Optical property inversion of biological materials using Fourier series expansion and LS-SVM for hyperspectral imaging

Figures & data

Figure 1. Schematic of the steady-state spatially resolved measurement technique.

Figure 2. Acquisition of hyperspectral images for liquid phantoms.

Figure 3. Flowchart of the model development for predicting optical properties.

Figure 4. Comparison of the spatially resolved diffuse reflectance profiles obtained from MC simulation: (a) ${\mathit{\mu }}_a=0.04{\text{cm}}^{-1}$, ${\mathit{\mu }}_s^{\prime }=4{\text{cm}}^{-1}$ (dotted line) and ${\mathit{\mu }}_a=0.29{\text{cm}}^{-1}$, ${\mathit{\mu }}_s^{\prime }=4{\text{cm}}^{-1}$ (solid line) (b) ${\mathit{\mu }}_a=0.04{\text{cm}}^{-1}$, ${\mathit{\mu }}_s^{\prime }=8{\text{cm}}^{-1}$ (dotted line) and ${\mathit{\mu }}_a=0.04{\text{cm}}^{-1}$ ${\mathit{\mu }}_s^{\prime }=12{\text{cm}}^{-1}$ (solid line).

Figure 5. Relative errors of (a) μ_a and (b) ${\mathit{\mu }}_s^{\prime }$ with different combinations of the Fourier coefficients.

Table 1. Calibration and prediction results (in percent) for MC simulation.^a

Model	MRE ± SD
	Calibration		Prediction
	μa	${\mathit{\mu }}_s^{\prime }$	μa	${\mathit{\mu }}_s^{\prime }$
LS-SVM	0.86 ± 0.24	0.65 ± 0.18	5.82 ± 1.51	3.21 ± 0.87
PCA-LS-SVM	0.71 ± 0.19	0.52 ± 0.14	3.63 ± 1.03	1.96 ± 0.52
FSE-LS-SVM	0.65 ± 0.16	0.47 ± 0.12	1.52 ± 0.44	0.62 ± 0.16

^a These values shown are averages of 10 calibration/prediction runs.

Table 2. Calibration and prediction results (in percent) for MC simulation with different noise levels.^a

Model	MRE
	Calibration						Prediction
	μa			${\mathit{\mu }}_s^{\prime }$			μa			${\mathit{\mu }}_s^{\prime }$
	80^b	60^b	40^b	80	60	40	80	60	40	80	60	40
LS-SVM	0.89	0.95	1.14	0.68	0.73	0.96	7.72	9.68	20.11	5.34	6.41	9.15
PCA-LS-SVM	0.75	0.83	0.92	0.56	0.61	0.79	5.89	7.47	10.26	3.76	5.10	7.43
FSE-LS-SVM	0.67	0.71	0.78	0.49	0.54	0.62	2.42	2.93	4.28	0.92	1.34	1.72

^a These values shown are averages of 10 calibration/prediction runs.

^b The 80, 60 and 40 are SNR of the noise.

Figure 6. (a) Hyperspectral image of a blue dye liquid phantom and (b) diffuse reflectance profiles for the three selected wavelengths.

Table 3. Calibration and prediction results (in percent) for liquid phantoms using experimental data.^a

Model	MRE ± SD
	Calibration		Prediction
	μa	${\mathit{\mu }}_s^{\prime }$	μa	${\mathit{\mu }}_s^{\prime }$
LS-SVM	4.92 ± 1.21	3.75 ± 0.92	19.80 ± 5.62	15.34 ± 4.05
PCA-LS-SVM	3.27 ± 0.81	2.35 ± 0.57	16.47 ± 4.11	12.19 ± 3.58
FSE-LS-SVM	2.18 ± 0.49	1.54 ± 0.42	11.03 ± 3.06	7.16 ± 1.95

^a These values shown are averages of 10 calibration/prediction runs.

Figure 7. The prediction results of μ_a and ${\mathit{\mu }}_s^{\prime }$ for three liquid phantoms using experimental data: (a1) μ_a of blue dye, (b1) ${\mathit{\mu }}_s^{\prime }$ of blue dye, (a2) μ_a of green dye, (b2) ${\mathit{\mu }}_s^{\prime }$ of green dye, (a3) μ_a of black ink and (b3) ${\mathit{\mu }}_s^{\prime }$ of black ink.

Table 4. Calibration and prediction results (in percent) for liquid phantoms using MC simulation data.^a

Model	MRE ± SD
	Calibration		Prediction
	μa	${\mathit{\mu }}_s^{\prime }$	μa	${\mathit{\mu }}_s^{\prime }$
LS-SVM	2.16 ± 0.45	1.75 ± 0.48	31.63 ± 6.48	20.22 ± 4.76
PCA-LS-SVM	1.58 ± 0.37	1.21 ± 0.24	20.16 ± 4.35	16.54 ± 3.97
FSE-LS-SVM	1.26 ± 0.25	0.94 ± 0.20	15.96 ± 3.49	10.91 ± 3.14

^a These values shown are averages of 10 calibration/prediction runs.

Figure 8. The prediction results of μ_a and ${\mathit{\mu }}_s^{\prime }$ for three simulation phantoms using MC simulation data: (a1) μ_a of blue dye, (b1) ${\mathit{\mu }}_s^{\prime }$ of blue dye, (a2) μ_a of green dye, (b2) ${\mathit{\mu }}_s^{\prime }$ of green dye, (a3) μ_a of black ink and (b3) ${\mathit{\mu }}_s^{\prime }$ of black ink.