A Review of Atom Recognition Strategies for Greedy Class Reconstruction Algorithms Based on Compressed Sensing
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摘要: 在压缩感知(CS)重构算法中，贪婪类算法因其硬件实现的简易性与良好的恢复精度得到了广泛研究，但算法多样化的同时出现了算法选择困难的问题。原子识别策略作为贪婪类算法的核心，其差异往往决定了算法重构性能的优劣。该文以贪婪类算法最关键的一环原子识别作为研究对象，对贪婪类重构算法的原子识别策略进行了提取与分类。根据不同策略的适用阶段和特点归纳提炼出3种一步式原子识别策略、8种进阶式原子识别策略以及3种稀疏度自适应原子识别策略。最后对原子识别策略所对应原始算法的重构性能进行了分类仿真对比。整理后的策略方便于实际应用中对算法的选择，同时为贪婪类重构算法的进一步优化提供了参考。Abstract: Among the Compressed Sensing(CS) reconstruction algorithms, greedy algorithm has been widely studied for its simple hardware implementation and excellent recovery accuracy. However, the diversity of algorithms also presents the problem of difficult algorithm selection. As the core of greedy algorithms, the difference of atomic recognition strategy often determines its recovery performance. In this paper, atomic recognition strategy, which is the most important part of greedy algorithm, is taken as the research object. Three one-step atom recognition strategies, eight advanced atom recognition strategies and three sparsity adaptive atom recognition strategies are summarized according to the applicable stages and characteristics. Finally, the recovery performance of the original algorithms corresponding to the atomic recognition strategies are simulated and compared. The sorted strategies are convenient for the selection of algorithms in practical application, and they provide references for the further optimization of greedy algorithms.
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算法1 模糊阈值策略[37] 输入：内积向量${\boldsymbol{P}}$，潜在支撑集${{\boldsymbol{C}}_t}$ 执行： (1) 计算模糊阈值：${\boldsymbol{w}} = {\boldsymbol{\alpha }} \times ({P_1} + {P_2}) \times \tau$ (2) 模糊阈值缩减：${\boldsymbol{\varGamma} } = \{ j|\left| { {{\boldsymbol{P}}_{ {C_t} } }(j)} \right| > w\}$ (3) 缩减后的潜在支撑集：${{\boldsymbol{\varLambda}} _t} = {{\boldsymbol{C}}_t} \cap {\boldsymbol{\varGamma}}$ 输出：${{\boldsymbol{\varLambda}} _t}$ 
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算法2 增量最小二乘投影回溯策略[41] 输入：${\boldsymbol{A}}$, ${\boldsymbol{y}}$，开始标志${\rm{TR}}$，当前迭代次数$ t $，候选支撑集${{\boldsymbol{S}}_t}$ (1) 投影：${\hat {\boldsymbol{\theta} } _{ {{\boldsymbol{S}}_t} } } = {\boldsymbol{A} }_{_{ {{\boldsymbol{S}}_t} } }^\dagger {\boldsymbol{y} }$ (2) 判断：如果$t > {\rm{TR}}$并且$ t\% 2 = 1 $，则回溯: 选择出${\hat {\boldsymbol{\theta} } _{ {{\boldsymbol{S}}_t} } }$的绝对值的最小值所对应的索引：
${ {\boldsymbol{D} }_t} = \arg \min (\left| { { {\hat {\boldsymbol{\theta} } }_{ {{\boldsymbol{S}}_t} } } } \right|)$(3) 剔除错误索引并更新索引集：${{\boldsymbol{I}}_t} = {{\boldsymbol{S}}_t}/{{\boldsymbol{D}}_t}$ 输出：${{\boldsymbol{I}}_t}$
