基于非局部相似性和低秩矩阵的遥感图像重构方法
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摘要
针对遥感图像非局部相似的特性,提出了一种基于图像非局部相似性、低秩矩阵和最小全变分(TV)的压缩感知(CS)重构算法。充分利用了遥感图像的非局部相似性先验、局部平滑性先验以及低秩矩阵的特性,同时引入了一种新的基于欧氏距离和结构相似度的联合块匹配方式,使匹配结果更准确,最终实现了高质量的遥感图像重构。仿真结果表明,与传统的基于变换域稀疏或TV约束的重构算法相比,所提出的算法能获得更高的图像重构质量,峰值信噪比和结构相似度等评价值都有较大的提高,验证了算法的有效性。
A compressed sensing reconstruction method based on nonlocal similarity,low rank matrix and minimum total variation(TV)is proposed,considering the non-local similarity of remote sensing images.It fully exploits the nonlocal similarity prior,local smoothness prior of remote sensing images and the low rank properties of matrix.A new joint block matching method based on Euclidean distance and structural similarity is developed,which makes the matching result more accurate.The reconstruction of high quality remote sensing image is realized finally.Simulation results confirm that the proposed algorithm can achieve high reconstruction quality comparing with the traditional reconstruction method based on sparse transform domain or TV regularization.The peak signal to noise ratio and structural similarity have a great improvement,and the effectiveness of the proposed method is verified.
A compressed sensing reconstruction method based on nonlocal similarity,low rank matrix and minimum total variation(TV)is proposed,considering the non-local similarity of remote sensing images.It fully exploits the nonlocal similarity prior,local smoothness prior of remote sensing images and the low rank properties of matrix.A new joint block matching method based on Euclidean distance and structural similarity is developed,which makes the matching result more accurate.The reconstruction of high quality remote sensing image is realized finally.Simulation results confirm that the proposed algorithm can achieve high reconstruction quality comparing with the traditional reconstruction method based on sparse transform domain or TV regularization.The peak signal to noise ratio and structural similarity have a great improvement,and the effectiveness of the proposed method is verified.
引文
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10 Buades A,Coll B,Morel J M.A non-local algorithm for image denoising[C].Computer Vision and Pattern Recognition,Computer Society Conference on.IEEE,2005,2:60-65.
11 Dong W,Shi G,Li X.Nonlocal image restoration with bilateral variance estimation:A low-rank approach[J].Image Processing,IEEE Transactions on,2013,22(2):700-711.
12 Candes E J,Romberg J K,Tao T.Stable signal recovery from incomplete and inaccurate measurements[J].Communications on pure and applied mathematics,2006,59(8):1207-1223.
13 Chambolle A.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
14 Dabov K,Foi A,Katkovnik V,et al..Image restoration by sparse 3Dtransform-domain collaborative filtering[C].Electronic Imaging,International Society for Optics and Photonics,2008:681207.
15 Wang Z,Bovik A C,Sheikh H R,et al..Image quality assessment:From error visibility to structural similarity[J].Image Processing,IEEE Transactions on,2004,13(4):600-612.
16 Candes E J,Recht B.Exact matrix completion via convex optimization[J].Foundations of Computational Mathematics,2009,9(6):717-772.
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18 Goldstein T,Osher S.The split bregman method for l1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
19 Chen Baolin.Optimization theory and algorithm[M].Second edition.Beijing:Tsinghua University Press,2005:294-306. 陈宝林.最优化理论与算法[M].第2版.北京:清华大学出版社,2005:294-306.
20 Verbanck M,Josse J,Husson F.Regularised PCA to denoise and visualise data[J].Statistics and Computing,2013,25(2):471-486.
21 Li C,Yin W,Jiang H,et al..An efficient augmented lagrangian method with applications to total variation minimization[J].Computational Optimization and Applications,2013,56(3):507-530.
22 Egiazarian K,Foi A,Katkovnik V.Compressed sensing image reconstruction via recursive spatially adaptive filtering[C].Image Processing,International Conference on.IEEE,2007:549-552.
23 Zhang J,Liu S,Xiong R,et al..Improved total variation based image compressive sensing recovery by nonlocal regularization[C].Circuits and Systems,International Symposium on.IEEE,2013:2836-2839.
