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Variational and PDE-based image processing


The project aims at achieving better understanding of image models of structure and texture by using powerful mathematical tools, recently proposed for this purpose, from the fields of calculus of variations and functional analysis.

Based on this insight, new theoretical concepts and practical algorithms would be suggested as solutions to some fundamental problems and open question in modern image processing such as regularization and denoising, texture processing, image decomposition and optimal scale selection.

The mathematical tools require knowledge in nonlinear partial differential equations (PDE's), variational theory, differential geometry and functional and convex analysis. Also more classical knowledge in image and signal processing such as linear and nonlinear filtering, Fourier and harmonic analysis and basic statistical concepts would be utilized.

Variational and PDE-based image processing is today a rapidly advancing field with established success in both state-of-the-art applications and deeper theoretical understanding on the modeling of images.

The Department of Mathematics at UCLA is a world-leading centre of this research. Prof. Osher is a key player in developing and understanding these new image models and techniques.

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