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算法3 基于投影的原子选择策略[17] 输入：${\boldsymbol{A}}$,${\boldsymbol{y}}$，最终支撑集${{\boldsymbol{I}}_{t - 1} }$，潜在支撑集${{\boldsymbol{C}}_t}$ 假设：${{\boldsymbol{C}}_t} \cap {{\boldsymbol{I}}_{t - 1} } = \varnothing$ 初始化：$\hat {\boldsymbol{\theta}} = 0 \in {\mathbb{R}^{M \times 1} }$ 执行： (1) 候选支撑集：${{\boldsymbol{S}}_t} = {{\boldsymbol{I}}_{t - 1} } \cup {{\boldsymbol{C}}_t}$ (2) 正交投影：${\hat {\boldsymbol{\theta} } _{ { {\boldsymbol{S} }_t} } } = {\boldsymbol{A} }_{_{ {{\boldsymbol{S}}_t} } }^\dagger {\boldsymbol{y} }$ (3) 部分置0：${\hat {\boldsymbol{\theta} } _{ { {\bar {\boldsymbol{C}}}_t} } } = 0$ (4) 索引集选择：${ {\boldsymbol{\varOmega} } _t} = {\rm{supp} }\_{\rm{max} }\_L({\hat {\boldsymbol{\theta} } _{ {{\boldsymbol{S}}_t} } },L)$ 输出：${{\boldsymbol{\varOmega}} _t}$
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算法4 压缩采样原子选择策略 输入：${\boldsymbol{A}}$, $ {\boldsymbol{y}} $, $ K $，最终支撑集${{\boldsymbol{I}}_{t - 1} }$, 潜在支撑集${{\boldsymbol{C}}_t}$ 初始化：$\hat {\boldsymbol{\theta}} = 0 \in {\mathbb{R}^{M \times 1} }$ 执行： (1)$ t = t + 1 $,${ {\boldsymbol{C} }_t} = {\rm{supp} }\_{\rm{max} }\_L{\text{(} }|\left\langle {{\boldsymbol{A}},{{\boldsymbol{r}}_{t - 1} } } \right\rangle |,2K{\text{)} }$ (2) 候选支撑集：${ {\boldsymbol{S} }_t} = { {\boldsymbol{I} }_{t - 1} } \cup {{\boldsymbol{C}}_t}$ (3) 正交投影：${\hat {\boldsymbol{\theta} } _{ {{\boldsymbol{S}}_t} } } = {\boldsymbol{A} }_{_{ {{\boldsymbol{S}}_t} } }^\dagger {\boldsymbol{y} }$ (4) 更新支撑集：${ {\boldsymbol{I} }_t} = {\rm{supp} }\_{\rm{max} }\_L{\text{(} }{\hat {\boldsymbol{\theta} } _{ {{\boldsymbol{S}}_t} } },K{\text{)} }$ (5) 残差更新：${{\boldsymbol{r}}_t} = {\boldsymbol{y}} - {{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} } }{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} }^\dagger {\boldsymbol{y}}$ 输出：${{\boldsymbol{I}}_t}$
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算法5 展望策略[17, 29] 输入：${\boldsymbol{A}}$,${\boldsymbol{y}}$,$ K $,${{\boldsymbol{I}}_{t - 1} }$，潜在索引$i(i \notin {{\boldsymbol{I}}_{t - 1} })$ 初始化： 迭代次数: $t = {\rm{length}}({{\boldsymbol{I}}_{t - 1} } \cup i)$ 更新支撑集：${{\boldsymbol{I}}_t} = {{\boldsymbol{I}}_{t - 1} } \cup i$ 更新残差：${ {\boldsymbol{r} }_t} = {\boldsymbol{y} } - { {\boldsymbol{A} }_{ { {\boldsymbol{I} }_t} } }{\boldsymbol{A} }_{ { {\boldsymbol{I} }_t} }^\dagger {\boldsymbol{y}}$ 迭代： (1) 迭代次数增加：$ t = t + 1 $ (2) 原子识别${i_t} = {\rm{supp}}\_{\rm{max}}\_L{\text{(} }|\left\langle {{\boldsymbol{A}},{{\boldsymbol{r}}_{t - 1} } } \right\rangle |,1{\text{)} }$ (3) 支撑集扩充：${{\boldsymbol{I}}_t} = {{\boldsymbol{I}}_{t - 1} } \cup {i_t}$ (4) 残差更新：${{\boldsymbol{r}}_t} = {\boldsymbol{y}} - {{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} } }{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} }^\dagger {\boldsymbol{y}}$ (5) 判断是否停止：如果${\left\| { {{\boldsymbol{r}}_t} } \right\|_2} > {\left\| { {{\boldsymbol{r}}_{t - 1} } } \right\|_2}$或者$ t > K $则