2 Donoho D L.Compressed sensing[J].Information Theory,IEEE Transactions on,2006,52(4):1289-1306.
3 Ruan Tao,Na Yan,Wang Shu.Remote sensing image fusion based on compressed sensing[J].Electronic Science and Technology,2012,25(4):43-46. 阮 涛,那 彦,王 澍.基于压缩感知的遥感图像融合方法[J].电子科技,2012,25(4):43-46.
4 Wu Jianrong,Shen Xia,Yu Hong,et al..Snapshot compressive imaging by phase modulation[J].Acta Optica Sinica,2014,34(10):1011005. 吴建荣,沈 夏,喻 虹,等.基于相位调制的单次曝光压缩感知成像[J].光学学报,2014,34(10):1011005.
5 Weng Jiawen,Qin Yi,Yang Chuping,et al..Reconstruction of single low-coherence digital hologram by compressive sensing[J].Laser and Optoelectronics Progress,2015,52(10):100901. 翁嘉文,秦 怡,杨初平,等.单幅弱相干光数字全息图的压缩感知重建[J].激光与光电子学进展,2015,52(10):100901.
6 Tang Chaoying,Chen Yueting,Li Qi,et al..Motion detection and image restoration based on video reconstruction from a single coded exposure photograph[J].Acta Optica Sinica,2015,35(4):0410002. 唐超影,陈跃庭,李 奇,等.基于视频重建的颤振探测与图像复原方法[J].光学学报,2015,35(4):0410002.
7 Candes E J,Tao T.Near-optimal signal recovery from random projections:Universal encoding strategies[J].Information Theory,IEEE Transactions on,2006,52(12):5406-5425.
8 Tan Shiyu,Liu Zhentao,Li Enrong,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.
9 Aharon M,Elad M,Bruckstein A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].Signal Processing,IEEE Transactions on,2006,54(11):4311-4322.
10 Buades A,Coll B,Morel J M.A non-local algorithm for image denoising[C].Computer Vision and Pattern Recognition,Computer Society Conference on.IEEE,2005,2:60-65.
11 Dong W,Shi G,Li X.Nonlocal image restoration with bilateral variance estimation:A low-rank approach[J].Image Processing,IEEE Transactions on,2013,22(2):700-711.
12 Candes E J,Romberg J K,Tao T.Stable signal recovery from incomplete and inaccurate measurements[J].Communications on pure and applied mathematics,2006,59(8):1207-1223.
13 Chambolle A.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
14 Dabov K,Foi A,Katkovnik V,et al..Image restoration by sparse 3Dtransform-domain collaborative filtering[C].Electronic Imaging,International Society for Optics and Photonics,2008:681207.
15 Wang Z,Bovik A C,Sheikh H R,et al..Image quality assessment:From error visibility to structural similarity[J].Image Processing,IEEE Transactions on,2004,13(4):600-612.
16 Candes E J,Recht B.Exact matrix completion via convex optimization[J].Foundations of Computational Mathematics,2009,9(6):717-772.
17 Cai J F,Candes E J,Shen Z.A singular value thresholding algorithm for matrix completion[J].SIAM Journal on Optimization,2010,20(4):1956-1982.
18 Goldstein T,Osher S.The split bregman method for l1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
19 Chen Baolin.Optimization theory and algorithm[M].Second edition.Beijing:Tsinghua University Press,2005:294-306. 陈宝林.最优化理论与算法[M].第2版.北京:清华大学出版社,2005:294-306.
20 Verbanck M,Josse J,Husson F.Regularised PCA to denoise and visualise data[J].Statistics and Computing,2013,25(2):471-486.
21 Li C,Yin W,Jiang H,et al..An efficient augmented lagrangian method with applications to total variation minimization[J].Computational Optimization and Applications,2013,56(3):507-530.
22 Egiazarian K,Foi A,Katkovnik V.Compressed sensing image reconstruction via recursive spatially adaptive filtering[C].Image Processing,International Conference on.IEEE,2007:549-552.
23 Zhang J,Liu S,Xiong R,et al..Improved total variation based image compressive sensing recovery by nonlocal regularization[C].Circuits and Systems,International Symposium on.IEEE,2013:2836-2839.