Ewha Womans University Mathematics

 
홈

Research Areas

Prof. Jungho Yoon

Applied Analysis and Data Approximation Lab

Faculty Introduction
Prof. Jungho Yoon
Prof. Jungho Yoon
Research Area
  • Multivariate scattered data approximation
  • Image Processing
  • Numerical PDE
  • Computer Aided Geometric Design (CAGD)
Lab Introduction

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:

Nonlinear data approximation

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.

Multi-dimensional large-scale data approximation

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.

CAGD (computer aided geometric design)

We study subdivision and spline theories and algorithms for geometric modeling for computer graphics, animation, and multi-resolution analysis.

Mathematical Image processing

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.

Major research projects and Research achievements
딥러닝 알고리즘에 의한 color image demosaic기법
Hermite 서브디비젼 알고리즘

딥러닝 알고리즘에 의한 color image demosaic기법 (왼쪽), Hermite 서브디비젼 알고리즘 (오른쪽)

Non-linear Data Approximation
  • Scattered data approximation by radial basis function and nonlinear moving least squares method​
  • Approximation of multivariate functions on Sparse grid
  • Subdivision for Computer Aided Geometric Design
  • Mathematical Image Processing: image interpolation, super-resolution, denoising, deblurring
  • Construction of nonlinear scheme for hyperbolic conservation laws.​
Selected research papers
Mathscinet
Mathscinet
  • B. Jeong, S. Kersey, J. Yoon, Approximation of multivariate functions on sparse grids, by kernel-based quasi-interpolation, SIAM J. Sci. Comput. 43 (2021), A953-41A05
  • Y. Ha, C. Kim , H. Yang, and J. Yoon, Improving accuracy of the fifth-order WENO scheme by using the exponential approximation space , SIAM J. Numer. Anal. 59 (2021), 143-172
  • B. Jeong and J. Yoon, Analysis of non-stationary Hermite subdivision schemes reproducing exponential polynomials, J. Comput. Appl. Math. 349 (2019), 452-469.
  • H. Yang and J. Yoon, A short note on the error estimates of Yuan- Shu discontinuous Galerkin method based on non-polynomial approximation spaces, J. of Comp. Phys. , 320 (2016), 33-39.
  • Y. Ha, C. Kim, H. Yang and J. Yoon, Sixth-order weighted essentially non-oscillatory schemes based on exponential polynomials, SIAM J. Sci. Comput. , 38 (2016), 1987-2017.
Graduate Students
  • Seo-yeon Eo Masters student
    Research Area: Data Approximation
  • Jinyoung Kim Masters student
    Research Area: Data Approximation