$ t = t - 1 $并停止迭代，否则跳转到步骤1继续迭代输出：${\boldsymbol{r}} = {\boldsymbol{y}} - {{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} } }{\boldsymbol{A}}_{ {{\boldsymbol{I}}_t} }^\dagger {\boldsymbol{y}}$, ${{\boldsymbol{I}}_t}$
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算法6 并行展望策略[30] 输入：${\boldsymbol{A}}$,${\boldsymbol{y}}$,$ K $，最终支撑集${{\boldsymbol{I}}_{t - 1} }$，潜在索引集
${ {\boldsymbol{C} }_t}({ {\boldsymbol{C} }_t} \notin {{\boldsymbol{I}}_{t - 1} })$, ${\rm{length}}({{\boldsymbol{C}}_t}) = L$执行： (1) for j = 1 to L $[{\boldsymbol{R} },{ {\boldsymbol{\varLambda} } _j}] = {\rm{Look}}\_{\rm{Ahead}}\_{\rm{Resi}}({\boldsymbol{A}},{\boldsymbol{y}},{\boldsymbol{K}},{{\boldsymbol{I}}_{t - 1} },{{\boldsymbol{C}}_t})$ ${{\boldsymbol{n}}_j} = {\left\| {\boldsymbol{R}} \right\|_2}$ end for (2) 选择出残差$ {l_2} $范数最小值所对应的一组索引：
${ {\boldsymbol{\varLambda} } _t} = \mathop {\arg \min }\limits_j ({{\boldsymbol{n}}_j})$(3) 取交集：${{\boldsymbol{\varGamma}} _t} = {{\boldsymbol{\varLambda}} _t} \cap {{\boldsymbol{C}}_t}$ 输出：${{\boldsymbol{\varGamma}} _t}$
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算法7 正交最小二乘一步展望策略[17] 输入：${\boldsymbol{A}}$,${\boldsymbol{y}}$,${{\boldsymbol{I}}_{t - 1} }$，潜在索引$i(i \notin {{\boldsymbol{I}}_{t - 1} })$ 执行： (1) 候选支撑集扩充：${{\boldsymbol{S}}_t} = {{\boldsymbol{I}}_{t - 1} } \cup i$ (2) 残差更新：${{\boldsymbol{r}}_t} = {\boldsymbol{y}} - {{\boldsymbol{A}}_{ {{\boldsymbol{S}}_t} } }{\boldsymbol{A}}_{ {{\boldsymbol{S}}_t} }^\dagger {\boldsymbol{y}}$ (3) 计算残差$ {l_2} $范数：${\boldsymbol{R} } = {\left\| { {{\boldsymbol{r}}_t} } \right\|_2}$ 输出：${\boldsymbol{R}}$
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算法8 固定步长稀疏度自适应策略[12,26] 输入：当前迭代过程中得到的残差${\boldsymbol{R}}$，上一次迭代后得到的残差
${{\boldsymbol{r}}_{t - 1} }$，最终支撑集${\boldsymbol{ F}}$，当前迭代次数$ t $，步长$ s $，阶段数$ j $判断：if ${\left\| {\boldsymbol{R}} \right\|_2} \le \varepsilon$ 退出主函数大循环 else if ${\left\| {\boldsymbol{R} } \right\|_2} \ge {\left\| { {{\boldsymbol{r}}_{t - 1} } } \right\|_2}$ 阶段数增加：$ j = j + 1 $ 支撑集长度更新：$ L = j \times s $ else 更新最终支撑集：${{\boldsymbol{I}}_t} = {\boldsymbol{F}}$ 更新最终残差：${{\boldsymbol{r}}_t} = {\boldsymbol{R}}$ 迭代次数增加：$ t = t + 1 $ end if 输出： $ L $, ${{\boldsymbol{I}}_t}$, ${{\boldsymbol{r}}_t}$, $ t $
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算法9 两阈值变步长稀疏度自适应策略[16] 输入：当前迭代得到的残差${\boldsymbol{R}}$，上一次迭代后得到的残差
${{\boldsymbol{r}}_{t - 1} }$,$\varepsilon_1$, $\varepsilon_2$，当前稀疏向量估计值$\hat {\boldsymbol{z}}$，上一次迭代后得到
的稀疏向量估计值${\hat {\boldsymbol{x}}_{t - 1} }$，最终支撑集${\boldsymbol{F}}$，当前迭代次数
