基于改进的近似l₀范数的稀疏信号重构算法
A Sparse Signal Reconstruction Algorithm Based on Improved Approximate l₀ Norm

DOI: 10.12677/CSA.2021.118223, PP. 2179-2189

Keywords: 压缩感知，信号重构，近似l₀范数，共轭梯度法
Compressive Sensing, Signal Reconstruction, Approximate l₀ Norm, Conjugate Gradient Method

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Abstract:

稀疏信号重构算法是压缩感知的关键。基于近似l₀范数的稀疏信号重构可以通过选取一个光滑函数近似l₀范数，从而将l₀范数最小化问题转化为光滑函数的优化问题。为了提高压缩感知中稀疏信号重构的精度，本文提出了一种基于改进的近似l₀范数的稀疏信号重构算法。该算法首先利用一种改进的光滑函数来近似l₀范数；其次利用外点罚函数法和共轭梯度法求解基于该光滑函数的优化问题的稀疏解；最后进行了多项实验来验证所提出算法的有效性。实验结果表明：相比于光滑l0算法、基追踪算法和非凸复合稀疏基算法，本文所提算法在重构误差、信噪比和恢复成功率等方面更具优越性。
The sparse signal reconstruction algorithm is the key to compressive sensing. The sparse signal reconstruction based on approximate l₀ norm can be achieved by choosing a smooth function to approximate l₀ norm, thus the minimization problem of l₀ norm is transformed into an optimization problem of a smooth function. To improve the accuracy of the sparse signal reconstruction in compressive sensing, a sparse signal reconstruction algorithm based on an improved approximate l₀ norm is proposed in this paper. Firstly, a smooth function is proposed to approximate l₀ norm. Then, the sparse solution of this optimization problem that based on the smooth function is solved by exterior point penalty function method and conjugate gradient method. Finally, a number of experiments are carried out to verify the performance of the proposed algorithm. The experimental results show that the proposed algorithm is more superior in reconstruction error, signal-to-noise ratio and recovery success rate compared with smoothed l0 algorithm, the basis pursuit algorithm and the non-convex composite sparse bases algorithm.

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