In the lab. of Applied Analysis, we conduct research on data approximation theories and algorithms which are fundamental components in the area of data science. We develops linear or non-linear approximation schemes for various types of data that are generated in various fields of scientific computation. Specifically, our research interests include the following topics:
We develop non-linear theories and algorithm for multi-dimensioan (scattered) data containing various types of singular points that are arising in the areas such as image processing, fluid PDEs and computer visualizations.
In order to handle large-scale data efficiently, we study sparse-grid approximation and multi-resolution analysis by using radial basis functions and subdivision methods.
We study subdivision and spline theories and algorithms for geometric modeling for computer graphics, animation, and multi-resolution analysis.
Based on non-linear data approximation theories, we develop algorithms of image super-resolution, image denoising, and deblurring. In addition, we solve image processing problems that occur in industries such as 3D semi-conductors and medical imaging,
This research topic is being studied in connection with data science, especially deep learning algorithms of artificial intelligence.
딥러닝 알고리즘에 의한 color image demosaic기법 (왼쪽), Hermite 서브디비젼 알고리즘 (오른쪽)