Finalist EPFL doctorate Award 2016 – Ulugbek Kamilov
Special distinction from the selection committee to Ulugbek Kamilov for his thesis "Sparsity-Driven Statistical Inference for Inverse Problems". Thesis n°6545 (2015). Thesis director: Prof. M. Unser.
This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being re- placed by nonlinear alternatives that rely on the sparsity of naturally occurring signals. We adopt a statistical perspective and model the signal as a realization of a stochastic process that exhibits sparsity as its central property.
Our general strategy for solving in- verse problems then lies in the development of novel iterative solutions for performing the statistical estimation. As a key application of our methodology, we present a novel optical tomographic imaging technique called Learning Tomography (LT) that can be used to visualize the distribution of the refractive index in an object such as biological cell.