RESEARCH PUBLICATIONS

  1. Iterative filtering decomposition based on local spectral evolution kernel. To appear in J. Scientific Computing (with Guowei Wei and Siyang Yang)

  2. Source extraction in audio via background learning. To appear in Inverse Problem and Imaging (with Zhengfang Zhou.)

    (Listen to these sample examples, which are real recordings, not artifiically mixed: Ex1 Mixture, Ex1 Source Extracted, Ex2. Mixture, Ex2. Source Extracted, Ex3. Mixture, Ex3. Source Extracted.)

  3. Sparse PCA by iterative elimination algorithm. To appear in Advances in Computational Math. (with Qiang Wu).

  4. Coarse quantization for random interleaved sampling of bandlimited signals. To appear in Mathematical Modelling and Numerical Analysis. (with A. Powell, J. Tanner and O. Yilmaz)

  5. Reconstruction from Irregular Fourier Samples and Gaussian Spectral Mollifiers. To appear in Far East J. of Mathematics (with L. Wang)

  6. Constructing tight fusion frames, Applied and Comp. Harmonic Analysis 30 (2011), 175–187. (with P. Casazza, M. Fickus, D. Mixon and Z. Zhou)

  7. Modeling and simulation of the horizontal component of the magnetic field by fractional stochastic differential equation in conjunction with empirical mode decomposition. Journal of Geophysical Research VOL. 115 (2010), A10219 (with Zu-Guo Yu, Vo Anh and Dong Mao).

  8. Lipschitz equivlance of Cantor sets and algebraic properties of contraction ratios, Transactions of AMS, to appear. (with Hui Rao and Huojun Ruan)

  9. The golden ratio encoder, IEEE Info. Theory, to appear. (with Ingrid Daubechies, Sinan Gunturk and Ozgur Yilmaz)

  10. Classification of refinable splines in Rd, Constructive Approximation, to appear. (with Xinrong Dai)

  11. On the distribution of uniform quantization errors, Applied and Computational Harmonic Analysis 27 (2009), no. 3, 334--341 (with Sergiy Borodachov)

  12. Convergence of a convolution-filtering-based algorithm for empirical mode decomposition, Advances in Adaptive Data Analysis 1 No. 4 (2009), 561--571. (with Chao Huang and Lihua Yang)

  13. On the structures of generating iterated function systems of cantor sets, Adv. in Math. 222 (2009), 1964-1981. (with Dejun Feng)

  14. Iterative filtering as an alternative for empirical mode decomposition, Advances in Adaptive Data Analysis 1 No. 4 (2009), 543--560. (with Luan Lin and Haomin Zhou)

  15. The β-α encoder for robust A/D conversion, Acta Appl. Math. 107, Issue 1 (2009), 313--323. (with D. Jimenez)

  16. Multifractal analysis and authentication of Jackson Pollock paintings, SPIE Proceeding on Computer Image Analysis in the Study of Art Vol 6810, 68100F (2008). (with Jim Coddington, John Elton and Dan Rockmore)

  17. On refinable sets, Methods in Analysis and Applications 14, No. 2 (2007), 165--178. (with Xinrong. Dai)

  18. Sigma-delta quantization and the travelling salesman problem, Advances in Computational Math. 28 (2008), no. 2, 101--118.

  19. Structure of refinable splines, Appl. and Computatioanl Harm. Anal. 22 (2007), no. 3, 374--381. (with Xinrong Dai and Dejun Feng)

  20. The white noise hypothesis for uniform quantization errors, SIAM J. Math Analysis 38 (2007), no. 6, 2042--2056. (with D. Jimenez and L. Wang)

  21. Refinable functions with non-integer dilations, J. Funct. Anal. 250 (2007), no. 1, 1--20. (with Xinrong Dai and Dejun Feng)

  22. Simultaneous Translational and Multiplicative Tiling and Wavelet Sets in R2, Ind. J. Math. 55 (2006), no. 6, 1935--1949. (with E. Ionascu)