$ t $，步长$ s $，阶段数$ j $判断：if ${\left\| {\hat {\boldsymbol{z} } - { {\hat {\boldsymbol{x}}}_{t - 1} } } \right\|_2} \ge \varepsilon_1$ if ${\left\| {\boldsymbol{R} } \right\|_2} \ge {\left\| { {{\boldsymbol{r}}_{t - 1} } } \right\|_2}$ 阶段数增加：$ j = j + 1 $ 支撑集长度更新：$ L = L + s $ else 更新最终支撑集：${{\boldsymbol{I}}_t} = {\boldsymbol{F}}$ 更新最终残差：${{\boldsymbol{r}}_t} = {\boldsymbol{R}}$ 迭代次数增加：$ t = t + 1 $ end if else if $\varepsilon_2 \le {\left\| {\hat {\boldsymbol{z} } - { {\hat {\boldsymbol{x} } }_{t - 1} } } \right\|_2} \le \varepsilon_1$ if ${\left\| {\boldsymbol{R} } \right\|_2} \ge {\left\| { {{\boldsymbol{r}}_{t - 1} } } \right\|_2}$ 阶段数增加：$ j = j + 1 $ 步长变化：$ s = \left\lceil {0.5 \times s} \right\rceil $ 支撑集长度更新：$ L = L + s $ else 更新最终支撑集：$ L = L + s $ 更新最终残差：${{\boldsymbol{r}}_t} = {\boldsymbol{R}}$ 迭代次数增加：$ t = t + 1 $ end if else if ${\left\| {\hat {\boldsymbol{z} } - { {\hat {\boldsymbol{x} } }_{t - 1} } } \right\|_2} \le \varepsilon_2$ 退出主函数大循环 end if 输出：$ L $,${{\boldsymbol{I}}_t}$,${{\boldsymbol{r}}_t}$,$ t $
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算法10 基于能量的变步长稀疏度自适应策略[12,33] 输入：当前迭代得到的残差${\boldsymbol{R}}$，上一次迭代后得到的残差
${{\boldsymbol{r}}_{t - 1} }$,${\boldsymbol{y}}$，当前稀疏向量估计值$\hat {\boldsymbol{z}}$，最终支撑集${\boldsymbol{F}}$，当前迭
代次数$ t $，步长$ s $，阶段数$ j $判断： if ${\left\| {\boldsymbol{R}} \right\|_2} \le \varepsilon$ 退出主函数大循环 else if ${\left\| {\boldsymbol{R}} \right\|_2} \ge {\left\| { {{\boldsymbol{r}}_{t - 1} } } \right\|_2}$ if $\dfrac{ {\left\| {\boldsymbol{y}} \right\|_2^2} }{ {\left\| {\hat {\boldsymbol{z}}} \right\|_2^2} } \ge \rho$ 状态数增加：$ j = j + 1 $ 支撑集长度更新：$ L = j \times s $ else 状态数增加：$ j = j + 1 $ (1)支撑集长度更新：$ L = L + \left\lceil {0.5 \times s} \right\rceil $[15] (2)步长变化：$ s = \left\lceil {0.5 \times s} \right\rceil $[42] 支撑集长度更新：$ L = L + s $ end if else 更新最终支撑集：${{\boldsymbol{I}}_t} = {\boldsymbol{F}}$ 更新最终残差：${{\boldsymbol{r}}_t} = {\boldsymbol{R}}$ 迭代次数增加：$ t = t + 1 $ end if end if 输出： $ L $,${{\boldsymbol{I}}_t}$,${{\boldsymbol{r}}_t}$,$ t $
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[1] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306. doi: 10.1109/TIT.2006.871582 [2] WEN Jinming, ZHANG Rui, and YU Wei. Signal-dependent performance analysis of orthogonal matching pursuit for exact sparse recovery[J]. IEEE Transactions on Signal Processing, 2020, 68: 5031–5046. doi: 10.1109/TSP.2020.3016571 [3] CANDES E J and WAKIN M B. An introduction to compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2): 21–30. doi: 10.1109/MSP.2007.914731 [4] MALLAT S G and ZHANG Zhifeng. Matching pursuits with time-frequency dictionaries[J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3397–3415. doi: 10.1109/78.258082 [5] PATI Y C, REZAIIFAR R, and KRISHNAPRASAD P S. Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition[C]. 27th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, 1993: 40–44. [6] NEEDELL D and VERSHYNIN R. