论文标题
球形数据的反卷积因未知噪声而损坏
Deconvolution of spherical data corrupted with unknown noise
论文作者
论文摘要
在噪声分布未知并且没有任何其他观察结果的情况下，我们考虑了在$（d-1）$ - 尺寸球体上支持的密度的反卷积问题。我们提出了半径，中心和球体信号密度的估计量，而没有进一步的信息证明是一致的。事实证明，半径的估计器对于任何维度$ d $都具有几乎参数收敛率。当$ d = 2 $时，事实证明，密度的估计器与Sobolev规则性类别的密度相同，与已知噪声分布相同。
We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We propose estimators of the radius, of the center, and of the density of the signal on the sphere that are proved consistent without further information. The estimator of the radius is proved to have almost parametric convergence rate for any dimension $d$. When $d=2$, the estimator of the density is proved to achieve the same rate of convergence over Sobolev regularity classes of densities as when the noise distribution is known.
