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Colloquia Patavina: The total variation norm in computational fluid dynamics and image processing

Martedì 14 Maggio 2013, ore 16:00 - Aula 1A150 - Antonio Marquina

ARGOMENTI: Seminari

Martedì 14 Maggio 2013, alle ore 16:00 in aula 1A150 della Torre Archimede, Antonio Marquina (Universidad de Valencia) terrà una conferenza della serie Colloquia Patavina dal titolo:
The total variation norm in computational fluid dynamics and image processing.

Riassunto
In this talk we shall review the relevance of the total variation norm in the development of computational fluid dynamics and lately as a useful and accurate mathematical tool in image processing and data treatment. The pursue of efficient and accurate algorithms for the simulation of supersonic flows where jump discontinuities (shock waves) propagate and interact are present makes the L2 norm limited because the development of the unavoidable Gibbs phenomenom around jumps, that causes the presence of spurious oscillations in the simulated flow. Then, the total variation norm, (and the L1 norm in general) replaced the L2 norm in the design of numerical schemes to preserve edges and other singular points of the flows, avoiding unphysical oscillations. Through the last three decades digital image processing has been developed since the relevant applications arising from new sensors, (digital cameras, CAT scanners, MRI, ....). Typical digital signals (like images) contain edges, noise and other undesirable artifacts, and therefore classical methods for image restoration and enhancement based on Fourier transform and L2 norms, are very limited due to the presence of spurious oscillation ({sl ringing}). Thus, the use of the total variation norm as a regularizer is a significant improvement in the numerical outputs. We shall describe the role of this new L1-mathematics in the development and treatment of images and digital data as well as the new challenges established from this new perspective.

Breve biografia
Antonio Marquina is an applied mathematician. He is Professor of Applied Mathematics at the University of Valencia, Spain. His main contributions are in the field of nonlinear partial differential equations with applications in fluid dynamics and image processing.
He has developed shock capturing numerical schemes for solving hydrodynamic equations and relativistic flows as well as high resolution reconstruction procedures to increase the order of accuracy of those.
He has also authored several results on mathematical models and numerical schemes for deblurring, denoising and super-resolution of images.

Rif. Int. C. Bonotto, M.A. Garuti, M. Pavon, F. Rossi.

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