2.793

2018影响因子

(CJCR)

• 中文核心
• EI
• 中国科技核心
• Scopus
• CSCD
• 英国科学文摘

## 留言板

 引用本文: 周洁容, 李海洋, 凌军, 陈浩, 彭济根. 基于非凸复合函数的稀疏信号恢复算法. 自动化学报, 2021, 47(x): 1−12
Zhou Jie-Rong, Li Hai-Yang, Ling Jun, Chen Hao, Peng Ji-Gen. Sparse signal reconstruction algorithm based on non-convex composite function. Acta Automatica Sinica, 2021, 47(x): 1−12 doi: 10.16383/j.aas.c200666
 Citation: Zhou Jie-Rong, Li Hai-Yang, Ling Jun, Chen Hao, Peng Ji-Gen. Sparse signal reconstruction algorithm based on non-convex composite function. Acta Automatica Sinica, 2021, 47(x): 1−12

## Sparse Signal Reconstruction Algorithm Based on Non-Convex Composite Function

Funds: Supported by National Natural Science Foundation of P. R. China (11771347), National Natural Science Foundation of P. R. China (12031003)
• 摘要: 本文基于泛函深度作用的思想, 通过将两种非凸稀疏泛函进行复合, 构造了一种新的稀疏信号重构模型, 实现了对0范数的深度逼近. 综合运用MM技术、外点罚函数法和共轭梯度法, 提出了一种求解该模型的算法, 称为NCCS算法. 为降低重构信号陷入局部极值的可能性, 提出了在算法的每步迭代中以BP模型的解作为初始迭代值. 为验证所建模型和所提算法的有效性, 本文进行了多项数值实验. 实验结果表明: 相较于SL0算法、IRLS算法、SCSA算法以及BP算法等经典算法, 本文提出的算法在重构误差、信噪比、归一化均方差、支撑集恢复成功率等方面都有更优的表现.
• 图  1  四种函数在$\sigma = 0.1$时的一元函数分布

Fig.  1  The unary distribution of the four functions at $\sigma = 0.1$

图  2  ${p_\sigma }(x)$${h_\sigma }(x)$${g_\sigma }(x)$和函数${f_\sigma }(x)$$\sigma = 0.1$时的二元函数分布

Fig.  2  The bivariate distribution of ${p_\sigma }(x)$, ${h_\sigma }(x)$, ${g_\sigma }(x)$ and the function ${f_\sigma }(x)$ at $\sigma = 0.1$

图  3  待定数$\alpha$对NCCS算法运行时间的影响

Fig.  3  The influence of undetermined number $\alpha$ on the running time of NCCS algorithm

图  4  NCCS算法的一维信号重构仿真图, 信号大小为: $500 \times 1$, 稀疏度为$65$

Fig.  4  One-dimensional signal reconstruction simulation diagram of NCCS algorithm, the signal size is: 500×1, the sparsity is 65

图  5  SL0、IRLS、BP、SCSA、NCCS五种算法的重构误差和稀疏度的变化关系

Fig.  5  The relationship between the reconstruction error and sparsity of the five algorithms of SL0, IRLS, BP, SCSA, and NCCS

图  6  SL0、IRLS、BP、SCSA、NCCS五种算法的重构信噪比和稀疏度的变化关系

Fig.  6  The relationship between the reconstructed signal-to-noise ratio and sparsity of the five algorithms of SL0, IRLS, BP, SCSA, and NCCS

图  7  SL0、IRLS、BP、SCSA、NCCS五种算法的运行时间和稀疏度的变化关系

Fig.  7  The relationship between the running time and sparsity of the five algorithms of SL0, IRLS, BP, SCSA, and NCCS

图  8  SL0、IRLS、BP、SCSA、NCCS五种算法的支撑集恢复成功和稀疏度的变化关系

Fig.  8  The relationship between the recovery success rate of the support set and sparsity of the five algorithms of SL0, IRLS, BP, SCSA, and NCCS

图  9  SL0、IRLS、BP、SCSA、NCCS五种算法的归一化均方差和稀疏度的变化关系

Fig.  9  The relationship between the normalized mean square error and sparsity of the five algorithms of SL0, IRLS, BP, SCSA, and NCCS

