Gradient-phase retrieval from spectrogram measurements

The retrieval of the gradient of the phase from spectrogram measurements is a challenging mathematical problem that has received less attention in the mathematical literature compared to the standard phase retrieval problem. The technique used to collect the measurements is called ptychography, an innovative imaging technique that provides high-resolution data. This thesis first focuses on the mathematical analysis and the development of a numerical algorithm for the reconstruction of the gradient, and ultimately provides an application of the derived model in simple settings.