Even though Deep Neural Networks are extremely powerful for image restoration tasks, they have several limitations. They are poorly understood and suffer from strong biases inherited from the training sets. One way to address these shortcomings is to have a better control over the training sets, in particular by using synthetic sets. In this paper, we propose a synthetic image generator relying on a few simple principles. In particular, we focus on geometric modeling, textures, and a simple modeling of image acquisition. These properties, integrated in a classical Dead Leaves model, enable the creation of efficient training sets. Standard image denoising and super-resolution networks can be trained on such datasets, reaching performance almost on par with training on natural image datasets. As a first step towards explainability, we provide a careful analysis of the considered principles, identifying which image properties are necessary to obtain good performances. Besides, such training also yields better robustness to various geometric and radiometric perturbations of the test sets.