Sparse representations for online-learning-based hyperspectral image compression

İrem Ülkü; Behçet Uğur Töreyin

doi:10.1364/AO.54.008625

Applied Optics
Vol. 54,
Issue 29,
pp. 8625-8631
(2015)
•https://doi.org/10.1364/AO.54.008625

Sparse representations for online-learning-based hyperspectral image compression

İrem Ülkü and Behçet Uğur Töreyin

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İrem Ülkü and Behçet Uğur Töreyin, "Sparse representations for online-learning-based hyperspectral image compression," Appl. Opt. 54, 8625-8631 (2015)

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Abstract

Sparse models provide data representations in the fewest possible number of nonzero elements. This inherent characteristic enables sparse models to be utilized for data compression purposes. Hyperspectral data is large in size. In this paper, a framework for sparsity-based hyperspectral image compression methods using online learning is proposed. There are various sparse optimization models. A comparative analysis of sparse representations in terms of their hyperspectral image compression performance is presented. For this purpose, online-learning-based hyperspectral image compression methods are proposed using four different sparse representations. Results indicate that, independent of the sparsity models, online-learning-based hyperspectral data compression schemes yield the best compression performances for data rates of 0.1 and 0.3 bits per sample, compared to other state-of-the-art hyperspectral data compression techniques, in terms of image quality measured as average peak signal-to-noise ratio.

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Sparse Rep.	Sparse Coding Equation	Dictionary Update Equation
(SIP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ x_{t} - D_{t - 1} α ‖}_{2}^{2} + λ {‖ α ‖}_{1}$ (8)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} (\frac{1}{2} {‖ x_{i} - D α_{i} ‖}_{2}^{2} + λ {‖ α_{i} ‖}_{1}),$ (9) where $t = 1, \dots, T$
(LASSO)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ D_{t - 1} α - x_{t} ‖}_{2}^{2} + λ {‖ α ‖}_{1}$ (10)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} (\frac{1}{2} {‖ D α_{i} - x_{i} ‖}_{2}^{2} + λ {‖ α_{i} ‖}_{1}),$ (11) where $t = 1, \dots, T$
(BP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} {‖ α ‖}_{1} s.t. D_{t - 1} α = x_{t}$ (12)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} {‖ α_{i} ‖}_{1} s.t. \frac{1}{t} \sum_{i = 1}^{t} (D α_{i}) = x_{i},$ (13) where $t = 1, \dots, T$
(gOMP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ x_{t} - D_{t - 1} α ‖}_{2}$ (14)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} ({‖ x_{i} - D α_{i} ‖}_{2}),$ (15) where $t = 1, \dots, T$

AVIRIS HYPERSPECTRAL DATA
Name	No. Samples	No. Lines	No. Bands	Bit depth	Flight Number	Year
Jasper Ridge	614	2587	224	16	f970403t01p02_r03	1997
Lunar Lake	614	1432	224	16	f970623t01p02_r07	1997
Low Altitude	614	3689	224	16	f960705t01p02_r05	1996
HYPERION HYPERSPECTRAL DATA
Name	No. Samples	No. Lines	No. Bands	Bit depth	Image Number		Year
Lake Monona	256	3176	242	12	EO1H0240302009166110PF		2009
Mt. St. Helens	256	3242	242	12	EO1H0460282009231110KF		2009
Erta Ale	256	3187	242	12	EO1H1680502010057110KF		2010

		HYPERSPECTRAL IMAGES
BPS	ALGORITHM	Jasper Ridge	Low Altitude	Lunar Lake	Mean PSNR
0.1	BCS PL-3DBS + 3DWPT	56.78	54.70	61.34	57.61
	BCS PL-2DBS + 2D DDWT	50.60	47.97	54.62	51.06
	BCS SPL-2DBS + 2D DDWT	50.30	48.02	54.05	50.79
	CPPCA	30.20	47.47	48.43	42.03
	SIP	58.06	58.34	58.86	58.42
	gOMP	59.40	59.79	58.37	59.19
	BP	59.41	59.96	59.55	59.64
	LASSO	59.30	59.59	59.54	59.48
0.3	BCS PL-3DBS + 3DWPT	64.21	61.74	69.38	65.11
	BCS PL-2DBS + 2D DDWT	54.18	51.67	59.39	55.08
	BCS SPL-2DBS + 2D DDWT	53.67	51.46	58.18	54.43
	CPPCA	71.31	60.98	72.19	68.16
	SIP	66.74	66.18	70.71	67.87
	gOMP	70.01	70.28	73.84	71.37
	BP	69.23	70.16	73.85	71.08
	LASSO	70.67	68.85	73.34	70.95
0.5	BCS PL-3DBS + 3DWPT	69.95	67.08	72.62	69.88
	BCS PL-2DBS + 2D DDWT	57.11	54.45	63.06	58.21
	BCS SPL-2DBS + 2D DDWT	56.45	54.40	61.35	57.40
	CPPCA	76.40	70.01	76.82	74.41
	SIP	71.34	71.20	72.39	71.64
	gOMP	71.14	72.68	74.92	72.91
	BP	71.71	73.24	76.55	73.60
	LASSO	73.17	73.52	75.20	73.96

Sparse Rep.	Sparse Coding Equation	Dictionary Update Equation
(SIP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ x_{t} - D_{t - 1} α ‖}_{2}^{2} + λ {‖ α ‖}_{1}$ (8)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} (\frac{1}{2} {‖ x_{i} - D α_{i} ‖}_{2}^{2} + λ {‖ α_{i} ‖}_{1}),$ (9) where $t = 1, \dots, T$
(LASSO)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ D_{t - 1} α - x_{t} ‖}_{2}^{2} + λ {‖ α ‖}_{1}$ (10)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} (\frac{1}{2} {‖ D α_{i} - x_{i} ‖}_{2}^{2} + λ {‖ α_{i} ‖}_{1}),$ (11) where $t = 1, \dots, T$
(BP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} {‖ α ‖}_{1} s.t. D_{t - 1} α = x_{t}$ (12)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} {‖ α_{i} ‖}_{1} s.t. \frac{1}{t} \sum_{i = 1}^{t} (D α_{i}) = x_{i},$ (13) where $t = 1, \dots, T$
(gOMP)	$α_{t} = \underset{α \in R^{k}}{\arg \min} \frac{1}{2} {‖ x_{t} - D_{t - 1} α ‖}_{2}$ (14)	$D_{t} = \underset{D \in C}{\arg \min} \frac{1}{t} \sum_{i = 1}^{t} ({‖ x_{i} - D α_{i} ‖}_{2}),$ (15) where $t = 1, \dots, T$

AVIRIS HYPERSPECTRAL DATA
Name	No. Samples	No. Lines	No. Bands	Bit depth	Flight Number	Year
Jasper Ridge	614	2587	224	16	f970403t01p02_r03	1997
Lunar Lake	614	1432	224	16	f970623t01p02_r07	1997
Low Altitude	614	3689	224	16	f960705t01p02_r05	1996
HYPERION HYPERSPECTRAL DATA
Name	No. Samples	No. Lines	No. Bands	Bit depth	Image Number		Year
Lake Monona	256	3176	242	12	EO1H0240302009166110PF		2009
Mt. St. Helens	256	3242	242	12	EO1H0460282009231110KF		2009
Erta Ale	256	3187	242	12	EO1H1680502010057110KF		2010

Abstract

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Applied Optics