对残差信号用类高斯分布建模，通过分析回溯型自适应正交匹配追踪(backtracking-based adaptive orthogonal matching pursuit, BAOMP) 算法的阈值选择方法与常规信号稀疏度方法的一致性和差异，提出一种改进的BAOMP 算法. 采用80–20 准则判断信号的粗匹配状态，然后对后续匹配步骤引入可变步长阈值，实现
选入原子集容量的精细调整，提高选入原子的正确匹配率，避免了残差信号的准周期性失配. 实验结果表明，与BAOMP算法相比，在500次重复实验中，改进的BAOMP算法对高斯稀疏信号的精确重建概率提高17%-26%，对自然图像的精确重建概率提高70%以上.
This paper models residual signals with Gaussian-like distributions, based on which consistency between the Backtracking-based adaptive orthogonal matching pursuit (BAOMP) threshold and signal sparselevel is analyzed. An improved BAOMP (IBAOMP) method is thenproposed. Themethod estimates the
preliminary matching state usingthe 80-20 rule, and introduces a threshold with variable step size to subtly adjust atom set to raise the correct rate of selected atoms and avoid quasi-periodic mismatches of residual signals. Simulation results of 500 tests show that the exact recovery probability of IBAOMP is 17%-26% higher than BAOMP for Gaussian sparse signals, and more than70% higher than BAOMP for natural images.
[1] GIRYES R, ELAD M. RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT [J]. IEEE Transactions on Signal Processing, 2012, 60(3): 1465-1468.
[2] YANG Jing Yu, PENG Yi Gang, XU Wen Li, DAI Qiong Hai. Ways to sparse representation: a comparative study[J]. Tsinghua Science and Technology, 2009, 14(4): 434-443.
[3] TROPP J A, WRIGHT S J. Computational methods for sparse solution of linear inverse problems[J]. Proceedings of the IEEE, 2010, 98(6): 948-958.
[4] MALLAT S G, ZHANg Zhi Feng. Matching pursuits with time-frequency dictionaries[J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3397–3415.
[5] TROPP J A , GILBERT A C. Signal recovery from random measurements via Orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666.
[6] VARADARAJAN B, KHUDANPUR S, TRAN T D. Stepwise optimal subspace pursuit for improving sparse recovery[J]. IEEE Signal Processing Letters, 2011, 18(1): 27-30.
[7] NEEDELL D, TROPP J A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2009, 26(3): 301-321.
[8] BLUMENSATH T, DAVIES M E. Iterative hard thresholding for compressed sensing[J]. Applied and Computational Harmonic Analysis, 2009, 27(3): 265-274.
[9] HUANG Hong Lin, MAKUR Anamitra. Backtracking-Based Matching Pursuit Method for Sparse Signal Reconstruction[J]. IEEE Signal Processing Letters, 2011, 18(7): 391-394.
[10] GURBUZ A C, PILANCI M, ARIKAN O. Expectation maximization based matching pursuit[C]// IEEE International Conference on Acoustics, Speech and Signal Processing, 2012:3313-3316.
[11] DAI Wei, MILENKOVIC Olgica. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Transactions on Information Theory, 2009, 55(5): 2230-2249.