  23. Total Variation Wavelet Based Medical Image Denoising, Int. J. Biomedical Imaging Vol 2006 (2006), 1--6. (with Haomin Zhou)

  24. Classification of refinable splines, Constr. Approx. 24 (2006), no. 2, 187--200. (with Xinrong Dai and Dejun Feng).

  25. Some properties of spectral measures, Appl. and Computaional Harm. Anal. 20 (2006), no. 1, 149--157. (with Izabella Laba)

  26. A class of self-affine measures, J. Fourier Anal. and Appl. 11 (2005), pp 107--124 (with Dejun Feng).

  27. Self-similar measures associated to IFS with non-uniform contraction ratios, Asian J. Math. 9 (2005), no. 2, pp 227--244. (with S-M Ngai)

  28. Generation of finite frames by Householder transformations, Advances in Comp. Math. 24 (2006), no. 1-4, 297--309. (with Dejun Feng and Long Wang).

  29. Quantum integers and cyclotomy, J. Num.Theory, 109 (2004), no.1, 120--135. (with Alex Borisov and Mel Nathanson).

  30. Bernoulli convolutions associated with certain non-pisot numbers, Adv. in Math. {187} (2004), 173--194. (with Dejun Feng)

  31. The existence of Gabor Bases, Contemporary Math. Volume 345 (2004), (special issue), 183--192. (with D. Han)

  32. Substitution Delone sets, Disc. and Comp. Geom. 29 (2003) 175--209. (with J.C. Lagarias)

  33. On sparse complete Gabor systems, Appl. and Comp. Harm. Anal. 16 (2004), 60--67.

  34. Self-affine tiling via substitution dynamical systems and Rauzy fractals, Pacific J. Math. 206, no. 2 (2002), 465--485. (with V. Sirvent)

  35. On sparse complete Gabor systems, Appl. and Comp. Harm. Anal. 16 (2004), 60--67.

  36. The uniformity of non-uniform Gabor basis, Advances in Computational Math. 18 (2003), pp 345--355. (with You-Ming Liu)

  37. On spectral Cantor measures, J. Functional Analysis 193 (2002), 409-420. (with Izabella Laba)

  38. Wavelets, tiling and spectral sets, Duke Math. J. 114, no. 1 (2002), 43--57.

  39. Disk-like self-affine tiles in R^2, J. Disc. and Comp. Geometry. 26 (2001), no. 4, 591--601. (with C. Bandt)

  40. Subdivision schemes and refinement equations with nonnegative masks, J. Approx. Th. 113 (2001), no. 2, 207--220.

  41. Lattice tiling and the Weyl-Heisenberg frames, GAFA 11 (2001), no. 4, 742--758. (with Deguang Han)

  42. Hausdorff dimension of overlapping self-similar sets, J. London Math. Soc. (2) 63 (2001), 655-672. (with S.-M. Ngai)

  43. On the number of Daubechies scaling functions and a conjecture of Chyzak et al. Experimental Mathematics , Vol 10 (2001), 87--89.

  44. On 2-reptiles in the plane, Geom. Ded., Vol 82 (2000), 325--344. (with S. Ngai, V. Sirvent, P. Veerman)

  45. Orthogonality criteria for refinable functions and function vectors, J. Funct. Anal. Appl., Vol 6, Issue 2 (2000), 173--190. (with J. Lagarias)

  46. Orthonormal bases of exponentials for the n-cube, Duke Math. J. , Vol 103, No. 1 (2000), 25--37. (with J. Lagarias, J. Reeds)

  47. Universal spectra, universal tiling sets and the spectral set conjecture, Math. Scand. 88 (2001), 246--256. (with S. Pedersen)

  48. Geometry of self-affine tiles I, Indiana J. Math. , Vol 48, No. 1 (1999), 1-23. (with R. Strichartz)

  49. Geometry of self-affine tiles II, Indiana J. Math. , Vol 48, No. 1 (1999), 24-42. (with R. Kenyon, J. Li, R. Strichartz)

