 In this paper, the authors propose a new approach to solving inverse problems using generalized statistics. They show that these statistics are more resilient to outliers than traditional Gaussian statistics and can provide better results in terms of accuracy and speed. Furthermore, they demonstrate that the three proposed methods are equivalent, meaning that they all produce similar results but require less computation time. This makes them ideal for use in real world applications where accuracy and efficiency are both important. This article was authored by Gustavo Z. dos Santos Lima, Joao V. T. de Lima, Joao M. de Orojo and others.