Research Interests:

My primary objective is to develop new theories (and their corresponding algorithms) for data approximation: Given a set of data (possibly contaminated), construct a function/surface which is close in some sense to the original (unknown) function/image/surface. Specifically, my research interests are as follows: Subdivision Scheme, Wavelet, Scattered Data Approximation by RBF (Radial Basis functions), Image Processing and Numerical PDE.

Publication List:

  • (with Y. Ha, C. Kim and H. Yang), Sixth-Order Weighted Essentially Non-Oscillatory Schemes Based on Exponential Polynomials, SIAM J. on Sci. Comput., (2016) **-**

  • (with H. Yang), A short note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces, Journal of Computational Physics, Vol. 320, 33-39, Sep. 2016.

  • (with C. Conti and L. Romani) Approximation order and approximate sum rules in subdivision, Journal of Approximation Theory, 207, 380-401, July 2016.

  • (with R. Lucia and P. Novara) Improving smoothness and accuracy of Modified Butterfly subdivision scheme, Appl. Math. Comp., 272. 64-79, 2016.

  • (with Y. Ha and C. Kim ), Modified Non-linearWeights for Fifth-Order Weighted Essentially Non-oscillatory Schemes, Journal of Sci. Comput., 67, 299-323, 2016.

  • (with Y. Lee) Image zooming method using edge-directed moving least squares interpolation based on exponential polynomials, Appl. Math. Comp., 269. 569-583, 2015.

  • (with H. Nam, et. al) Motion correction of magnetic resonance imaging data by using adaptive moving least squares method, Magnetic Resonance Imaging, 33. 659-670, 2015.

  • (with Y. Lee, C. Micchelli) A study on multivariate interpolation by increasingly flat kernel functions, J. of Math. Anal and its Appl., 427, 74-87, 2015.

  • (with H. Kim et al.) Superresolution of 3-D computational integral imaging based on moving least square method, Optics Express, 22, 28606-28622, 2014.

  • (with N. Dyn, D. Levin), Some Tools for Analyzing Non-Uniform Subdivision Schemes, Constructive Approximation, 40 (2), 173-188, 2014.

  • (with S. Lee, Y. Lee), A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization, Journal of Mathematical Imaging and Vision, 48, 566-582, 2014.

  • (with Y. Lee, C. Micchelli), Convergence of flat multivariate interpolation by translation kernels with finite smoothness Constructive Approximation, 40 (1), 37-60, 2014.

  • (with S. Jang, et al), Data-adapted moving least squares method for 3-D image interpolaiton. Minimizing Regularization, Phys. in Med. and Biol., 58, 8401-8418, 2013.

  • (with Y. Ha, Y. Lee), Modified Essentially Non-Oscillatory schemes based on exponential polynomial interpolation for hyperbolic conservation law, SIAM J. Numer. Anal., 52 (2), 864-893 , 2013

  • (B. Jung, Y. Lee) A family of subdivisionscheme reproducing exponential polynomial, J. of Math. Anal. and Appl., 402 (1), 207-219, 2013

  • (with B. Jung, et al.), Exponential polynomial reproduction property of non-stationary subdivision schemes and normalized exponential B-splines, Advances in Comp. Math., 38 (3), 647-666, 2013

  • (with Y. Ha, C. Kim, Y. Lee), An improved weighted essentially non-oscillatory scheme with a new smoothness indicator, J. of Comp. Physics, 232, 68-86, 2013.

  • (with Y. Ha et al.) Mapped WENO schemes based on a new smoothness indicator for Hamilton-Jacobi Equations, J. of Math. Anal. and Appl. vol. 394, 670-682, 2012.

  • (with K. Kwon D. Lee) Band-Limited Scaling Functions with Oversampling Property, IEICE Trans. Fund. of Ele. Comm. and Comp. E95A, 661-665, (2012)

  • (with Y. Lee, M. Lee), Sobolev-type Lp-Approximation Orders of Radial Basis Function Interpolation to Functions in Fractional Sobolev Spaces, IMA Journal of Numerical Analysis, 32, 279-293, 2012.

  • (with Y. Lee), Analysis of Compactly Supported Non-stationary biorthogonal Wavelwet Systems based on Exponential B-splines, Abstract Applied Analysis, vol 2011, 1085-3375, 2011.

  • (with S. Hasik, M. Lee, Y. Lee), Some issues on interpolation matrices of locally scaled radial basis functions, Applied Mathematics and Computation, 217, 5011-5014 (2011).

