Mathematical Approaches to Image Processing with Carola Schönlieb

TL;DR

Carola Schönlieb describes her trajectory from studying partial differential equations (Cahn–Hilliard) to mathematical image processing, focusing on handcrafted models (total variation regularization, median filtering) that preserve edges and provide provable stability guarantees, versus deep neural networks that achieve higher performance on in-distribution data but fail on out-of-distribution ex

Key insights

• Edges are the most visually important features in an image; denoising methods must preserve them, which Fourier-based techniques fail to do because they remove all high frequencies uniformly.
• Total variation regularization explicitly models sharp discontinuities and preserves edges; median filtering is a simpler related approach.
• Handcrafted models (e.g., total variation) offer provable properties (stability, error estimates) and generalization to domains unseen by neural networks, whereas neural networks only work well on dat