  50. Haar-type multiwavelet bases and self-affine multi-tiles, Asian J. Math. Vol 3, No 2 (1999), 387-400. (with T. Flaherty)

  51. Construction of compactly supported symmetric scaling functions, Applied and Computational Harmonic Analysis , 7 (1999), 137-150. (with E. Belogay)

  52. Corrigendum and addendum to: haar bases and algebraic number theory, , J. Number Th. , Vol 76, 330-336 (1999). (with J. Lagarias)

  53. Self-affine tiles, In Advances In Wavelet , K.S. Lau ed., Springer 1998, p. 261-285.

  54. Arbitrarily smooth orthogonal nonseparable wavelets in R2,, SIAM Math. Analysis, Vol 30, No 3 (1999), pp. 678-697. (with E. Belogay)

  55. On the use of high order ambiguity functions for multicomponent polynomial phase signals, Signal Processing, 65 (1998), 283-296. (with Guotong Zhou)

  56. Exploiting lag diversity in the high order ambiguity functions for polynomial phase signals, IEEE Letters on Signal Processing, 4 (1997) 240-242. (with Guotong Zhou)

  57. Integral self-affine tiles in Rn part II: lattice tilings, J. Fourier Analysis and Appl., 3 (1997), 83-101. (with J.C. Lagarias)

  58. The spectral set conjecture and factorization of finite abelian groups, J. Functional Analysis, 145 (1997), 73-98. (with J. C. Lagarias)

  59. Tiling the line with the translates of one tile, Inven. Math., 124, fasc 2 (1996), 341-365. (with J.C. Lagarias)

  60. Radix expansions for the orthant Rn, Trans. of AMS, 348 (1996), 99-117. (with J.C. Lagarias)

  61. Two-scale dilation equations and the mean spectral radius, Random and Computational Dynamics, 4 (1996), 49-72.

  62. Haar bases and algebraic number theory, J. Number Theory, 57 (1996), 181-197. (with J.C. Lagarias)

  63. Self--affine tiles in Rn, Advances in Math., 121, No. 1 (1996), 21-49. (with J.C. Lagarias)

  64. Integral self--affine tiles in Rn I. Standard and nonstandard digit set, J. of London Math. Soc., (2) 54 (1996), 161-179. (with J.C. Lagarias)

  65. Two-scale dilation equations and the cascade algorithm, Random and Computational Dynamics, 3 (1995), 289-309.

  66. Existence and regularity of solutions to a variational problem of Mumford and Shah: a constructive approach, SIAM J. Optimization, 5 (1995), 892-913.

  67. Haar-type orthonormal wavelet bases in R2, J. Fourier Analysis and Appl., 2 (1995), 1-14. (with J. C. Lagarias)

  68. The finiteness conjecture for the generalized spectral radius of a set of matrices, Linear Algebra and its Applications, 214 (1995), 17-42. (with J.C. Lagarias)

  69. On the non-existence of limiting processes for Browning models of multi-class queeing networks, Queueing Systems Theory and Applications, 13 (1993), 41-46. (with Jim Dai)

  70. Bounded semigroups of matrices, Linear Algebra and its Applications, 166 (1992) 21-27. (with M. Berger)

  71. Multidimensional two-scale dilation equations, in Wavelets: A Tutorial in Theory and Applications, (C. K. Chui, ed.), Academic Press, New York, (1992), 295-325. (with M. Berger) [missing figures]

  72. Image segmentation by variational methods and elliptic boundary value problems, Ph.D. Thesis, Harvard University, 1989.

  73. On the order and number of zero divisors of a finite ring, Journal of University of Science and Technology of China, September 1982, 140-142. (in Chinese)


For a list of preprints please check out my preprints site.

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[Last updated on January 17, 2011]