אירועים

Inverse problems in the field of signal processing refer to the estimation of a (clean) signal when given corrupted or partial measurements of it. In this research thesis, we focus on solving such problems, using both the traditional sparse representation model and the more recent deep neural networks approach. In a series of papers, we show how one could utilize the mathematically well-understood results of the former, to improve the common practice of the latter, leading to novel architectures and optimization techniques. During the talk, we will focus on two papers. The first suggests a method for performing image morphing (or image interpolation) by solving the well-known Wasserstein barycenter problem while constraining the output image to a specific image prior, such as the sparse prior or neural network generative models. In our second work, we will explore the problem of inverting deep generative models for solving inverse problems. Here we utilize sparse representation theory for relaxing previously known bounds on the dimensions of the hidden layers that assure the model's inversion. In addition, we suggest provable methods for inverting ReLU activated deep generative models.