Alvarez Navarro, Michael A.

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    Computational optics techniques using neural networks to extract quantitative information from biomedical signals
    (2024-07-10) Alvarez Navarro, Michael A.; Sierra, Heidy; College of Engineering; Arzuaga, Emmanuel; Hunt, Shawn D.; Medina, Rafael; Department of Electrical and Computer Engineering; Harmsen, Eric W.
    Computational optics is an advanced field that combines various methods and technologies to design, simulate, and enhance optical systems and processes. Despite their potential, these advances encounter significant limitations in terms of being widely adopted as the standard technology beyond being used by specialized centers and applications. One major challenge is the complexity and computational cost required to create reliable technology that allows the capture of information at the temporal and spatial resolution required in biomedical applications. This research contributes to addressing this challenge to improve the capabilities of computational optical sensors by developing methodologies that integrate light-tissue interactions and artificial intelligence (AI) models with advanced data acquisition techniques. The main contributions include using deep learning (DL) models to simulate the resulting electric field from the propagation of a light source in heterogeneous objects. The results are compared to the direct solution of the wave equation using the Finite-Difference Time-Domain method. Additionally, a framework to generate photoplethysmography (PPG) signals with Monte Carlo simulations was created for the design and training of a hybrid DL model for estimating hemoglobin levels from PPG signals. A similar approach was explored for generating quantitative phase images from intensity microscopy images. Overall, this research resulted in new methodologies that integrate traditional computational techniques with modern AI models that promise to expand the use of current technologies in health and biomedical applications.
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    Método LDG para la ecuación de difusión fraccionaria en 1D
    (2018-01-24) Alvarez Navarro, Michael A.; Castillo, Paul E.; College of Arts and Sciences - Sciences; Steinberg, Lev; Rozga, Krzysztof; Department of Mathematics; Araya, Guillermo
    This thesis describes an implementation of the Local Discontinuous Galerkin LDG method applied to a problem of fractional diffusion. The discrete formulation of the associated system is discussed, with emphasis on the construction of the fractional operator. A strategy is provided to add a term of stability in the primary variable, unlike other implementations that stabilize the method by penalizing in the auxiliary variable, in such a way that convergence order is obtained O (h p+1 ) for polynomials of degree p. Additionally, numerical experiments are shown in which little regularity is needed, on the part of the exact solution, to obtain optimum convergence.