On the Uniqueness of Group Sparse Coding

TL;DR

This paper proves the uniqueness of group sparse coding using a theoretical approach based on the block ACS theorem, extending the original ACS theorem to the group sparse setting.

Contribution

It introduces a proof demonstrating the uniqueness of group sparse coding, expanding the theoretical understanding of sparse coding methods.

Findings

Proves the uniqueness of group sparse coding.

Extends the original ACS theorem to group sparse coding.

Provides a theoretical foundation for group sparse coding methods.

Abstract

In this technical document we present a proof on the uniqueness of group sparse coding through the block ACS theorem. Leveraging the original ACS theorem of Hillar and Sommer for sparse coding, we demonstrate a similar uniqueness property holds for the task of group sparse coding.