# Inversion of the Toeplitz-block Toeplitz matrices and the structure of the corresponding inverse matrices

## TL;DR

This paper investigates the inversion of 2-D Toeplitz-block Toeplitz matrices, identifying minimal information needed for inversion and providing a complete characterization of their inverse matrices.

## Contribution

It extends classical 1-D Toeplitz inversion results to 2-D matrices, offering new insights into their structure and inversion process.

## Key findings

- Characterization of inverse matrices for 2-D Toeplitz-block Toeplitz matrices
- Identification of minimal information required for inversion
- Complete description of inverse matrix structure

## Abstract

The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal information, which is necessary to recover the inverse matrices, and give a complete characterisation of the inverse matrices.