Image processing using nonlinear partial differential equations
 
 
Description:  When assigned with the task of image reconstruction, the first challenge one faces is the derivation of a truthful model for both the information we want to extract and the data. The natural question arises: how can we make our model adaptive to the given data? Diffusion processes are commonly used in image processing in order to remove noise. The main idea is that if one pixel is affected by noise, than the noise should be diffused among the neighboring pixels in order to smooth the region. In this way, proper diffusion partial differential equations (PDE) have been considered to achieve this end. The choice of the diffusion parameter plays a very important role for the purpose of denoising. Roughly speaking, one wants to allow diffusion on homogeneous areas affected only by noise and to forbid diffusion on edges to preserve features of the original denoised image. Consequently, the efficient models exhibit solution-dependent adaptivities in form of nonlinearities or non-smooth terms in the PDE. After a critical discussion of models based on nonlinear diffusion, we will turn towards the second modelling strategybased on nonlinear complex diffusion, which is suggested taking into account its advantages with regard to edge preservation, speckle filtering capabilities and potential to recover the original (uncorrupted) signal.
The models will be compared by means of illustrative practical examples. Some applications of the complex diffusion filter, namely for despeckling optical coherence tomograms from the human retina, will be highlighted.
Date:  2016-10-14
Start Time:   15:40
Speaker:  Sílvia Barbeiro (CMUC, Univ. Coimbra)
Institution:  CMUC
Place:  Room 2.5
Organization:  UC|UP Joint PhD Program in Mathematics
See more:   <Main>   <UC|UP MATH PhD Program>  
 
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