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 310–316. doi: 10.1109/JSTSP.2010.2042412 [7] GOYAL P and SINGH B. Sparse signal recovery through regularized orthogonal matching pursuit for WSNs applications[C]. 2019 6th International Conference on Signal Processing and Integrated Networks (SPIN), Noida, India, 2019: 461–465. [8] WANG Jian, KWON S, and SHIM B. Generalized orthogonal matching pursuit[J]. IEEE Transactions on Signal Processing, 2012, 60(12): 6202–6216. doi: 10.1109/TSP.2012.2218810 [9] 申滨, 吴和彪, 崔太平, 等. 基于最优索引广义正交匹配追踪的非正交多址系统多用户检测[J]. 电子与信息学报, 2020, 42(3): 621–628. doi: 10.11999/JEIT190270SHEN Bin, WU Hebiao, CUI Taiping, et al. An optimal number of indices aided gOMP algorithm for multi-user detection in NOMA System[J]. Journal of Electronics &Information Technology, 2020, 42(3): 621–628. doi: 10.11999/JEIT190270 [10] DONOHO D L, TSAIG Y, DRORI I, et al. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2012, 58(2): 1094–1121. doi: 10.1109/TIT.2011.2173241 [11] CHEN Jing, CHEN Yan, WU Lei, et al. An improved stagewise weak orthogonal matching pursuit method for electric power transmission tower evaluation using differential sar tomography[C]. IGARSS 2019 - 2019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan, 2019: 3637–3640. [12] DO T T, GAN Lu, NGUYEN N, et al. Sparsity adaptive matching pursuit algorithm for practical compressed sensing[C]. 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, 2008: 581–587. [13] 吴新杰, 闫诗雨, 徐攀峰, 等. 基于稀疏度自适应压缩感知的电容层析成像图像重建算法[J]. 电子与信息学报, 2018, 40(5): 1250–1257. doi: 10.11999/JEIT170794WU Xinjie, YAN Shiyu, XU Panfeng, et al. Image reconstruction algorithm for electrical capacitance tomography based on sparsity adaptive compressed sensing[J]. Journal of Electronics &Information Technology, 2018, 40(5): 1250–1257. doi: 10.11999/JEIT170794 [14] 李保珠, 邵建华, 聂梦雅, 等. 基于能量的稀疏自适应匹配追踪算法[J]. 计算机应用与软件, 2015, 32(11): 121–125. doi: 10.3969/j.issn.1000-386x.2015.11.028LI Baozhu, SHAO Jianhua, NIE Mengya, et al. Energy-based sparsity adaptive matching pursuit algorithm[J]. Computer Applications and Software, 2015, 32(11): 121–125. doi: 10.3969/j.issn.1000-386x.2015.11.028 [15] ZHANG Yi, VENKATESAN R, DOBRE O A, et al. Efficient estimation and prediction for sparse time-varying underwater acoustic channels[J]. IEEE Journal of Oceanic Engineering, 2020, 45(3): 1112–1125. doi: 10.1109/JOE.2019.2911446 [16] 朱延万, 赵拥军, 孙兵. 一种改进的稀疏度自适应匹配追踪算法[J]. 