Regularized sparsity variable step-size adaptive matching pursuit algorithm for compressed sensing
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摘要:
压缩感知（CS）能够突破Nyquist采样定理的瓶颈，使得高分辨率信号采集成为可能。重构算法是压缩感知中最为关键的部分，迭代贪婪算法是其中比较重要的研究方向。对压缩感知理论进行了详细分析，并在现有重构算法的基础上提出了一种新的迭代贪婪算法——正则化稀疏度变步长自适应匹配追踪（RSVssAMP）算法，可在信号稀疏度未知的情况下，结合正则化和步长自适应变化思想，快速精确地进行重构。相比于传统迭代贪婪算法，本文算法不依赖于信号稀疏度，并且应用正则化以确保选取支撑集的正确性。此外，应用自适应变化步长代替固定步长，能够提高重构速率，而且达到更高的精度。为了验证本文算法的正确性，选取高斯稀疏信号和离散稀疏信号分别进行仿真，并与现有算法进行比较。仿真结果表明，本文算法相比于现有算法可以实现更加精确快速的重构。
Abstract:Compressed sensing (CS), which could break through the bottleneck of the Nyquist sampling theorem, makes the high resolution signal acquisition possible. Reconstruction algorithm is the key part of compressed sensing, and the iterative greedy algorithm is one of highly significant research directions. A novel iterative greedy algorithm for compressed sensing, named regularized sparsity variable step-size adaptive matching pursuit (RSVssAMP) algorithm, was proposed in this paper. The regularized idea and the variable step-size adaptive idea were utilized in the new algorithm to achieve a quick and accurate reconstruction under the condition that the sparsity of a signal was unknown. Compared with traditional greedy algorithms, RSVssAMP could reconstruct the signal without prior information of the sparsity, and it could accelerate the reconstruction speed obviously and achieve better performance by acquiring a better candidate set. The Gaussian sparse signal and discrete sparse signal were taken as trial signals, and the comparisons of reconstruction probability and time were demonstrated in this paper. The simulation results indicate that the proposed algorithm could achieve a higher reconstruction precision and take shorter time when compared with the existing greedy algorithms.
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Key words:
- compressed sensing (CS) /
- adaptive /
- regularized /
- variable step-size /
- matching pursuit
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图 1 正则化稀疏度变步长自适应匹配追踪算法流程图
Figure 1. Flowchart of regularized sparsity variable step-size adaptive matching pursuit algorithm
图 2 不同稀疏度下重构成功率比较
Figure 2. Comparison of reconstruction success rate under different sparsity
图 4 不同观测值下重构成功率比较
Figure 4. Comparison of reconstruction success rate under different observed values
图 5 不同观测值下重构时间比较
Figure 5. Comparison of reconstruction time under different observed values
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