Modeling the neuro-metabolism-vascular coupling ​   ​​​​​​​

​This project focuses on the control of solar collectors. Per its distributed nature, the control of the solar collector is challenging. We aim at developing different control strategy and compare their performance. 

We are interested in extending some mathematical methods, including observer-based and modulating functions techniques, generally used for ODEs, to study and solve some inverse problems for  dynamical systems,  PDEs  (such as the wave equation and the Cauchy problem for the Laplace equation) and fractional PDEs.

We are interested in the a semi-classical signal analysis method, which considers the signal as a potential of the Schrodinger operator and uses  the discrete spectrum of this operator to analyze the signal.  We try to understand the mathematical  properties of this method  and study its extension to image analysis. We also work on the application of this method for signal/image denosing with  a  focus on biomedical signals/images. 

We focus in this project on developing appropriate models and efficient strategy for the optimal control of a solar-driven membrane distillation plant.  

​The main of the chall​​enge of Magnetic Resonance Imaging (MRI) is dealing with high levels of noise which may corrupt the image especially since the noise is almost correlated with the image details. In this regard, we propose a new MRI enhancement method to overcome this limitation. The proposed MRI enhancement method relies on square sub-images enhancement depending on the noise level in each position using spatial adaptation of the Semi-Classical Signal Analysis (SCSA) method, where an enhancement parameter h is subject to a Gaussian distribution. ​

​The idea of the modulating function-based method (MFBM) is to multiply the considered differential equation by a set of modulating functions to transform the differential equation into a set of algebraic integral equations by applying integration by parts, where the unknown initial conditions are eliminated by the properties of the modulating functions. The method does not require solving the direct problem by which the computational cost is reduced. Further, approximating the derivatives of the measurements, which are usually noisy, is avoided with this method. ​​