论文标题
使用压缩感中的渐近残差估算噪声方差
Noise Variance Estimation Using Asymptotic Residual in Compressed Sensing
论文作者
论文摘要
在压缩感应中，通常会受到添加噪声污染测量值，因此，设计算法通常需要有关噪声方差的信息。在本文中，我们提出了一种估计压缩感应问题中未知噪声方差的方法。所提出的方法称为渐近残留匹配（ARM），根据$ \ ell_ {1} $优化问题的渐近结果估算单个测量向量的噪声差异。具体而言，我们得出与$ \ ell_ {1} $优化相对应的渐近残差，并表明它取决于噪声方差。提出的ARM方法通过将渐近残留物与实际的渐近残差进行比较，可以通过经验重建获得估计值，而无需有关噪声方差的信息。对于拟议的臂，我们还提出了一种基于渐近残差选择合理参数的方法。仿真结果表明，所提出的噪声方差估计的表现优于几种常规方法，尤其是当问题大小很小时。我们还表明，通过使用建议的方法，我们可以调整$ \ ell_ {1} $优化的正则化参数，即使噪声方差未知，也可以实现良好的重建性能。
In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise variance in compressed sensing problems. The proposed method, called asymptotic residual matching (ARM), estimates the noise variance from a single measurement vector on the basis of the asymptotic result for the $\ell_{1}$ optimization problem. Specifically, we derive the asymptotic residual corresponding to the $\ell_{1}$ optimization and show that it depends on the noise variance. The proposed ARM approach obtains the estimate by comparing the asymptotic residual with the actual one, which can be obtained by empirical reconstruction without the information on the noise variance. For the proposed ARM, we also propose a method to choose a reasonable parameter based on the asymptotic residual. Simulation results show that the proposed noise variance estimation outperforms several conventional methods, especially when the problem size is small. We also show that, by using the proposed method, we can tune the regularization parameter of the $\ell_{1}$ optimization to achieve good reconstruction performance, even when the noise variance is unknown.
