压缩感知OMP算法下信号重建方法研究

Abstract

CLC Number:

O175.5

Min Fu,Jiajun Hao,Liejun Xie,Jinping Wang. Exact Support Recovery of Sparse Signals from Noisy Measurements[J].Acta mathematica scientia,Series A, 2021, 41(5): 1555-1565.

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SNR	支撑的识别
337.85	成功
187.69	成功
112.62	成功
93.85	成功
80.44	成功
3.38	失败

Exact Support Recovery of Sparse Signals from Noisy Measurements

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输入: 样本${\bf y}$, 采样矩阵$\Phi$, 稀疏度K
步骤1(识别): $\Lambda^{k} = \mathop{\arg\max}\limits _{\Upsilon\in\Gamma\setminus \Lambda_{k-1}}\mid \langle \Phi_{\Upsilon}, r^{k-1}\rangle\mid$
步骤2(增加): $\Lambda_{k} = \Lambda_{k-1}\cup\Lambda^{k}$
步骤3(估计): ${\bf x}^{(k)} = \mathop{\arg\min}\limits_{{\rm supp}({\bf u}) = \Lambda_{k}}\parallel {\bf y}-\Phi {\bf u}\parallel_{2}$
步骤4(更新): ${\bf r}_{k} = {\bf y}-\Phi {\bf x}^{(k)}$
输出: 重建信号${\bf x}^{(K)}$, 最优原子集$\Lambda_{K}$

输入: 样本${\bf y}$, 采样矩阵$\Phi$, 稀疏度K
步骤1(识别): $\Lambda^{k} = \mathop{\arg\max}\limits_{\Upsilon\in\Gamma\setminus \Lambda_{k-1}}\mid \langle \Phi_{\Upsilon}, r^{k-1}\rangle\mid$
步骤2(增加): $\Lambda_{k} = \Lambda_{k-1}\cup\Lambda^{k}$
步骤3(估计): ${\bf x}^{(k)} = \mathop{\arg\min}\limits_{{\rm supp}({\bf u}) = \Lambda_{k}}\parallel {\bf y}-\Phi {\bf u}\parallel_{2}$
步骤4(筛选): 若$\parallel {\bf x}^{(k)}-{\bf x}^{(k-1)}\parallel_{2}\leq \parallel {\bf y}\parallel_{2}$,
是, 接着步骤5, 否则, 步骤1.
步骤5(更新): ${\bf r}_{k} = {\bf y}-\Phi {\bf x}^{(k)}$
输出: 输出信号$x^{K}$, 最优原子集$\Lambda_{K}$