•  [1] Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289−1306 [2] Gross D, Liu R K, Flammia R T, Becker R, Eisert R. Quantum state tomography via compressed sensing. Physical Review Letters, 2010, 105(15): 150401 [3] Wiaux Y, Jacques L, Puy G, Scaife A M M, Vandergheynst P. Compressed sensing imaging techniques for radio interf- erometry. Monthly Notices of the Royal Astronomical Soci- ety, 2010, 395(3): 1733−1742 [4] Lustig M, Donoho D, Pauly J M. Sparse MRI: The applica- tion of compressed sensing for rapid MR imaging. Magnet- ic Resonance in Medicine, 2010, 58(6): 1182−1195 [5] Shi Bao-Shun, Lian Qiu-Sheng, Chen Shu-Zhen. Compres- sed sensing magnetic resonance imaging based on dictionary updating and block matching and three dimensional filtering regularization. Image Processing Iet, 2016, 10(1): 68−79 [6] Herman M, Strohmer T. High-Resolution Radar via Compr- essed Sensing. IEEE Transactions on Signal Processing, 2009, 57(6): 2275−2284 [7] Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing letters, 2007, 14(10): 707−710 [8] Peng Ji-Gen, Yue, Shi-Gang, Li Hai-Yang. NP/CMP equivalence: A phenomenon hidden among sparsity models ℓ0 minimization and ℓP minimization for information processing. IEEE Transactions on Information Theory, 2015, 61(7): 4028−4033 [9] Tropp J A, Gilbert A C. Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit. IEEE Tr- ansactions on Information Theory, 2007, 53(12): 4655−4666 [10] Beck A, Teboulle M. A Fast Iterative Shrinkage Thresholdi- ng Algorithm for Linear Inverse Problems. Siam J Imaging sciences, 2009, 2(1): 183−202 [11] Dai W, Milenkovic O. Subspace Pursuit for Compressive Sensing Signal Reconstruction. IEEE Transactions on Information Theory, 2009, 55(5): 2230−2249 [12] Saadat S A, Safari A, Needell D. Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP). Pure and Applied Geophysics, 2016, 173(6): 2087−2099 [13] Figueiredo M A T, Nowak R D, Wright S J. Gradient Projection for Sparse Reconstruction: Application to Comp- ressed Sensing and Other Inverse Problems. IEEE Journal of Selected Topics in Signal Processing, 2008, 1(4): 586−597 [14] Foucart S, Rauhut H, Rauhut H. A mathematical introducti- on to compressive sensing. Springer New York, 2013, 5: 65−75 [15] Emmanuel J C, Michael B W, Stephen P B. Enhancing spa- rsity by reweighted L1 minimization. Journal of Fourier Analysis and Applications, 2008, 14(5): 877−905 [16] Chartrand R, Yin W. Iteratively reweighted algorithms for compressive sensing. In: Proceedings of the IEEE Internati- onal Conference on Acoustics, USA: IEEE, 2008.3869−3872. [17] Zhang Z, Xu Y, Yang J, Li X, Zhang D. A Survey of Sparse Representation: Algorithms and Applications. IEEE Access, 2017, 3: 490−530 [18] Chen S S, Donoho D L, Saunders M A. Atomic decompos- etion by basis pursuit. SIAM Review, 2001, 43(1): 129−159 [19] Chartrand R, Staneva V. Restricted isometry properties and nonconvex compressive sensing. Inverse Problems, 2010, 24(3): 657−682 [20] 赵瑞珍, 林婉娟, 李浩, 胡绍海. 基于光滑ℓ0范数和修正牛顿法的压缩感知重建算法. 计算机辅助设计与图形学学报, 2012, 24(4): 478−484Zhao Rui-Zhen, Lin Wan-Juan, Li Hao, Hu Shao-Hai. Reco- nstruction Algorithm for Compressive Sensing Based on Smoothed ℓ0 Norm and Revised Newton Method. Journal of Computer-Aided Design & Computer Graphics, 2012, 24(4): 478−484 [21] Mohimani H, Babaie Z M, Jutten C. A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed L0 Norm. IEEE Transactions on Signal Processing, 2009, 57(1): 289−301 [22] Zhang C J, Hao D B, Hou C B, Yin X J. A New Approach for Sparse Signal Recovery in Compressed Sensing Based on Minimizing Composite Trigonometric Function. IEEE Access, 2018, 6: 44894−44904 [23] Malek M M, Babaie M, Koochakzadeh A, Jansson M, Rojas C R. Successive Concave Sparsity Approximation for Compressed Sensing. IEEE Transactions on Signal Proces- sing, 2016, 64(21): 5657−5671 [24] Li Hai-Yang, Zhang Qian, Cui An-Gang, Peng Ji-Gen. Mi- nimization of Fraction Function Penalty in Compressed Se- nsing. IEEE Transactions on Neural Networks, 2020, 31(5): 1626−1637 [25] Hunter D R, Lange K. A Tutorial on MM Algorithms. The American Statistician, 2004, 58(1): 30−37 [26] Al-Naffouri T Y, Masood M. Distribution agnostic structu- red sparsity recovery algorithms. In: Proceedings of the 8th International Workshop on Systems, Signal Processing and their Applications (WoSSPA). Algiers: IEEE, 2013. 283−290. [27] 陈金立, 李伟, 朱筱嵘, 陈宣, 李家强. 基于修正近似双曲正切函数的平滑ℓ0范数算. 计算机工程与设计, 2018, 39(12): 3717−3721+3754.Chen Jin-Li, Li Wei, Zhu Xiao-Rong, Chen Xuan, Li Jia-Q- iang. Smooth ℓ0 norm calculation based on modified appr- oximate hyperbolic tangent function. Computer engineerin- g and design, 2018, 39(12): 3717−3721+3754. [28] Elad M. Sparse and Redundant Representations: From Th- eory to Applications in Signal and Image Processing. New York: Springer, 2010. 28−43. [29] Emmanuel J, Michael B W, Stephen P B. Enhancing Sparsity by Reweighted ℓ1 Minimization. Journal of Fourier Anal- ysis & Applications, 2007, 14(5): 877−905 [30] 袁亚湘, 孙文瑜. 北京: 最优化理论与方法. 科学出版社, 1997. 455−482Yuan Ya-Xiang, Sun Wen-Yu. Optimization theory and method. Beijing: Science Press, 1997. 455−82 [31] F. H. Clarke. Optimization and non-smooth analysis. New York: Classics in Applied Mathematics, SIAM, 1983. 37−187.

##### 计量
• 文章访问数:  38
• HTML全文浏览量:  7
• 被引次数: 0
##### 出版历程
• 收稿日期:  2020-12-01
• 录用日期:  2020-12-14
• 网络出版日期:  2021-01-06

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