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摘要: 针对压缩感知（Compressive sensing，CS）中未知稀疏度信号的重建问题，本文提出一种变步长稀疏度自适应子空间追踪算法.首先，采用一种匹配测试的方法确定固定步长，然后以该固定步长与变步长方式相结合，通过不同支撑集原子个数下的重建残差变化确定信号稀疏度，算法采用子空间追踪方法确定相应支撑集原子，并完成原始信号准确重建.实验结果表明，与同类算法相比，该算法可以更准确重建原始信号，且信号稀疏度值较高时，运算量低于同类算法.Abstract: A novel variable step size sparsity adaptive subspace pursuit algorithm is proposed to rebuild the sparse signals with unknown sparsity in compressive sensing. Firstly, the initial fixed step size is obtained by matching test, which is combined with the variable step size method. Then, the sparsity is accurately estimated according to the change of signal rebuilding residual error under vary support set. Subspace pursuit algorithm is used to determine the support set and exactly rebuild the sparse signal. Simulation results show that the proposed algorithm is competitive in recovering accuracy and running speed, compared to other similar algorithms, when sparsity is large.
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图 1 支撑集原子个数与残差对应关系示意图
Fig. 1 The relationship of residual error and the number of support set atom
图 2 不同信噪比下稀疏度K估计误差
Fig. 2 Estimating error of signal sparsity under different noise level
图 3 不同算法信号准确重建率
Fig. 3 Exact recovery ratio of recovery algorithms by different reconstruction algorithms
图 4 噪声环境下的重建精度(M=80, N=256, K=20)
Fig. 4 Reconstruction accuracy in noise environment (M=80, N=256, K=20)
图 5 算法运行时间对比(M=1 024, N=2 048)
Fig. 5 Running time by different reconstruction algorithms (M=1 024, N=2 048)
图 6 样率0.5时, Lena原图像及各算法重建图像
Fig. 6 Original image and reconstructed image of different algorithms for Lena when sampling rate is 0.5
表 1 各算法的重建质量及运行时间对比
Table 1 Comparison of the qualities of images reconstructed and running time by different algorithms
重建算法 M=0.3 × N M=0.4 × N M=0.5 × N PSNR(dB) 运算时间 PSNR(dB) 运算时间 PSNR(dB) 运算时间 OMP 23.07 0.69 27.48 1.06 30.96 1.24 ROMP 24.72 0.32 27.89 0.68 31.52 1.05 SP 23.15 0.76 26.51 0.96 30.84 1.32 SAMP1 24.80 11.57 27.79 18.25 30.96 26.96 SAMP5 24.14 2.71 27.49 4.55 30.85 7.46 SAMP10 23.65 1.55 27.42 2.84 30.72 3.91 VssSASP 25.26 3.21 28.13 4.92 31.63 7.63 
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