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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...
Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a ...
Araújo, Adérito; Sousa, Ercília; Albuquerque, AntónioWe present a numerical solution for the dead zone model which describes the solute transport in a subsurface and horizontal flow constructed wetland. This model is a system of two mass balance equations for two conceptual areas: the main channel and the storage zone. We use finite difference schemes to determine the numerical solution of the system and we study its convergence by presenting properties related t...
Application of the advection-dispersion equation to characterize the hydrodynam...
Albuquerque, António; Araújo, Adérito; Sousa, ErcíliaThe hydraulic characteristics of a laboratory submerged packed bed, filled with a volcanic stone, pozzuolana, have been experimentally investigated through tracer tests. Sets of essays at flow rates from 1 to 2.5 l/h in clean conditions were performed. The results showed a considerable amount of dispersion through the filter as the hydraulic loading was changed, indicating a multiplicity of hydrodynamic states,...
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