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为了获得成像质量较好且成像时间较少的新型傅里叶望远镜成像策略, 本文比较了三种降采样成像策略(压缩感知方法(CS)、低频全采样方法(LF)和变密度随机采样方法(VD))与传统傅里叶望远镜(FT)在图像质量和成像时间上的差异. 分析方法如下: 利用传统FT外场实验所获得的目标频谱数据作为基础, 三种降采样方法(LF, VD和CS)分别按照各自的采样模式和重构方法实现目标图像的重构; 通过直观观察和Strehl比两种方法比较三种降采样方法与传统FT在图像质量上的差异; 通过分析成像时间的组成要素, 初步比较三种降采样方法与传统FT在成像时间上的差异. 分析表明: 1) 压缩感知方法的图像质量优于其他两种降采样方法(LF和VD), 但略低于传统成像结果; 2) 压缩感知方法在成像质量上略低于传统FT, 但在成像时间上却明显小于传统FT; 3)分析中采用的外场数据均含噪声, 这说明上述三种降采样重构过程对噪声有较好的鲁棒性. 综合上述分析结果可以看出, 基于压缩感知的傅里叶望远镜(CS-FT)是在实际含噪情况下可大幅减少成像时间的优良成像策略.In order to obtain a new imaging strategy of the Fourier telescope (FT) with a better imaging quality and a less imaging time, we optimize and compare three down-sampling imaging strategies in this paper: the compressed sensing method (CS), the low-frequency full sampling method (LF) and the variable-density random sampling method (VD), which are different from the traditional Fourier telescope in both of the image quality and the imaging time. The analytical methods are as follows: based on the target’s spectral data obtained from the field experiment of traditional FT, three down-sampling methods (LF, VD and CS) are used to reconstruct the target’s images according to their own sampling modes and reconstruction methods, respectively; the differences between the three down-sampling methods and the traditional FT regarding the image quality are compared by the instinctive observation and the Strehl ratio; based on the analysis of the imaging time, the differences between the three down-sampling methods and the traditional FT regarding the imaging time are preliminarily compared. The analysis shows that: 1) the image quality of the compressed sensing method is better than that of the other two down-sampling methods (LF and VD), slightly lower than that of the traditional imaging; 2) although the image quality of the compressed sensing method is slightly lower than that of the traditional FT, its imaging time is much lower than that of the traditional FT; 3) the field data used in the analysis contain noises, which means that the reconstruction methods of the above three down-sampling strategies have a better robustness to the noises. Based on the above results, it can be seen that the Fourier telescope based on compressed sensing (CS-FT) is an excellent imaging strategy which can greatly reduce the imaging time in the condition with actual noises.
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Keywords:
- synthetic aperture imaging /
- Fourier telescope /
- image reconstruction techniques /
- compressed sensing
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Google Scholar
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Google Scholar
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Dong L, Liu X Y, Lin X D, et al. 2012 Acta Opt. Sin. 32 0201004-1
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图 9 OPDF的影响 (a) 和 (b) 分别是OPDF = 3时的VD图像和CS图像; (c) 和 (d) 分别是OPDF = 4时的VD图像和CS图像; (e) 和 (f) 分别是OPDF = 5时的VD图像和CS图像
Fig. 9. The effect of the OPDF: (a) and (b) are the VD image and the CS image, respectively, when OPDF = 3; (c) and (d) are the VD image and the CS image, respectively, when OPDF = 4; (e) and (f) are the VD image and the CS image, respectively, when OPDF = 5
图 10 LSR的影响 (a) 和 (b) 分别是LSR = 0时的VD图像和CS图像; (c) 和 (d) 分别是LSR = 0.1时的VD图像和CS图像; (e) 和 (f) 分别是LSR = 0.3时的VD图像和CS图像; (g) 和 (h) 分别是LSR = 0.4时的VD图像和CS图像