信号处理, 2012, 28(1): 80–86. doi: 10.3969/j.issn.1003-0530.2012.01.012ZHU Yanwan, ZHAO Yongjun, and SUN Bing. A modified sparsity adaptive matching pursuit algorithm[J]. Signal Processing, 2012, 28(1): 80–86. doi: 10.3969/j.issn.1003-0530.2012.01.012 [17] CHATTERJEE S, SUNDMAN D, VEHKAPERA M, et al. Projection-based and look-ahead strategies for atom selection[J]. IEEE Transactions on Signal Processing, 2012, 60(2): 634–647. doi: 10.1109/TSP.2011.2173682 [18] HANG Jinwei and HUANG Yuanhao. A high-SNR projection-based atom selection OMP processor for compressive sensing[J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2016, 24(12): 3477–3488. doi: 10.1109/TVLSI.2016.2554401 [19] AMBAT S K, CHATTERJEE S, and HARI K V S. On selection of search space dimension in compressive sampling matching pursuit[C]. TENCON 2012 IEEE Region 10 Conference, Cebu, Philippines, 2012: 1–5. [20] NEEDELL D and TROPP J A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2009, 26(3): 301–321. doi: 10.1016/J.ACHA.2008.07.002 [21] CHENG Jiawei. An improved off-grid algorithm based on CoSaMP for ISAR imaging[C]. 2020 5th International Conference on Mechanical, Control and Computer Engineering (ICMCCE), Harbin, China, 2020: 1643–1646, [22] CHAE J and HONG S. Greedy algorithms for sparse and positive signal recovery based on Bit-Wise MAP detection[J]. IEEE Transactions on Signal Processing, 2020, 68: 4017–4029. doi: 10.1109/TSP.2020.3004700 [23] DAI Wei and MILENKOVIC O. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Transactions on Information Theory, 2009, 55(5): 2230–2249. doi: 10.1109/TIT.2009.2016006 [24] LIU Yizhong, SONG Tian, and ZHUANG Yiqi. A high-throughput subspace pursuit processor for ECG recovery in compressed sensing using square-root-free MGS QR decomposition[J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2020, 28(1): 174–187. doi: 10.1109/TVLSI.2019.2936867 [25] LIU Lufeng, DU Xinpeng, and CHENG Lizhi. Stable signal recovery via randomly enhanced adaptive subspace pursuit method[J]. IEEE Signal Processing Letters, 2013, 20(8): 823–826. doi: 10.1109/LSP.2013.2267796 [26] LIU Guangcan, ZHANG Zhao, LIU Qingshan, et al. Robust subspace clustering with compressed data[J]. IEEE Transactions on Image Processing, 2019, 28(10): 5161–5170. doi: 10.1109/TIP.2019.2917857 [27] AMBAT S K, CHATTERJEE S, and HARI K V S. Subspace pursuit embedded in orthogonal matching pursuit[C]. TENCON 2012 IEEE Region 10 Conference, Cebu, Philippines, 2012: 1–5. [28] LIU Jing, HUANG Kaiyu, and YAO Xianghua. Common-innovation subspace pursuit for distributed compressed sensing in wireless sensor networks[J]. IEEE Sensors Journal, 2019, 19(3): 1091–1103. doi: 10.1109/JSEN.2018.2881056 [29] CHATTERJEE S, SUNDMAN D, and SKOGLUND M. Look ahead orthogonal matching pursuit[C]. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, 2011: 4024–4027. [30] MURALIKRISHNNA G S, AMBAT S K, and HARI K V S. Batch look ahead orthogonal matching pursuit[C]. 2018 Twenty Fourth National Conference on Communications (NCC), Hyderabad, India, 2018: 1–5. [31] SWAMY P B, AMBAT S K, CHATTERJEE S, et al. Reduced look ahead orthogonal matching pursuit[C]. 