论文标题
在未知噪声水平上稀疏信号的强劲实例 - 最佳恢复
Robust Instance-Optimal Recovery of Sparse Signals at Unknown Noise Levels
论文作者
论文摘要
我们考虑了从嘈杂测量结果中稀疏信号恢复的问题。许多经常使用的恢复方法取决于某种调整，具体取决于噪声或信号参数。如果没有任何两个可用的估计值，则嘈杂的恢复问题将很难。平方根套索和最小绝对偏斜的拉索已知是噪声盲的，因为可以独立于噪声和信号独立选择调谐参数。我们将这些恢复方法推广到\ hrlone {}，并在调谐参数高于阈值后提供恢复保证。此外，我们分析了不良选择的调整参数在理论层面上误以为的效果，并证明了我们的恢复保证的最佳性。此外，对于高斯矩阵，我们对调谐参数的阈值进行了精制分析，并证明了尺寸上调谐参数的新关系。实际上，对于一定量的测量值，调整参数变得独立于稀疏性。最后，我们验证在随机选择的左左常规双载图上均匀地将绝对偏差的拉索与随机行走矩阵一起使用。
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are available, the noisy recovery problem is significantly harder. The square root LASSO and the least absolute deviation LASSO are known to be noise-blind, in the sense that the tuning parameter can be chosen independent on the noise and the signal. We generalize those recovery methods to the \hrlone{} and give a recovery guarantee once the tuning parameter is above a threshold. Moreover, we analyze the effect of a bad chosen tuning parameter mistuning on a theoretic level and prove the optimality of our recovery guarantee. Further, for Gaussian matrices we give a refined analysis of the threshold of the tuning parameter and proof a new relation of the tuning parameter on the dimensions. Indeed, for a certain amount of measurements the tuning parameter becomes independent on the sparsity. Finally, we verify that the least absolute deviation LASSO can be used with random walk matrices of uniformly at random chosen left regular biparitite graphs.
