Zhihua Zhang

Postdoc

Department of Mathematics
University of California at Davis
Davis, California, USA 95616

Office: MSB 2151
E-mail: zhangzh AT math.ucdavis.edu

Education

PhD in Applied Mathematics, University of California at Davis, USA, September 2007
MS in Computational Mathematics, Chinese Academy of Sciences, China, June 2004
BS in Mathematics, Shandong University, China, June 2001

Teaching

MATH 16B Short Calculus, Summer 2008
MATH 185A, Complex Variables, Winter 2008

Research Interests

Harmonic Analysis, Scientific Computing, PDEs
Image Analysis, Astronomical Signal Processing

Publications

  1. Z.Zhang and N.Saito, Ring-like structures of frequency domains of wavelets, Appl. Comput. Harmon. Anal., accepted, 2009.[PDF]
  2. Z.Zhang, A New Method of Constructions of Non-tensor Product Wavelets, Acta Appl.Math., published online, 2009 [PDF]
  3. N. Saito and Z. Zhang, On an Efficient Sparse Representation of Objects of General Shape via continuous extension and wavelet approximation, Int. J. Wavelets, Multiresolut. Inf. Process., accepted, 2009. [PDF]
  4. Z. Zhang, Convergence of Periodic Wavelet Frame Series and Gibbs Phenomenon. Rocky Mountain J. Math., 39:4, 2009 [PDF]
  5. Z. Zhang, Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets, Acta Math. Sin., accepted, 2009. [PDF]
  6. Z. Zhang and N. Saito, Constructions of Periodic Wavelet Frames Using Extension Principles, Appl. Comput. Harmon. Anal., 27:1, 2009. [PDF]
  7. Z. Zhang, Supports of Fourier Transforms of Scaling Functions, Appl. Comput. Harmon. Anal., 22:2, 2007. [PDF]
    Remark. ScienceDirect indicated that this paper ranked first in the top 25 hottest articles of Appl. Comput. Harmon. Anal. in Jan.-Mar. 2007
  8. Z. Zhang, Measures, Densities and Diameters of Frequency Bands of Scaling Functions and Wavelets. J. Approx. Theory, 148:2, 2007.[PDF]
  9. Z. Zhang, Continuity of Fourier Transforms of Band-limited Wavelets, J. Comput. Anal. Appl., 9:4, 2007. [PDF]
  10. Z. Zhang, A Pair of Quasi-biorthogonal Frame Wavelets, Acta. Math. Sin. (A), 51:1, 2008. [PDF]
  11. Z. Zhang and N. Saito, An Approximation Formula in Hilbert Space, in Recent Advances in Computational Sciences, P. Jorgensen, X. Shen, C-W Shu, and N. Yan, ed., World Scientific, 218-228, Aug. 2008. [PDF]
  12. Z. Zhang and N. Saito, High Dimensional Data Compression via PHLCT, in Wavelets XII, D. Van De Ville, V. K. Goyal, and M. Papadakis, eds., Proc. SPIE 6701, 2007. [PDF]
  13. Z. Zhang, Convergence of Weyl-Heisenberg Frame Series, Indian J. Pure Appl. Math, 39:2, 2008. [PDF]
  14. Z. Zhang, Pointwise Convergence and Uniform Convergence of Wavelet Frame Series, Acta. Math. Sin., (Engl. Ser.), 22:3, 2006. [PDF]
  15. Z. Zhang, A Characterization of Generalized Frame MRAs Deriving Orthonormal Wavelets, Acta. Math. Sin. (Engl. Ser.), 22:4, 2006. [PDF]
  16. Z. Zhang, Periodic Wavelet Frames, Adv. Comput. Math. 22:2, 2005.[PDF]
  17. Z. Zhang, L. Mu, and P. Zhang, Construction of p-band Frame Wavelet Consisting of the Fewest Functions, Indian J. Pure Appl. Math. 36:5, 2005. [PDF]
  18. Z. Zhang, Characterization of Compact Support of Fourier Transform for Orthonormal Wavelet, Acta. Math. Sin. (Engl. Ser.) 21:4, 2005. [PDF]
  19. L. Mu, Z. Zhang, and P. Zhang, On the Higher-dimensional Wavelet Frames, Appl. Comput. Harmon. Anal, 16:1, 2004. [PDF]
    Remark. ScienceDirect indicated that this paper ranked second in the top 26 hottest articles of Appl. Comput. Harmon. Anal. in Jan.-Aug. 2004
  20. Z. Zhang, L. Mu, and P. Zhang, An Improvement of Papadakis’ Theorem, Progr. Natur. Sci., 14:5, 2004. [PDF]
  21. Z. Zhang, Generalized Dyadic Wavelet and Signal Processing, Math. Econ, 21:2, 2004.
  22. L. Mu, Z. Zhang, and P. Zhang, An Extension of Papadakis' Theorem, Mu'tah J., 19:3, 2004. [PDF]
  23. Z. Zhang, Wavelet Analysis in Sobolev Space of Periodic Distributions, Approx. Theory Appl., 18:3, 2002. [PDF]
  24. Z. Zhang, On a New Kind of Inversion Formula for the Wavelet Transform, J. Math. Study, 35:3, 2002. [PDF]
  25. Z. Zhang, Parseval-type Equality of Dyadic Wavelet and its Extension, Guangxi Sci., 9:1, 2002.
  26. Z. Zhang, A Reconstruction Formula Based on a New Kind of Half-discrete Wavelet Transform, Math. Econ, 18:1, 2001. [PDF]
  27. Z. Zhang, Generalization of Meyer Wavelet, Guangxi Sci., 7:4, 2000. [PDF]
  28. Z. Zhang, Generalized Periodic Wavelet and Half-discrete Wavelet Transform, Distinguished B.S.Thesis Award of Shandong Province, 2002.

