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基于空间域压缩采样和谱域Karhunen-Loève变换的光谱成像与重构

Spectral Imaging and Reconstruction Based on Spatial Compressive Sampling and Spectral Karhunen-Loève Transform

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摘要

光谱图像包含丰富的空间信息和光谱信息,能够为天基预警探测任务提供重要的信息支撑,但其庞大的数据量给硬件设备带来了极大的挑战。传统的基于奈奎斯特采样的“先采样后压缩”的处理方式不仅无法从根本上解决数据量庞大的问题,还会造成资源浪费;针对此问题,利用单波段二维图像的稀疏性和空间编码数据的谱间冗余,设计了一种基于空间域压缩采样和谱域Karhunen-Loève (KL)变换编码的光谱图像重构方法,并建立基于1范数和全变分约束的单波段二维图像复合正则重构模型,同时结合投影梯度法和软阈值收缩算子设计2D-CRPG模型求解算法。结果表明:基于空间域压缩采样和谱域KL变换编码的光谱图像重构方法能够有效降低数据采样成本,有利于天基预警探测光谱成像;2D-CRPG重构算法能够有效保留光谱图像的结构信息,从而在有限的采样率下较好地重构原始光谱图像。

Abstract

Spectral images contain abundant space information and spectral information, which can provide important information support for space-based early warning detection. However, the huge amounts of data also brings great challenge for hardware. The traditional treatment of first sampling and then compressing based on Nyquist sampling not only can’t solve the problem of mass-data fundamentally, but also causes wasting of sources. To solve this problem, we propose a spectral imaging and reconstruction method based on spatial compressive sampling and spectral Karhunen-Loève (KL) transform by using the sparsity of single-band images and the spectral redundant of spatial encoded data. A two-dimensional composite regular reconstruction model based on 1-norm and total variation is constructed for single band images, and an inference algorithm named two-dimensional compound regularized projection gradient (2D-CRPG) is then proposed for the model by combining the projection gradient method with the soft-threshold operator. The results show that the spectral imaging and reconstruction method based on spatial compressive sampling and KL transform can effectively reduce the cost of data sampling, and thus can benefit the spectral imaging of space-based early warning detection. The 2D-CRPG reconstruction algorithm can effectively preserve structural information of spectral images, thus the original spectral image can be reconstructed at a limited sampling rate.

Newport宣传-MKS新实验室计划
补充资料

中图分类号:TP751.1

DOI:10.3788/aos201838.0530004

所属栏目:光谱学

基金项目:国家自然科学基金(61273275)

收稿日期:2017-11-20

修改稿日期:2017-12-27

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唐意东:空军工程大学防空反导学院, 陕西 西安 710051
黄树彩:空军工程大学防空反导学院, 陕西 西安 710051
黄达:空军工程大学防空反导学院, 陕西 西安 710051

联系人作者:黄树彩(hsc67118@126.com)

备注:唐意东(1989-),男,博士研究生,主要从事压缩感知、光谱图像处理方面的研究。E-mail: 18109267859@163.com

【1】Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

【2】Candes E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

【3】Wang Q, Ma L L, Li C R, et al. Improved method of dictionary atom selection in compressive sensing spectral reconstruction[J]. Acta Optica Sinica, 2016, 36(9): 0930002.
汪琪, 马灵玲, 李传荣, 等. 压缩感知光谱重构中的字典原子选取优化方法[J]. 光学学报, 2016, 36(9): 0930002.

【4】Jing N, Bi W H, Hu Z P, et al. A survey on dynamic compressed sensing[J]. Acta Automatica Sinica, 2015, 41(1): 22-37.
荆楠, 毕卫红, 胡正平, 等. 动态压缩感知综述[J]. 自动化学报, 2015, 41(1): 22-37.

【5】Tan S Y, Liu Z T, Li E R, et al. Hyperspectral compressed sensing based on prior images constrained[J]. Acta Optica Sinica, 2015, 35(8): 0811003.
谭诗语, 刘震涛, 李恩荣, 等. 基于先验图像约束的多光谱压缩感知[J]. 光学学报, 2015, 35(8): 0811003.

【6】Yan J W, Liu L, Qu X B. Compressive sensing and its applications[M]. Beijing: National Defense Industry Press, 2015: 67-89.
闫敬文, 刘蕾, 屈小波. 压缩感知及应用[M]. 北京: 国防工业出版社, 2015: 67-89.

【7】Rivenson Y, Stern A. Compressed imaging with a separablesensing operator[J]. IEEE Signal Processing Letters, 2009, 16(6): 449-452.

【8】Wu Q, Zhou L J, Yin J F. Matrix analysis[M]. Shanghai: Tongji University Press, 2017: 54-58.
吴群, 周羚君, 殷俊锋. 矩阵分析[M]. 上海: 同济大学出版社, 2017: 54-58.

【9】Li Z L. Study on image compressive sensing reconstruction algorithms[D]. Beijing: Beijing Jiaotong University, 2012: 95-109.
李志林. 图像压缩感知重建算法研究[D]. 北京: 北京交通大学, 2012: 95-109.

【10】Lu G. Block compressed sensing of natural images[C]∥Proceedings of the 15th International Conference on Digital Signal Processing, 2007: 403-406.

【11】Cen Y G, Chen X F, Cen L H, et al. Compressed sensing based on the single layer wavelet transform for image processing[J]. Journal on Communications, 2010, 31(8A): 52-55.
岑翼刚, 陈晓方, 岑丽辉, 等. 基于单层小波变换的压缩感知图像处理[J]. 通信学报, 2010, 31(8A): 52-55.

【12】Fang Y, Wu J J, Huang B. 2D sparse signal recovery via 2D orthogonal matching pursuit[J]. Science China: Information Sciences, 2012, 55(4): 889-897.

【13】Ghaffari A, Babaie-Zadeh M, Jutten C. Sparse decomposition of two dimensional signals[C]∥Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, 2009: 3157-3160.

【14】Wimalajeewa T, Eldar Y C, Varshney P K. Recovery of sparse matrices via matrix sketching[EB/OL]. (2013-11-11)[2017-11-20]. http: ∥arxiv.org/abs/1311.2448.

【15】Liao L, Zhang Y N, Zhang C. 2DCS: two dimensional random underdetermined projection for image representation and classification[C]∥Proceedings of the International Conference on Multimedia Technology, 2011: 1-5.

【16】Daubechies I, Fornasier M, Loris I. Accelerated projected gradient method for linear inverse problems with sparsity constraints[J]. Journal of Fourier Analysis and Applications, 2008, 14(5/6): 764-792.

【17】Tang Y D. Research on detection and classification method for compressive spectral imaging[D]. Xi’an: Air Force Engineering University, 2017: 75-89.
唐意东. 压缩感知光谱成像目标检测与分类识别方法研究[D]. 西安: 空军工程大学, 2017: 75-89.

引用该论文

Tang Yidong,Huang Shucai,Huang Da. Spectral Imaging and Reconstruction Based on Spatial Compressive Sampling and Spectral Karhunen-Loève Transform[J]. Acta Optica Sinica, 2018, 38(5): 0530004

唐意东,黄树彩,黄达. 基于空间域压缩采样和谱域Karhunen-Loève变换的光谱成像与重构[J]. 光学学报, 2018, 38(5): 0530004

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