Classifying Signals Under a Finite Abelian Group Action: The Finite Dimensional Setting

Understand

Let $G$ be a finite group acting on $\mathbb{C}^N$.

• We study the problem of identifyng the class in $\mathbb{C}^N / G$ of a given signal: this encompasses several types of problems in signal processing.
• Some instances include certain generalizations of phase retrieval, image recognition, the analysis of textures, etc.
• In our previous work \cite{prev}, based on an algebraic approach, we constructed a Lipschitz translation invariant transform -- the case when $G$ is cyclic.