	Automatic target generation process
CEM	Constrained energy minimization
GLRT	Generalized likelihood ratio test
HFC	Harsanyi-Farrand-Chang
MF	Matched filter
R^2	Coefficient of determination
RMSE	Root mean square error
SAM	Spectral angle mapper