2014 Twentieth National Conference on Communications (NCC), Kanpur, India, 2014: 1–6. [32] AMBAT S K, CHATTERJEE S, and HARI K V S. Adaptive selection of search space in look ahead orthogonal matching pursuit[C]. 2012 National Conference on Communications (NCC), Kharagpur, India, 2012: 1–5. [33] KOPPARTHI V R, PEESAPATI R, and SABAT S L. System on chip implementation of low complex orthogonal matching pursuit algorithm on FPGA[C]. 2020 6th International Conference on Signal Processing and Communication (ICSC), Noida, India, 2020: 178–184. [34] CAI T T and WANG Lie. Orthogonal matching pursuit for sparse signal recovery with noise[J]. IEEE Transactions on Information Theory, 2011, 57(7): 4680–4688. doi: 10.1109/TIT.2011.2146090 [35] WANG Zhizhan, LI Yuzhou, WANG Chengcai, et al. A-OMP: An adaptive OMP algorithm for underwater acoustic OFDM channel estimation[J]. IEEE Wireless Communications Letters, 2021, 10(8): 1761–1765. doi: 10.1109/LWC.2021.3079225 [36] ZHANG Yi, VENKATESAN R, DOBRE O A, et al. An adaptive matching pursuit algorithm for sparse channel estimation[C]. 2015 IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, USA, 2015: 626–630. [37] HU Yunfeng and ZHAO Liquan. A fuzzy selection compressive sampling matching pursuit algorithm for its practical application[J]. IEEE Access, 2019, 7: 144101–144124. doi: 10.1109/ACCESS.2019.2941725 [38] MOURAD N, SHARKAS M, and ELSHERBENY M M. Orthogonal matching pursuit with correction[C]. 2016 IEEE 12th International Colloquium on Signal Processing & Its Applications (CSPA), Melaka, Malaysia, 2016: 247–252. [39] ZHAO Juan and BAI Xia. Adaptive matching pursuit method based on auxiliary residual for sparse signal recovery[C]. 2019 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), Lanzhou, China, 2019: 774–778. [40] HUANG Honglin and MAKUR A. Backtracking-based matching pursuit method for sparse signal reconstruction[J]. IEEE Signal Processing Letters, 2011, 18(7): 391–394. doi: 10.1109/LSP.2011.2147313 [41] ZENG Chunyan, MA Lihong, DU Minghui, et al. Regularized sequential selection and backtracking removal for CS atom matching[C]. 2012 IEEE 14th International Workshop on Multimedia Signal Processing (MMSP), Banff, Canada, 2012: 209–214, [42] GAO Guangyong, ZHOU Caixue, CUI Zongmin, et al. Improved sparsity adaptive matching pursuit algorithm[C]. 2017 3rd IEEE International Conference on Computer and Communications (ICCC), Chengdu, China, 2017: 1761–1766. [43] ZHENG Baifu, ZENG Cao, LI Shidong, et al. Joint sparse recovery for signals of spark-level sparsity and MMV tail- $ \ell _{2, 1}$ minimization[J]. IEEE Signal Processing Letters, 2021, 28: 1130–1134. doi: 10.1109/LSP.2021.3084517 -
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