  • (with Y. Lee), Non-liear Image Zooming Upsampling Method based on Radial Basis Function Interplation, IEEE Transactions on Image Processing, Vol 19 Issue 10, 2682 - 2692 (2010)

  • (with H. Kim, R. Kim, Y. Lee), Quasi-Interpolatory Refinable Functions and Construction of Biorthogonal Wavelet Systems, Adv. in Comp. Math , 33, no. 3, 255-283, (2010).

  • (with Y. Lee), Non-stationary Subdivision Schemes for Surface Interpolation based on Exponential Polynomials, Applied Numerical Mathematics , vol. 60, 130-141 (2010).

  • (with Y. Lee), Analysis of Stationary Subdivision Schemes for Curve Designs based on Radial Basis Function Interpolation, Applied Mathematics and Computation, vol. 215, 3851-3859 (2010).

  • (with R. Archibald, A. Gelb), Determining the Locations and Discontinuities in the Derivatives of Functions, Applied Numerical Mathematics , Vol 58, 577-592 (2008).

  • (Y. Lee, G. Yoon) Convergence Property of Increasingly Flat Radial Basis function Interpolation to Polynomial Interpolation, PostScript-file, SIAM J. Mathematical Analysis, Vol 39 537-553, (2007).

  • (N. Dyn, D. Levin) Analysis of Univariate Non-stationary Subdivision Schemes with Application to Gaussian-Based Interpolatory Schemes, SIAM J. Mathematical Analysis, Vol 39, 470-488 (2007).

  • (Changho Kim, Sang Dong Kim) A collocation least-squares approximation for second-order elliptic partial differential equations Applied . Comp. Math. , to appear, (2007).
  • (with Choi, Y.-J. et. al), A New Class of Non-stationary Interpolatory Subdivision Schemes based on Exponential Polynomials, SpringerLink, Geometric Modeling and Processing - GMP 2006: Lecture Notes in Computer Science Vol 4077, pp.563-570, 2006.
  • (B. Lee, Y. Lee), Stationary Binary Subdivision Schemes Using Radial Basis Function Interpolation, Advances in Comp. Math. Vol 25. 57-72 (2006).
  • (with S. Choi et al.) Stationary Subdivision Schemes Reproducing Polynomials, Computer Aided Geometric Design , Vol 23, 351-360 (2006).
  • Changho Kim, Sangdong Kim, Yong Hun Lee, Jungho Yoon, Convergence analysis for a second-order elliptic Equation by a collocation method using scattered points, Journal of Comp. Appl. Math. , Vol 186 (2006) no. 1, 450-465,
  • (with R. Archibald, A. Gelb) Polynomial Fitting for Edge Detection in irregularly Sampled Signals and Images, PDF-file SIAM Numer. Analysis , Vol. 43, 259-279, (2005).
  • Improved Accuracy of $L_p$-Approximation to Derivatives by Radial Basis Function Interpolation Appl. Math. Comp. 161 (2005), no. 1, 109--119.
  • On the stationary $L\sb p$-approximation power to derivatives by radial basis function interpolation. Appl. Math. Comp. 150 (2004), no. 3, 875--887.
  • $L_p$ Error Estimates for `Shifted' Surface Spline Interpolation on Sobolev Space, Mathematics of Computation, 72 (2003), 243, 1349-1367.
  • A Nonstationary Approximation Scheme on Scattered Centers in $R^d$ by Radial Basis functions, Special Issue on "Wavelets and Approximation Theory", Journal of Comp. Appl. Math. , Vol 155 (2003) no. 1, 163-175.
  • Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space, SIAM J. Math Anal., Vol. 33, No 4, 946-958, (2001).
  • Approximation in $L_p(R^d)$ from a space spanned by the scattered shifts of a radial basis function, Constructive Approximation 17 (2001), no. 2, 227-247.
  • Computational Aspects of Approximation to Scattered Data by Using `Shifted' Thin-Plate Spline, Advances in Comp. Math. 14 (2001), no. 4, 329-359.
  • Jungho Yoon, Interpolation by Radial Basis Functions on Sobolev Space, Journal of Approx. Theory 112 (2001), no. 1, 1-15.
  • Approximation by Conditionally Positive Definite Functions With Finitely Many Centers, Trends in Approximation Theory, K. Kopotun, T. Lyche, and M. Neamtu (eds.), Vanderbilt University Press, Nashville, (2001), 437-446.

  • Jungho Yoon, Approximation to Scattered Data, PostScript-file, PDF-file, Ph.D. Thesis, 1998, University of Wisconsin-Madison, USA.