Plenary Lecture

Novel PDE-based Image Denoising and Restoration Models

Professor Tudor Barbu
Institute of Computer Science
Romanian Academy

Abstract: Over the last few decades, the mathematical models have been increasingly used in some traditionally engineering domains like signal and image processing, analysis, and computer vision. Numerous image processing and analysis methods making use of partial differential equation based algorithms and variational calculus have been developed recently. The PDE-based techniques have been widely used in these fields in the past years because of their modeling flexibility and some advantages of their numerical implementation. Image denoising and restoration represent an important image processing domain that has been successfully approached using the PDE-based models. The nonlinear PDE-based approaches are able to smooth the images while preserving their edges, also avoiding the localization problems of linear filtering. Since P. Perona and J. Malik introduced their influential anisotropic diffusion scheme in 1987, many nonlinear diffusion equation based image noise removal techniques have been proposed. In image processing it is very common to obtain the nonlinear PDEs from some variational problems. The variational models have important advantages in both theory and computation, compared with other techniques. An influential variational denoising and restoration model was developed by Rudin, Osher and Fetami in 1992. Their technique, named Total Variation (TV) denoising, is based on the minimization of the TV norm. We have proposed numerous PDE-based image denoising and restoration techniques in recent years. Thus, we have developed both diffusion-based filtering approaches and variational PDE denoising solutions. Both linear and nonlinear diffusion equation based techniques have been modeled. A novel linear anisotropic diffusion approach based on a modified Gaussian filter kernel will be described. Also, we present some robust nonlinear anisotropic diffusion based techniques, derived from and improving the Perona-Malik denoising scheme. Various diffusivity functions are used by these smoothing algorithms. Several novel variational PDE-based denoising and restoration approaches, based on some properly chosen minimization problems, will be also described.

Brief Biography of the Speaker: Dr. Tudor Barbu is currently Senior Researcher I at the Institute of Computer Science of the Romanian Academy, in Iasi, Romania. He is the coordinator of the Image and Video Processing and Analysis research collective of  the institute and also member of the leading Scientific Council of this institute. Mr. Barbu has a PhD degree in Computer Science, awarded by the Faculty of Automatic Control and Computers of the University “Politehnica” of Bucharest. He published 2 books and 4 book chapters as main author. Also, dr. Tudor Barbu published more than 70 articles in prestigious international journals and volumes of international scientific events (conferences, symposiums and workshops). His scientific activity also includes more than 35 research reports, elaborated with the institute research team coordinated by him or related to various research projects. His scientific publications have got over 120 citations, according to Google-Academic. In recent years he also coordinated various research directions in 6 projects based on contracts/grants. Dr. Tudor Barbu received also several awards for his research results, the most important being the Romanian Academy Prize “Gheorghe Cartianu”, in the Information Science and Technology domain, awarded on December 18, 2008. He is member of several conference scientific committees and also member of scientific and technical committee and editorial review boards of some journals. He is the Editor in Chief of a book. His main scientific areas of interest are: digital media (audio, video and image) signal processing and analysis, pattern recognition, computer vision, multimedia information storage, indexing and retrieval, biometric authentication using voice, face and digital fingerprint recognition, and partial differential equations.