满足重构概率约束的更少贝努利观测

宋晓霞; 石光明

doi:10.3724/SP.J.1004.2013.00053

满足重构概率约束的更少贝努利观测

doi: 10.3724/SP.J.1004.2013.00053 cstr: 32138.14.SP.J.1004.2013.00053

1.
西安电子科技大学智能感知与图像理解教育部重点实验室西安 710071

详细信息

通讯作者:
宋晓霞

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- 被引次数: 0
出版历程
- 收稿日期: 2011-07-21
- 修回日期: 2012-04-09
- 刊出日期: 2013-01-20

Fewer Bernoulli Measurements Satisfying the Constraint of Reconstruction Probability

1.
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi'an 710071

摘要

摘要: 在压缩感知(Compressed sensing, CS)中,一些方法统计地提供了给定观测数量下的信号重构概率. 然而,在重构概率有约束的情况下,现有方法不能找到满足约束的观测. 本文以压缩感知中常用的贝努利观测集为研究对象, 基于贝努利观测的特征和序列压缩感知理论获得了满足重构概率约束的观测. 另外,由于所提方法能从获取的过多观测中移除部分冗余观测, 观测结果包含更少的观测数据. 所提方法有三个优点:满足重构概率约束、包含更少的观测数据以及具有全局收敛的属性. 理论分析和实验结果验证了所提方法的有效性.
- 压缩感知 /
- 贝努利观测 /
- 信号重构 /
- 序列压缩感知
Abstract: In the compressed sensing (CS) framework, the previous methods statistically provide the probability of signal reconstruction when the number of measurements is given. However, when the reconstruction probability of the signal is constrained, these existing methods do not provide an effective mechanism to find the measurements satisfying the constraint. To handle the problem, we focus on Bernoulli measurements and utilize the reconstruction feature of Bernoulli measurements and sequential CS to determine the measurements such that they can satisfy the constraint of reconstruction probability. Moreover, the measurements obtained by the proposed method are fewer than those by the classical methods because some redundant measurements are removed from the obtained measurement sequence. In summary, the proposed method has three unique features: satisfying the constraint of reconstruction probability, containing fewer measurements, and having the property of global convergence. Both theoretical analysis and experimental results suggest that the proposed method can obtain fewer measurements which satisfy the required reconstruction probability for different sparse signals and different initial measurements.
- Compressed sensing (CS) /
- Bernoulli measurements /
- signal reconstruction /
- sequential compressed sensing

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参考文献(1)

[1]

Candés E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425[2] Lian Qiu-Sheng, Chen Shu-Zhen. Image reconstruction for compressed sensing based on the combined sparse image representation. Acta Automatica Sinica, 2010, 36(3): 385-391 (练秋生, 陈书贞. 基于混合基稀疏图像表示的压缩传感图像重构. 自动化学报, 2010, 36(3): 385-391)[3] Pan Rong, Liu Yu, Hou Zheng-Xin, Wang Shao-Chu. Image coding and reconstruction via compressed sensing based on partial DCT coefficients. Acta Automatica Sinica, 2011, 37(6): 674-680 (潘榕, 刘昱, 侯正信, 汪少初. 基于局部 DCT 系数的图像压缩感知编码与重构. 自动化学报, 2011, 37(6): 674-680)[4] Potter L C, Ertin E, Parker J T, etin M. Sparsity and compressed sensing in radar imaging. Proceedings of the IEEE, 2010, 98(6): 1006-1020[5] Shi G M, Gao D H, Song X X, Xie X M, Chen X Y, Liu D H. High-resolution imaging via moving random exposure and its simulation. IEEE Transactions on Image Processing, 2011, 20(1): 276-282[6] Haupt J, Bajwa W U, Rabbat M, Nowak Ro. Compressed sensing for networked data. IEEE Signal Processing Magazine, 2008, 25(2): 92-101[7] Bajwa W U, Haupt J, Sayeed A M, Nowak R. Compressed channel sensing: a new approach to estimating sparse multipath channels. Proceedings of the IEEE, 2010, 98(6): 1058-1076[8] Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306[9] Shi Guang-Ming, Liu Dan-Hua, Gao Da-Hua, Liu Zhe, Lin Jie, Wang Liang-Jun. Advances in theory and application of compressed sensing. Chinese Journal of Electronics, 2009, 37(5): 1070-1081 (石光明, 刘丹华, 高大化, 刘哲, 林杰, 王良君. 压缩感知理论及其研究进展. 电子学报, 2009, 37(5): 1070-1081)[10] Li Shu-Tao, Wei Dan. A survey on compressive sensing. Acta Automatica Sinica, 2009, 35(11): 1369-1377 (李树涛, 魏丹. 压缩传感综述. 自动化学报, 2009, 35(11): 1369-1377)[11] Baraniuk R G. Compressive sensing. IEEE Signal Processing Magazine, 2007, 24(4): 118-121[12] Candés E J, Wakin M B. An introduction to compressive sampling. IEEE Signal Processing Magazine, 2008, 25(2): 21-30[13] Bruckstein A M, Donoho D L, Elad M. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 2009, 51(1): 34-81[14] Candés E J, Wakin M B, Boyd S P. Enhancing sparsity by reweighted l1 minimization. Journal of Fourier Analysis and Applications, 2008, 14(5-6): 877-905[15] Saab R, zgür Y. Sparse recovery by non-convex optimization-instance optimality. Applied and Computational Harmonic Analysis, 2010, 29(1): 30-48[16] Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing Letters, 2007, 14(10): 707-710[17] Wipf D P, Rao B D. Sparse Bayesian learning for basis selection. IEEE Transactions on Signal Processing, 2004, 52(8): 2153-2164[18] Malioutov D M, Sanghavi S R, Willsky Alan S. Sequential compressed sensing. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 435-444[19] Ji S H, Xue Y, Carin L. Bayesian compressive sensing. IEEE Transactions on Signal Processing, 2008, 56(6): 2346-2356[20] Chrétien S. An alternating l_{1 approach to the compressed sensing problem. IEEE Signal Processing Letters, 2010, 17(2): 181-184[21] Donoho D L, Tanner J. Precise undersampling theorems. Proceedings of the IEEE, 2010, 98(6): 913-924

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