Continuum removal for ground-based LWIR hyperspectral infrared imagery applying non-negative matrix factorization

Bardia Yousefi; Saeed Sojasi; Clemente Ibarra Castanedo; Xavier P. V. Maldague; Georges Beaudoin; Martin Chamberland

doi:10.1364/AO.57.006219

Applied Optics
Vol. 57,
Issue 21,
pp. 6219-6228
(2018)
•https://doi.org/10.1364/AO.57.006219

Continuum removal for ground-based LWIR hyperspectral infrared imagery applying non-negative matrix factorization

Bardia Yousefi, Saeed Sojasi, Clemente Ibarra Castanedo, Xavier P. V. Maldague, Georges Beaudoin, and Martin Chamberland

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Bardia Yousefi, Saeed Sojasi, Clemente Ibarra Castanedo, Xavier P. V. Maldague, Georges Beaudoin, and Martin Chamberland, "Continuum removal for ground-based LWIR hyperspectral infrared imagery applying non-negative matrix factorization," Appl. Opt. 57, 6219-6228 (2018)

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Abstract

Continuum removal is vital in hyperspectral image analysis. It enables data to be used for any application and usually requires approximations or assumptions to be made. One of these approximations is related to the calculation of the spectra of the background’s blackbody temperature. Here, we present a new method to calculate the continuum removal process. The proposed method eliminates the calculation for ground-based hyperspectral infrared imagery by applying two acquisition sets before and after using the heating source. The approach involves a laboratory experiment on a long-wave infrared (LWIR; 7.7–11.8 μm), with a LWIR-macro lens, an Infragold plate, and a heating source. To calculate the continuum removal process, the approach applies non-negative matrix factorization (NMF) to extract Rank-1 NMF, estimate the downwelling radiance, and compare it with that of other conventional methods. NMF uses gradient-descent-based rules (GD) and non-negative least-squares (NNLS) optimization algorithms to obtain Rank-1 NMF. A comparative analysis is performed with 1%–20% additive noise for all algorithms by using the spectral angle mapper and normalized cross correlation (NCC). Results reveal the promising performance of NMF-GD (average of 72.5% similarity percentage using NCC) and NMF-NNLS (average of 77.6% similarity percentage using NCC).

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Minerals	Chemical Formula	Short Description
Biotite	$K {(Mg, Fe)}_{2 - 3} {Al}_{1 - 2} {Si}_{2 - 3} O_{10} {(OH, F)}_{2}$	Substantial group of dark mica minerals
Diopside	${MgCaSi}_{2} 0_{6}$	Forms complete solid solution series with hedenbergite ( $FeCaSi 20_{6}$ ) and augite, and partial solid solutions with orthopyroxene and pigeonite
Epidote	${Ca}_{2} ({Al}_{2}, Fe) ({SiO}_{4}) ({Si}_{2} O_{7}) O (OH)$	Silicate mineral
Tourmaline	$[(Na, Ca) {(Mg, Li, Al, {Fe}^{2 +})}_{3} {Al}_{6} {({BO}_{3})}_{3} {Si}_{6} O_{18} {(OH)}_{4}]$	Boron silicate minerals compounded with elements such as Al, Fe, Mg, Na, Li, or K
Olivine	$({Mg}^{+ 2}, {Fe}^{+ 2})_{2} {SiO}_{4}$
Pyrope	${Mg}_{3} {AI}_{2} {({SiO}_{4})}_{3}$	Garnet group minerals
Quartz	${SiO}_{2}$	The most abundant mineral in the Earth’s crust

