Title: Recovering data sparse in a frame
Abstract: In this talk, we will first review some classical results on compressed sensing, a subject about recovering sparse signals from undersampled linear measurements. The theory developed in compressed sensing is transformative as it has been applied to a broader class of data recovery problems such as matrix completion. Then we will focus on its generalization where signals are sparse in a redundant frame. We will discuss the challenges faced in this case, as well as some new results. A preliminary image inpainting application will also be addressed at the end of the talk.