1 Bit Compressed Sensing Reconstruction Algorithm Based on Blind Operation
-
摘要: 为了解决1比特压缩感知中符号匹配追踪算法(matching sign pursuit)在稀疏度未知的情况下不能自适应重构信号的问题,提出了向前/向后迭代符号匹配追踪算法(forward-backward matching sign pursuit, FBMSP).该算法以逐步逼近理论为核心,通过逐步扩大支撑集来扩大搜索范围,把相邻两次迭代的差值作为终止条件,在MSP算法模型下进行盲运算,以实现信号的重构.数值试验表明:在控制迭代系数=8,=1的情况下,FBMSP算法比传统的符号匹配追踪算法重构精度提高了3 dB,运算时间减少了40%.Abstract: To solve the problem that the matching sign pursuit (MSP) algorithm can not adaptively reconstruct signals when the sparsity is unknown, we proposed a forward-backward matching sign pursuit (FBMSP) algorithm. Based on successive approximation theory, by gradually expanding the support set to expand search scope, FBMSP algorithm takes a difference between adjacent iterations as a termination criterion and conducts blind operations to reconstruct the signals under the model of the MSP algorithm. The numerical experiments show that compared with the traditional MSP algorithm, the precision of FBMSP is increased by 3 dB, and the calculation time is reduced by 40% when the control iterative coefficient =8 and =1.
-
Key words:
- signal processing /
- compressed sensing /
- approximation theory /
- 1 bit /
- matching sign pursuit
-
DONOHO D L. Compressed sensing CANDS E J. Compressive sampling [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306. QAISAR S, BILAL R M, IQBAL W, et al. Compressive sensing: from theory to applications, a survey CANDS E J, FERNANDEZ-GRANDA C. Super-resolution from noisy data [C]//Proceedings of the International Congress of Mathematicians. Madrid: [s.n.], 2006: 1433-1452. CANDS E J, FERNANDEZ-GRANDA C. Towards a mathematical theory of super-resolution BOUFOUNOS P T, BARANIUK R G. 1-bit compressive sensing BOUFOUNOS P. Greedy sparse signal reconstruction from sign measurements [J]. Communications and Network, 2013, 15: 443-456. KARAHANOGLU N B, ERDOGAN H. Compressed sensing signal recovery via forward-backward pursuit CANDS E J, TAO T. Near optimal signal recovery from random projections and universal encoding strategies [J]. Journal of Fourier Analysis and Applications, 2013, 19(6): 1229-1254. MALLAT S G, ZHANG Z. Matching pursuits with time-frequency dictionaries TROPP J A, GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit [J]. Communications on Pure and Applied Mathematics, 2014, 67(6): 906-956. NEEDELL D,VERSHYNIN D. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit DONOHO D L, TSAIG Y, DRORI I, et al. Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit [C]//Proceedings of the 42nd Annual Conference on Information Sciences and Systems. Washington D C: IEEE, 2008: 16-21. DAI W, MILENKOVIC O. Subspace pursuit for compressive sensing signal reconstruction [C]//Proceedings of the 43rd Asilomar Conference on Signals, Systems and Computers. Piscataway: IEEE, 2009: 1305-1309. NEEDELL D, TROPP J A. CoSaMP: iterative signal recovery form incomplete and inaccurate samples 方红,杨海蓉. 贪婪算法与压缩感知理论 [J]. Digital Signal Processing, 2013, 23(5): 1539-1548. [J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425. [J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3397-3415. [J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666. [J]. Foundations of Computational Mathematics, 2009, 9(3): 317-334. [R]. Stanford: Department of Statistics, Stanford University, USA, 2006. [J]. IEEE Transactions on Information Theory, 2009, 55(5): 2230-2249. [J]. Applied and Computational Harmonic Analysis, 2008, 26(3): 301-321. [J]. 自动化学报,2011,37(12): 1413-1421. FANG Hong, YANG Hairong. Greedy algorithms and compressed sensing [J]. Acat Automatica Sinica, 2011, 37(12): 1413-1421.
点击查看大图
计量
- 文章访问数: 908
- HTML全文浏览量: 77
- PDF下载量: 534
- 被引次数: 0