This manuscript is the result of Manuel Sánchez Laguardia’s end-of-studies internship as part of his engineering studies at IMT Atlantique and Universidad de la República. The development of this work began the 1st of April 2023 and extended until the 30th of September 2023, for a total duration of six months. The internship was carried under the mentorship of Charles Kervrann and Emmanuel Moebel. It covered two main projects, both related to the subject of this internship: "Statistical learning and convolutional neural networks for supervised and unsupervised restoration of satellite images in low light conditions" This document is divided into 7 main Sections. First, the introduction to the mission, where the context, background and expected results are explained. Then, the presentation of the hosting organization. Next, the developed work and methodology, where the two main projects are presented in separate Sections. Then, the conclusions followed by the perspectives of the project. Finally, a reflection on my professional project for the future and its link with this internship. The first project consisted in studying the statistics behind the gradient descent used to estimate parameters of convolutional neural networks. This was achieved via the study of a well-known machine learning algorithm used for denoising: Deep Image Prior [1]. This analysis gave very interesting results. It showed that the direction of the parameters vector of the neural network throughout the iterations, could be explained almost entirely with just one PCA (Principal Component Analysis) vector. However, it also showed that from one iteration to the next, the parameters change almost randomly, and no information could be extracted from them as whole. This first project was set aside to be worked on, possibly, towards the end of the internship. The second project consisted in performing image restoration methods by combining denoising and deconvolution, using different techniques. I focused on satellite images in low light conditions, as this is what the team has been working since they partnered up with Airbus Space and Defense. The goal was to explore how this different methods performed, and draw conclusions in terms of performances (PSNR) and time computations. It was found that the type of noise had a high impact on the result of the methods. Also, it was shown experimentally that training one of the supervised methods using microscopy images, which are similar to night satellite images, produces very good results and are a good fit for the training phase.