Dr. Hyeona Lim
Associate Professor of Mathematics
Research interests: Numerical methods in partial differential equations, wave propagation, image processing, solid mechanics.
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My current research focuses on various types of image analysis and processing problems using partial differential equation models and non-local means filtering techniques. With my collaborators and students, I developed several mathematical models and numerical methods for image denoising and surface reconstruction that can be used to enhance/analyze images in biomaterials, medical, and earth sciences. Image denoising techniques involve efficient and robust model and algorithm construction for speckle noise removal based on non-local total variation method and Chambolle's dual approach. For surface reconstruction, a new minimum curvature based method was recently developed to overcome the drawbacks arising in conventional surface reconstruction methods. This method can be applied to image zooming, synthetic scattered data, and agricultural data acquired by light detection and ranging (LiDAR) technology.
I am also actively involved in interdisciplinary projects with engineers at MSU. We are currently developing automated edge detection methods for biomedical images, which is still in a nascent stage.
Degree: Ph.D. in Applied Mathematics, 2001, Department of Mathematics, Michigan State University