Given a real inner product space $V$ and a group $G$ of linear isometries, we construct a family of $G$-invariant real-valued functions on $V$ that we call coorbit filter banks, which unify previous notions of max filter banks and finite coorbit filter banks. When $V=\mathbb R^d$ and $G$ is compact, we establish that a suitable coorbit filter bank is injective and locally lower Lipschitz in the quotient metric at orbits of maximal dimension. Furthermore, when the orbit space $\mathbb S^{d-1}/G$ is a Riemannian orbifold, we show that a suitable coorbit filter bank is bi-Lipschitz in the quotient metric.

翻译：给定一个实内积空间 $V$ 和一个由线性等距变换构成的群 $G$，我们在 $V$ 上构造了一族 $G$ 不变的实值函数，称为共轨滤波器组，该构造统一了先前提出的最大滤波器组和有限共轨滤波器组。当 $V=\mathbb R^d$ 且 $G$ 为紧群时，我们证明了一个适当的共轨滤波器组在最大维轨道处关于商度量是单射且局部下利普希茨连续的。进一步地，当轨道空间 $\mathbb S^{d-1}/G$ 为黎曼轨道流形时，我们证明了一个适当的共轨滤波器组关于商度量是双利普希茨连续的。