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Stability of finite difference schemes for complex diffusion processes
Araújo, Adérito; Barbeiro, Sílvia; Serranho, PedroIn this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising.
Ocular fundus Imaging: from structure to function
Serranho, Pedro; Maduro, Cristina; Santos, Torcato; Bernardes, Rui; Vaz, José Cunha; Araújo, Adérito; Barbeiro, SílviaImaging the ocular fundus, namely the retina, to detect and/or monitor changes over time from the healthy condition is of fundamental importance to assess onset and disease progression and is a valuable tool to understand the basic mechanisms of ocular diseases. Current trends point to the need for less or non-invasive approaches, to the need for detailed (higher spatial and temporal resolution) imaging systems...
Stability of finite difference schemes for complex diffusion processes
Araújo, Adérito; Barbeiro, Sílvia; Serranho, PedroComplex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of complex diffusion finite differ...
Improved adaptive complex diffusion despeckling filter
Bernardes, Rui; Maduro, Cristina; Serranho, Pedro; Araújo, Adérito; Barbeiro, Sílvia; Cunha-Vaz, JoséDespeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis or as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders. In this study we propose a new formulation for a well-known nonlinear complex diffusion filter. A regularization factor is now made to be depe...
A priori error estimates for the numerical solution of a coupled geomechanics a...
Barbeiro, Sílvia; Wheeler, Mary F.In this paper we consider the numerical solution of a coupled geomechanics and a stress-sensitive porous media reservoir flow model.We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with respect to the L2-norm for the pres...
Discretely Compact Embeddings of Spaces of Cell-Centered Grid Functions
Barbeiro, SílviaCompactness of embeddings in discrete counterparts of Sobolev spaces is considered. We study the embeddings in spaces of cell-centered grid functions, in one- and two-dimensional domains. No restrictions are made on the mesh-ratios of the underlying meshes. ; http://www.informaworld.com/10.1080/01630560802099092
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