鲁棒原子范数降噪及其在线谱估计中的应用

针对测量数据中含有异常值的线谱估计问题,提出了一种对异常值鲁棒的原子范数降噪方法来提高线谱估计的性能。该方法构建了一个可以联合估计出异常值及原始信号的优化问题,并在代价函数中加入l₁范数和原子范数惩罚项来分别对异常值的稀疏性和信号本身的特性进行约束。一旦获得了该优化问题的解,那么就可利用现有的算法对降噪后的信号进行线谱估计。仿真结果表明,在数据中存在异常值的情况下,所提的算法能够更准确地恢复原始信号,从而使降噪后的谱估计的精度和分辨率明显提高。

Robust atomic norm denoising with its applications to line spectral estimation

To estimate the line spectrum of data corrupted with outliers, a robust atomic norm denoising method is proposed. In the method, an optimization problem jointly estimating the outliers and the original signal is formulated. By adding anl₁ norm penalty on the outliers and an atomic norm penalty on the signal to the cost function, the sparsity in the outliers and the signal own characteristics are constrained. Once the optimization problem is solved, the existed spectral estimation algorithms can be used to estimate the spectrum of the denoised signal. The simulation results indicate that when the observed data are corrupted with outliers, the proposed method can acquire a more accurate original signal estimation, thus the spectral estimation will be of higher precision and resolution.