稀疏度自适应的广义正交匹配追踪算法
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摘要
针对目前的压缩感知(CS)重构贪婪算法,为了进一步提高重构算法适用性,即对信号的稀疏度不用提前知道,并提高算法的重构速度。基于已有的稀疏度自适应算法SAMP、运算快的g OMP,提出一种基于有限等距性质(RIP)的一种稀疏度自适应的估计方式的改进算法,然后根据估计所得稀疏度对信号进行重构。仿真实验结果表明,所提出的算法与现有的重构算法相比较重构成功的概率良好,而且平均运行时间大大降低。
Aiming at the current Compressed Sensing(CS) reconstruction greedy algorithm, in order to further improve the applicability of the reconstruction algorithm, that is to say, the signal sparsity need not be known in advance, and the speed of reconstruction of the algorithm. Based on the existing sparseness adaptive algorithm(SAMP) and fast g OMP computation, this algorithm proposes a sparseness-adaptive estimation method based on Finite Isometric Property(RIP). The signal is then reconstructed based on the estimated sparsity. The simulation results show that the proposed algorithm has a better probability of successful reconstruction compared with the existing reconstruction algorithms, and the average running time is greatly reduced.
Aiming at the current Compressed Sensing(CS) reconstruction greedy algorithm, in order to further improve the applicability of the reconstruction algorithm, that is to say, the signal sparsity need not be known in advance, and the speed of reconstruction of the algorithm. Based on the existing sparseness adaptive algorithm(SAMP) and fast g OMP computation, this algorithm proposes a sparseness-adaptive estimation method based on Finite Isometric Property(RIP). The signal is then reconstructed based on the estimated sparsity. The simulation results show that the proposed algorithm has a better probability of successful reconstruction compared with the existing reconstruction algorithms, and the average running time is greatly reduced.
引文
[1]Donoho D L. Compressed Sensing[J]. IEEE Trans on Information Theory,2006,52(4):1289-1306.
[2]Candès E,Romberg J,Tao T. Robust Uncertainty Principles Exact Signal Reconstruction from Highly Incomplete Frequency Information[J]. IEEE Trans. on Information Theory,2006,52(2):489-509.
[3]Candès E,Tao T. Decoding by Linear Programming[J]. IEEE Trans. on Information Theory,2005,51(12):4203-4215.
[4]石光明,刘丹华,高大化等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.
[5]戴琼海,付长军,季向阳.压缩感知研究[J].计算机学报, 2011, 34(03):425-434.
[6]Joel A. Tropp,Anna C. Gilbert. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit[J]. IEEE Transactions on Information Theory,VOL.53, No.12, December 2007.
[7]Needell D,Vershynin R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. Foundations of Computational Mathematics,2009,9(3):317-334.
[8]Needell D,Vershynin R. Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit[J].IEEE Journal on Selected Topics in Signal Processing, 2010, 4(2):310—316.
[9]杨真真,杨震,孙林慧.信号压缩重构的正交匹配追踪类算法综述[J].信号处理,2013,29(4):486-496.
[10]Thong T.Do,Lu Gan,Nam Nguyen,Trac D.Tran. Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing[C].Asilomar Conference on Signals,Systems,and Computers,Pacific Grove,California,2008,10:581-587.
[11]许华杰,何敬禄,胡小明.基于块稀疏度估计的压缩感知自适应重构算法[J/OL].2017-01-19.http://www.arocmag.com/article/02-2018-01-012.html.
[12]J. Wang,S. Kwon,B. Shim. Generalized Orthogonal Matching Pursuit. IEEE Transactions on Signal Processing,vol.60,no.12,pp.6202-6216,Dec.2012.
[2]Candès E,Romberg J,Tao T. Robust Uncertainty Principles Exact Signal Reconstruction from Highly Incomplete Frequency Information[J]. IEEE Trans. on Information Theory,2006,52(2):489-509.
[3]Candès E,Tao T. Decoding by Linear Programming[J]. IEEE Trans. on Information Theory,2005,51(12):4203-4215.
[4]石光明,刘丹华,高大化等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.
[5]戴琼海,付长军,季向阳.压缩感知研究[J].计算机学报, 2011, 34(03):425-434.
[6]Joel A. Tropp,Anna C. Gilbert. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit[J]. IEEE Transactions on Information Theory,VOL.53, No.12, December 2007.
[7]Needell D,Vershynin R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. Foundations of Computational Mathematics,2009,9(3):317-334.
[8]Needell D,Vershynin R. Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit[J].IEEE Journal on Selected Topics in Signal Processing, 2010, 4(2):310—316.
[9]杨真真,杨震,孙林慧.信号压缩重构的正交匹配追踪类算法综述[J].信号处理,2013,29(4):486-496.
[10]Thong T.Do,Lu Gan,Nam Nguyen,Trac D.Tran. Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing[C].Asilomar Conference on Signals,Systems,and Computers,Pacific Grove,California,2008,10:581-587.
[11]许华杰,何敬禄,胡小明.基于块稀疏度估计的压缩感知自适应重构算法[J/OL].2017-01-19.http://www.arocmag.com/article/02-2018-01-012.html.
[12]J. Wang,S. Kwon,B. Shim. Generalized Orthogonal Matching Pursuit. IEEE Transactions on Signal Processing,vol.60,no.12,pp.6202-6216,Dec.2012.