Mineral	Noise	Method (%)
		NCC				SAM
		Average	NMFGD	NMFNNLS	Random Selection	Average	NMFGD	NMFNNLS	Random Selection
Biotite	0%	90.3	89.9	86.8	90.1	72.3	71.9	69.9	72.2
	1%	93.1	92.9	89.9	90.2	78.9	78.8	76.5	73.5
	2%	89.3	89.3	85.2	75.1	70.9	70.9	68.3	51.2
	5%	92.9	91.7	89.4	21.4	78.7	76.9	75.9	$< 1$
	10%	89.2	78.5	83.2	6.3	70.9	59.2	64.7	$< 1$
	20%	74.1	66.4	76.3	$< 1$	62.2	49.8	59.8	$< 1$
Diopside	0%	72.2	72.8	74.3	71.8	57.5	58.3	60.8	56.9
	1%	71.4	71.2	74.2	69.7	57.9	57.6	62.6	57.1
	2%	71.8	72.5	75.4	64.5	57.8	58.6	62.7	49.4
	5%	71.7	70.4	73.6	16.8	57.7	57.1	60.8	$< 1$
	10%	71.5	56.2	71.5	$< 1$	57.7	40.9	59.01	$< 1$
	20%	68.4	51.1	69.2	$< 1$	56.8	38.5	57.4	$< 1$
Epidote	0%	84.4	82.1	84.8	84.6	66.1	62.8	68.4	66.4
	1%	85.3	85.7	87.7	82.8	63.5	63.9	67.2	61.6
	2%	82.8	82.9	86.8	79.9	64.1	64.3	69.8	61.7
	5%	84.3	84.7	83.9	4.8	65.9	65.5	67.2	$< 1$
	10%	79.8	57.9	81.1	$< 1$	62.7	39.7	63.9	$< 1$
	20%	76.2	44.1	77.02	$< 1$	61.4	28.02	61.8	$< 1$
Tourmaline	0%	52.6	51.9	53.4	52.1	38.5	33.2	32.9	32.9
	1%	47.5	47.8	50.4	46.5	36.9	37.2	40.1	35.4
	2%	47.4	48.1	51.1	43.2	36.9	37.4	39.7	35.2
	5%	46.5	45.9	47.1	7.6	35.1	34.6	35.2	$< 1$
	10%	50.8	29.6	55.9	9.6	30.3	26.8	34.1	$< 1$
	20%	45.7	12.1	52.8	$< 1$	28.01	22.9	31.2	$< 1$
Pyrope	0%	93.5	94.1	75.4	93.5	44.9	46.1	28.4	44.5
	1%	93.9	93.9	86.6	88.4	54.8	56.1	41.5	51.8
	2%	92.7	93.4	85.9	75.2	55.8	56.5	43.1	48.3
	5%	92.2	93.3	87.5	4.1	62.3	63.7	53.1	$< 1$
	10%	92.9	55.9	84.2	$< 1$	56.2	33.3	45.1	$< 1$
	20%	87.01	32.2	81.2	$< 1$	52.2	28.2	42.1	$< 1$
Olivine	0%	84.9	84.9	80.8	84.7	64.9	64.6	56.8	64.5
	1%	86.4	86.1	85.5	86.1	66.7	66.01	64.2	66.4
	2%	87.6	88.2	87.2	75.5	68.3	69.1	65.7	53.9
	5%	86.1	82.1	81.1	16.01	65.9	61.7	58.3	$< 1$
	10%	86.1	28.1	81.1	$< 1$	65.8	51.4	59.2	$< 1$
	20%	80.9	21.5	80.4	$< 1$	61.2	47.5	57.9	$< 1$
Quartz	0%	73.6	75.2	82.3	75.3	62.2	62.8	65	62.5
	1%	70.4	69.6	80.7	66.5	61.9	61.7	65.9	58.7
	2%	73.5	75.5	80.3	64.1	62.1	62.9	63.3	53.7
	5%	68.6	63.4	77.1	11.6	63.7	57.5	66.8	$< 1$
	10%	69.7	50.5	73.3	11.8	61.5	38.8	60.3	$< 1$
	20%	64.2	47.9	70.6	5.8	57.3	28.1	57.8	$< 1$

Average NCC	Comparative Accuracy
Average NCC	PLSR	Random Selection	Averaging	NMFGD	NMFNNLS
Biotite	63.2	90.1	90.3	89.9	86.8
Diopside	61.2	71.8	72.2	72.8	74.3
Epidote	68.8	84.6	84.4	82.1	84.8
Tourmaline	44.7	52.6	51.9	53.4	52.1
Pyrope	90.1	93.5	93.5	94.1	75.4
Olivine	69.6	84.7	84.9	84.9	80.8
Quartz	70.7	75.3	73.6	75.2	82.3

Mineral	Computational Complexity
Mineral	Averaging	NMFGD	NMFNNLS	Random
Biotite	0.2	0.79	1.18	0.28
Diopside	0.18	0.68	1.31	0.28
Epidote	0.18	0.98	1.33	0.26
Tourmaline	0.18	0.62	1.32	0.26
Pyrope	0.16	0.60	1.21	0.23
Olivine	0.17	0.76	1.11	0.23
Quartz	0.19	0.79	1.12	0.24

Minerals	Chemical Formula	Short Description
Biotite	$K {(Mg, Fe)}_{2 - 3} {Al}_{1 - 2} {Si}_{2 - 3} O_{10} {(OH, F)}_{2}$	Substantial group of dark mica minerals
Diopside	${MgCaSi}_{2} 0_{6}$	Forms complete solid solution series with hedenbergite ( $FeCaSi 20_{6}$ ) and augite, and partial solid solutions with orthopyroxene and pigeonite
Epidote	${Ca}_{2} ({Al}_{2}, Fe) ({SiO}_{4}) ({Si}_{2} O_{7}) O (OH)$	Silicate mineral
Tourmaline	$[(Na, Ca) {(Mg, Li, Al, {Fe}^{2 +})}_{3} {Al}_{6} {({BO}_{3})}_{3} {Si}_{6} O_{18} {(OH)}_{4}]$	Boron silicate minerals compounded with elements such as Al, Fe, Mg, Na, Li, or K
Olivine	$({Mg}^{+ 2}, {Fe}^{+ 2})_{2} {SiO}_{4}$
Pyrope	${Mg}_{3} {AI}_{2} {({SiO}_{4})}_{3}$	Garnet group minerals
Quartz	${SiO}_{2}$	The most abundant mineral in the Earth’s crust

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Applied Optics