压缩感知OMP算法下信号重建方法研究

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压缩感知OMP算法下信号重建方法研究

付敏,郝嘉骏,解烈军,王金平

Exact Support Recovery of Sparse Signals from Noisy Measurements

Min Fu,Jiajun Hao,Liejun Xie,Jinping Wang

表 2 改进的OMP算法

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 $\Lambda_{K}$