论文标题
多元信号可能具有未知噪声分布的反卷积
Deconvolution with unknown noise distribution is possible for multivariate signals
论文作者
论文摘要
本文考虑了目标信号是多维且对噪声分布不了解的信息。更确切地说，没有对噪声分布做出任何假设，也没有任何样本可估算它：仅根据损坏的信号观察来解决反卷积问题。当信号具有拉普拉斯变换时，指数级的增长小于$ 2 $时，我们就可以确定模型的可识别性，直至翻译。然后，我们提出了信号的概率密度函数的估计值，而没有任何假设对噪声分布。由于该估计器取决于通常未知的信号分布尾部的轻度，因此提出了模型选择程序以在此参数中获得自适应估计器，其收敛速率与具有已知尾部参数的估计器相同。最后，我们建立了与上限匹配的最小收敛速率的下限。
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on the corrupted signal observations. We establish the identifiability of the model up to translation when the signal has a Laplace transform with an exponential growth smaller than $2$ and when it can be decomposed into two dependent components. Then, we propose an estimator of the probability density function of the signal without any assumption on the noise distribution. As this estimator depends of the lightness of the tail of the signal distribution which is usually unknown, a model selection procedure is proposed to obtain an adaptive estimator in this parameter with the same rate of convergence as the estimator with a known tail parameter. Finally, we establish a lower bound on the minimax rate of convergence that matches the upper bound.
