# Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications

## TL;DR

This paper establishes convergence of multivariate max-product neural network operators of Kantorovich type within Orlicz spaces, including applications to biomedical image reconstruction and enhancement.

## Contribution

It introduces a new convergence framework for neural network operators in Orlicz spaces using Kantorovich means, extending previous results to multivariate and real-world applications.

## Key findings

- Convergence proven for neural network operators in Orlicz spaces.
- Applications demonstrated in biomedical image reconstruction.
- Operators effectively enhance vascular images.

## Abstract

In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in the general frame of the Orlicz spaces, which includes as particular case the $L^p$-spaces. Examples of sigmoidal activation functions are discussed, for the above operators in different cases of Orlicz spaces. Finally, concrete applications to real world cases have been presented in both uni-variate and multivariate settings. In particular, the case of reconstruction and enhancement of biomedical (vascular) image has been discussed in details.