Fig. 10. The effect of the LSR: (a) and (b) are the VD image and the CS image, respectively, when LSR = 0; (c) and (d) are the VD image and the CS image, respectively, when LSR = 0.1; (e) and (f) are the VD image and the CS image, respectively, when LSR = 0.3; (g) and (h) are the VD image and the CS image, respectively, when LSR = 0.4
图 11 TSR的影响 (a) 和 (b) 分别是标准图像和传统FT图像; (c), (d) 和 (e) 分别是TSR = 0.05时的LF图像, VD图像和CS图像; (f), (g) 和 (h) 分别是TSR = 0.1时的LF图像, VD图像和CS图像; (i), (j) 和 (k) 分别是TSR = 0.2时的LF图像, VD图像和CS图像; (l), (m) 和 (n) 分别是TSR = 0.4时的LF图像, VD图像和CS图像; (o), (p) 和 (q) 分别是TSR = 0.8时的LF图像, VD图像和CS图像
Fig. 11. The effect of the TSR: (a) and (b) are the standard image and the traditional FT image, respectively; (c), (d) and (e) are the LF image, the VD image and the CS image, respectively, when TSR = 0.05; (f), (g) and (h) are the LF image, the VD image and the CS image, respectively, when TSR = 0.1; (i), (j) and (k) are the LF image, the VD image and the CS image, respectively, when TSR = 0.2; (l), (m) and (n) are the LF image, the VD image and the CS image, respectively, when TSR = 0.4; (o), (p) and (q) are the LF image, the VD image and the CS image, respectively, when TSR = 0.8
表 1 四种方法的比较
Table 1. Comparison of the four methods
TSR Traditional FT/s LF method/s VD method/s CS method/s 0.05 8289 529 530 554 0.1 8289 943 944 968 0.2 8289 1772 1773 1797 0.4 8289 3430 3431 3455 0.8 8289 6746 6747 6771 
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[1] Louis S 1991 Appl. Opt. 30 206
Google Scholar
[2] Campbell B F, Rubin L, Holmes R B 1995 Appl. Opt. 34 5932
Google Scholar
[3] Rider C D, Jingle C, Nielson E 1996 Proceeding of the 1996 p147
[4] Holmes R B, Ma S, Bhowmik A, et al. 1996 J. Opt. Soc. Am. 13 351
Google Scholar
[5] Brinkley T J, Sand1er D Effect 1999 SPIE 3815 42
[6] Bakut P A, Mandrosov V I 1999 SPIE 3815 49
[7] Cuellar E L, Stapp J, Cooper J 2005 SPIE 5896 58960D
[8] Mandrosov V I, Bakut P A, Gamiz V I 2001 SPIE 4167 192
[9] Be1en'kii M, Hughes K, Brinkley T, et al. 2002 SPIE 4821 62
[10] Ford S D, Voelz D G, Gamiz V L, et al. 1999 SPIE 3815 2
[11] Gamiz V L, Holmes R B, Czyzak S R, et al. 2000 SPIE 4091 304
[12] Thornton M A, Oldenettel J R, Hult D W, et al. 2002 SPIE 4489 78
[13] Stapp J, Spivey B, Chen L, et al. 2006 SPIE 6307 630701-1
[14] Spivey B, Stapp J, Sandler D 2006 SPIE 6307 630702-1
[15] Cuellar E L, Cooper J, Mathis J, et al. 2008 SPIE 7094 70940G-1
[16] Candes E J, Wakin M B 2008 IEEE Signal Processing Mag. 25 21
[17] Romberg J 2008 IEEE Signal Processing Mag. 25 14
[18] Lustig M, Donoho D, Pauly J M 2007 Mag. Reson. Med. 58 1182
Google Scholar
[19] Qi D, Sha W 2009 Mathematics 1 1
[20] Qu X B, Zhang W R, Guo D, Cai C B, Cai S H, Chen Z 2010 Inverse Prob. Sci. Eng. 18 737
Google Scholar
[21] 刘欣悦, 董磊, 王建立 2010 光学精密工程 18 521
Liu X Y, Dong L, Wang J L 2010 Optics and Precision Engineering 18 521
[22] Lu C M, Gao X, Tang J, et al. 2012 SPIE 8551 855110-1
[23] Li Y, Xiangli B, Zhang W X, et al. 2013 SPIE 887788770J-1
[24] Zhou Z S, Xiangli B, Zhang W X, et al. 2013 SPIE 8905 89052X-1
[25] Yu S H, Dong L, Liu X Y, Lin X D, Meng H R, Zhong X 2016 Appl. Opt. 55 6654
[26] Donoho D, Maleki A, Shahram M 2018 WAVELAB 850 http://statweb.stanford.edu/~wavelab/Wavelab_850/index_wavelab850.html
[27] 董磊, 刘欣悦, 陈宝刚等 2011 光子学报 40 1317
Dong L, Liu X Y, Chen B G, et al. 2011 Acta Photon. Sin. 40 1317
[28] 董磊, 刘欣悦, 林旭东等 2012 光学学报 32 32 0201004-1
Dong L, Liu X Y, Lin X D, et al. 2012 Acta Opt. Sin. 32 0201004-1
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