High-precision algorithm for restoration of spectral imaging based on joint solution of double sparse domains

Shi-Jie LIU; Chun-Lai LI; Rui XU; Guo-Liang TANG; Bing WU; Yan XU; Jian-Yu WANG

doi:10.11972/j.issn.1001-9014.2021.05.016

Journals >Journal of Infrared and Millimeter Waves >Volume 40 >Issue 5 >Page 685 > Article

Journal of Infrared and Millimeter Waves
Vol. 40, Issue 5, 685 (2021)

High-precision algorithm for restoration of spectral imaging based on joint solution of double sparse domains

Shi-Jie LIU^1、2, Chun-Lai LI^1、*, Rui XU¹, Guo-Liang TANG^1、2, Bing WU^1、2, Yan XU^1、2、4, and Jian-Yu WANG^{1、2、3、**}

Author Affiliations

¹Key Laboratory of Space Active Opto-Electronics Technology，Shanghai Institute of Technical Physics，Chinese Academy of Sciences，Shanghai 200083，China

²University of Chinese Academy of Sciences，Beijing 100049，China

³Hangzhou Institute for Advanced Study，University of Chinese Academy of Sciences，Hangzhou，310024China

⁴School of Information Science&Techno1ogy，ShanghaiTech University，Shanghai 200020，China

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DOI: 10.11972/j.issn.1001-9014.2021.05.016 Cite this Article

Shi-Jie LIU, Chun-Lai LI, Rui XU, Guo-Liang TANG, Bing WU, Yan XU, Jian-Yu WANG. High-precision algorithm for restoration of spectral imaging based on joint solution of double sparse domains[J]. Journal of Infrared and Millimeter Waves, 2021, 40(5): 685 Copy Citation Text

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Fig. 1. Spectrum data can be divided into contour and details

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Fig. 2. igh and low frequency distribution of corresponding signals when σ is 10，25，250

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Fig. 3. Recovery results of different sampling rates under different sparsity constraints (a) Sampling rate: 40%, σ: 10, (b) Sampling rate: 40%, σ: 25, (c) Sampling rate: 40%, σ: 250,(d) Sampling rate: 80%, σ: 10, (e) Sampling rate: 80%, σ: 25, (f) Sampling rate: 80%, σ: 250

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Fig. 4. Test results on 500 samples (a) (b): Comparison of recovery accuracy at different sampling rates (σ: 15) ,(c) (d):σ’s impact on recovery accuracy (Sampling rate: 40%)

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Fig. 5. Information distribution of carnauba wax spectrum corresponding to different sparse transforms（a）Distribution of different sparse transform coefficients，（b）：Distribution during signal reconstruction at σ=10，（c）Distribution during signal reconstruction at σ=100

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Fig. 6. Effect of σ on the recovery results of different sparse decompositions. (a) (b) at a sampling rate of 40%，(c) (d) at a sampling rate of 80%

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Fig. 7. Effect of σ on recovery speed of different sparse decompositions. (a) (b) at a sampling rate of 40%，(c) (d) at a sampling rate of 80%

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Fig. 8. Laboratory verification equipment and verification results（a）CASSI system，（b）recovered true color image by 80% sampling，（c）PHI imaging results，（d）~（g）Recovered results by two algorithms under 20%，40%，80% and 100%sampling

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输入： $y, Φ$

输出： $x$

1：设置σ，求解：

2：设置ζ，求解：其中：yh=y-ylyl=Φx̂l=ΦΨθ̂l =Θθ̂l

3、返回：

，其中：

Table 1. Method Based on Joint of Double Sparse Domains

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算法名称	采样率	DCT		DWT（db4）		DWT（sysm4）		DWT（coif4）		Average
算法名称	采样率	SAM	GSAM	SAM	GSAM	SAM	GSAM	SAM	GSAM	SAM	GSAM
OMP	20%	0.654	0.479	0.663	0.482	0.677	0.579	0.664	0.445	0.665	0.496
	40%	0.723	0.574	0.733	0.597	0.734	0.677	0.733	0.554	0.738	0.600
	80%	0.918	0.792	0.926	0.823	0.921	0.893	0.883	0.807	0.912	0.829
IRLS	20%	0.662	0.481	0.670	0.583	0.680	0.493	0.631	0.443	0.614	0.500
	40%	0.716	0.592	0.726	0.697	0.734	0.607	0.700	0.561	0.719	0.614
	80%	0.898	0.772	0.902	0.879	0.920	0.882	0.858	0.747	0.895	0.820
TwIST	20%	0.596	0.556	0.586	0.577	0.622	0.572	0.583	0.544	0.597	0.562
	40%	0.668	0.647	0.679	0.628	0.718	0.672	0.651	0.633	0.679	0.645
	80%	0.843	0.830	0.881	0.866	0.903	0.850	0.832	0.827	0.865	0.843
GPSR	20%	0.624	0.504	0.636	0.544	0.624	0.482	0.615	0.482	0.625	0.503
	40%	0.697	0.547	0.717	0.583	0.699	0.547	0.686	0.533	0.700	0.553
	80%	0.770	0.692	0.798	0.752	0.791	0.632	0.764	0.684	0.781	0.690
JDSD1 （OMP+IRLS）	20%	0.851	0.561	0.887	0.865	0.891	0.661	0.889	0.875	0.880	0.741
	40%	0.895	0.712	0.932	0.919	0.942	0.880	0.941	0.900	0.928	0.853
	80%	0.962	0.871	0.942	0.932	0.952	0.892	0.963	0.921	0.955	0.904
JDSD2 （OMP+TwIST）	20%	0.856	0.663	0.863	0.667	0.756	0.663	0.756	0.593	0.808	0.647
	40%	0.932	0.752	0.941	0.764	0.832	0.732	0.872	0.792	0.894	0.760
	80%	0.972	0.891	0.980	0.923	0.882	0.879	0.942	0.894	0.944	0.897
JDSD3 （OMP+ GPSR）	20%	0.831	0.561	0.827	0.661	0.731	0.541	0.661	0.591	0.762	0.589
	40%	0.865	0.700	0.853	0.779	0.865	0.765	0.765	0.724	0.837	0.742
	80%	0.942	0.847	0.936	0.907	0.902	0.837	0.902	0.877	0.921	0.891

Table 2. Comparison of JDSD algorithm recovery results of different combinations

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