Submitted papers

  1. Z. Zhang, Galaxylets: A new tool in Astronomical Image Processing, to be submitted, 2009
  2. Z. Zhang, The minimal Fourier supports of wavelets, submitted, 2009
  3. Z. Zhang and N. Saito, Harmonic Wavelet Transform and Image Approximation, submitted, 2008. [PDF]
  4. N. Saito and Z. Zhang, Decomposition and approximation of multivariate functions, submitted, 2009
  5. N. Saito and Z. Zhang, Wavelet Frame Packets, submitted, 2009

Papers in preparation

  1. N. Saito, A. Tyson and Z. Zhang, Shapelet-based Deblending Algorithms.
  2. N. Saito, A. Tyson and Z. Zhang, Modified Shapelets.
  3. N. Saito, A. Tyson and Z. Zhang, A New Deblending Algorithm: Repeated Symmetry Method.
  4. N. Saito and Z. Zhang, Framelet-Based Data Classification Algorithm.
  5. N. Saito and Z. Zhang, The Method of Particular Solution Involving Tangential Derivatives.
  6. N. Saito and Z. Zhang, Synthesis of Dirichlet-Laplacian Eigenfunctions by the Eigenfunctions of Integral Operators.
  7. Z. Zhang and N. Saito, Smooth Extension and Nonlinear Trigonometric Approximation on General Domains.

Presentations

  1. "Periodic Wavelet Frames" (talk), 20 Years of Wavelets, Chicago, 2009.
  2. “Wavelets, Framelets, and Shapelets”, Applied mathematics seminar, UC Davis, 2008
  3. “The Method of Particular Solutions Involving Tangential Derivatives” (poster), IPAM workshop Laplacian Eigenvalues and Eigenfunctions: Theory, Computation, Application, Los Angeles, 2009
  4. “High Dimensional Data Compression via PHLCT” (poster), SPIE Wavelet XII, San Diego, 2007
  5. “The Construction of Wavelet Frames” (poster), The International Workshop on Computational Science and its Education, 2005.
  6. “Generalized MRA with r Scaling Functions” (talk), The Second International Symposium on Computing Science, 2002.

Awards and Honors

  1. Chinese Government Award for Outstanding Students Abroad, 2007 pic
  2. Alice Leung Scholarship, Dept. of Math., Univ. of California at Davis, 2005  pic
  3. Gorge and Dorothy Zolk Fellowship, Univ. of California at Davis, 2006
  4. Block Grant Fellowship, Univ. of California at Davis, 2005
  5. Wakeham Fellowship, Univ. of California at Davis, 2004
  6. Presidential Excellence Award of Chinese Academy of Sciences, 2003
  7. Presidential Excellence Fellowship of Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 2003
  8. Liu Yongling Prize of Chinese Academy of Sciences, 2002
  9. Distinguished B.S.Thesis of Shandong Province, 2002
  10. Distinguished Undergraduate of Shandong Province, 2001
  11. Prize of Chinese Academy of Sciences, 2000