Topics in Denoising and Structure Recovery from Data

Graduate / Professional

Recovering signals and underlying structure from noisy observations is a fundamental problem in many areas of science and engineering. Over the past few decades, a rich body of work has emerged to address this challenge across diverse settings. A common guiding principle is to leverage structural assumptions—such as smoothness, sparsity, or low-rankness in the data—alongside models of the noise to enable effective recovery. This course explores both classical and modern approaches to denoising and structural data recovery, blending theoretical foundations with algorithmic and applied perspectives. Particular emphasis is placed on high-dimensional regimes relevant to modern data analysis, where noise can behave in counterintuitive ways, yet also exhibit predictable patterns that can be exploited for denoising. The course introduces tools and results from high-dimensional probability and random matrix theory that underpin many recent advances in this area. TTh 2:35pm-3:50pm