• compressed
• image
• immagini
• inverse
• inverso
• network
• neural
• neurali
• problem
• problema
• reti
• risoluzione
• sensing
• stabilità
• stability
• super resolution

In this thesis, we will analyze the issue of instability with respect to small perturbations in neural networks, focusing on the case of inverse problems. Here, we consider the case of recovering a vector x from a measurement y = Ax, where A is a linear sub-sampling operator. In this setting we show that small perturbations of the input can make the performance of an algorithm much worse. Thus, when considering measurements affected by random noise, stability becomes a key property for the recovery model. In order to establish whether a stable and accurate neural network can be computed, we follow the paper by Anthun, Colbrook, Hansen that exploits Compressed Sensing to produce a model with theoretically ensured stability properties, under some assumptions on the sub-sampling operator. Ultimately, we apply the resulting theory to a particular image reconstruction problem: Image Super Resolution. The problem consists of recovering the original high-resolution image by a corrupted low-resolution version of it. By applying the obtained model to this task, we get good results both in terms of performance and of time consumption.