Qingtang Jiang's Publications


Recent preprints:

L. Li, C.K. Chui and Q.T. Jiang, Direct signal separation via extraction of local frequencies with adaptive time-varying parameter, 2020. arXiv2010.01866 lcj_sso_arXiv_Jan2020.pdf

L. Li, N.N. Han, Q.T. Jiang and C.K. Chui, A separation method for multicomponent nonstationary signals with crossover instantaneous frequencies, 2020. arXiv:2010.01498 CrossIF_Feb5_2020.pdf

Book:

C.K. Chui and Q.T.Jiang, Applied Mathematics--Data Compression, Spectral Methods, Fourier Analysis, Wavelets and Applications, Springer Publ., 2013.

Selected Papers (from 1997):

71 C.K. Chui, Q.T. Jiang, L. Li and J. Lu, Time-scale-chirp_rate operator for recovery of non-stationary signal components with crossover instantaneous frequency curves, Applied and Computational Harmonic Analysis, 54 (2021), 323-344. arXiv2012.14010 TSC_R_Dec26_2020.pdf

70 C.K. Chui, Q.T. Jiang, L. Li and J. Lu, Analysis of an adaptive short-time Fourier transform-based multicomponent signal separation method derived from linear chirp local approximation, Journal of Computational and Applied Mathematics, 396 (2021), 113607. Adp_STFT_analysis_fromarXiv_Oct2020.pdf

69. C.K. Chui, Q.T. Jiang, L. Li and J. Lu, Signal separation based on adaptive continuous wavelet transform-like and analysis, Applied and Computational Harmonic Analysis, 53 (2021), 151-179. Adp_CWT_arXiv_v2_Dec2020.pdf

68. H. Alkhidhr and Q.T. Jiang, Correspondence between multiwavelet shrinkage and nonlinear diffusion, Journal of Computational and Applied Mathematics, 382 (2021), 113074. multiwavelet_diffusion_May28_2020.pdf

67. J. Lu, J.P. Tian, Q.T. Jiang, X.X. Liu, Z.W. Hua, Y.R. Zou, Rician noise removal via weighted nuclear norm penalization, Applied and Computational Harmonic Analysis, 53 (2021), 180-198. RNWNN_rev1_2020.pdf

66. J. Lu, J.H. Alzahrani and Q.T. Jiang, A second-order synchrosqueezing transform with a simple form of phase transformation, Numerical Mathematics: Theory, Methods and Applications, 14 (2021), 624-649. simplephase_2ndFSST_2020.pdf

65. H.Y. Cai, Q.T. Jiang, L. Li and B.W. Suter, Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform, Analysis and Applications, 19 (2021), 71-105. AFSST_Analysis_2018.pdf

64. J. Lu, Q.T. Jiang and L. Li, Analysis of adaptive synchrosqueezing transform with a time-varying parameter, Advance in Computational Mathematics, 46 (2020), Article number: 72. AWSST_Analysis_arXiv_Aug22_2020.pdf.pdf

63. L. Li, H.Y. Cai and Q.T. Jiang, Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation, Applied and Computational Harmonic Analysis, 49 (2020), 1075-1106. Adaptive_WSST_Apr16_2018.pdf

MATLAB Codes

62. L. Li, H.Y. Cai, H.X. Han, Q.T. Jiang, and H.B. Ji, Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation, Signal Processing, 166 (2020), 107231. Adaptive_FSST_May2_2018.pdf.

MATLAB Codes

61. H.Y. Cai, B. Goggin and Q.T. Jiang, A two-sample test based on classification, Statistical Analysis and Data Mining: The American Statistical Association Data Science Journal, 13 (2020), 5-13. Two_sample_test_arXiv_Sep2019.pdf.

60. L. Li, H.Y. Cai, Q.T. Jiang and H.B. Ji, An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis, Mechanical Systems and Signal Proc., 121 (2019), 791-809. Empirical_signal_separation.pdf.

59. J. Lu, J.P. Tian, L.X. Shen, Q.T. Jiang, X.Y. Zeng and Y.R. Zou, Rician noise removal via a learned dictionary, Mathematical Problems in Engineering, 6 (2019), 1-13. RNR_LD_reprint.pdf.

58. H.Y. Cai and Q.T. Jiang, A tree-based multiscale regression method, Frontiers Appl. Math. Stat - Mathematics of Computation and Data Science, 4 (2018), Article 63. Tree-based_Multiscale_Regres_Dec_2018_reprint.pdf.

57. B. Han, Q.T.Jiang, Z.W. Shen and X.S. Zhuang, Canonical quincunx tight framelets with symmetry and high vanishing moments, Mathematics of Computation, 87 (2018), 347-379. Quincunx_Aug16.pdf.

56. Q.T.Jiang and B.W. Suter, Instantaneous frequency estimation based on synchrosqueezing transform, Signal Processing, 138 (2017), 167-181. IFE_SST_July2016.pdf.

55. B. Dong, Q.T.Jiang and Z.W. Shen, Image restoration: wavelet frame shrinkage, nonlinear evolution PDEs, and beyond, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 15 (2017), 606-660. diffu_frame_2d_reprint.pdf.

54. Q.T.Jiang and D.K. Pounds, Highly symmetric square-root(3)-refinement bi-frames for surface multiresolution processing, Appl. Numer. Math., 118 (2017), 1-18. frame_sqrt3_6sym_Nov12.pdf.

53. B. Dong, Q.T.Jiang, C.Q. Liu and Z.W. Shen, Multiscale representation of surfaces by tight wavelet frames with applications to denoising, Appl. Comput. Harmonic Anal., 41 (2016), 561-589. surface_represen_denoising.pdf.

52. Q.T. Jiang and J.J. Smith, Tangents and curvatures of matrix-valued subdivision curves and their applications to curve design, Applicable Analysis 95 (2016), 1671-1699. curvature_matrix_subd.pdf.

51. Q.T.Jiang and Z.W. Shen, Tight wavelet frames in low dimensions with canonical filters, J. Approx. Theory, 196 (2015), 55-78. frame_canonical.pdf.

50. Q.T.Jiang and B.B. Li, Quad/triangle subdivision, nonhomogeneous refinement equation and polynomial reproduction, Mathematics and Computers in Simulation, 82 (2012), 2215-2237. quad_tri_approx.pdf.

49. Q.T.Jiang, Correspondence between frame shrinkage and high-order nonlinear diffusion, Appl. Numer. Math. 62 (2012), 51-66. diffu_frame_1d.pdf.

48. Q.T.Jiang and D.K. Pounds, Highly symmetric bi-frames for triangle surface multiresolution processing, Appl. Comput. Harmonic Anal. 31 (2011), 370-391. frame_triang_dyadic_6sym.pdf.

47. Q.T.Jiang, Biorthogonal wavelets with 4-fold axial symmetry for quadrilateral surface multiresolution processing, Adv. Comput. Math. 34 (2011), 127-165. bio_wavelet_4sym_quad.

46. Q.T.Jiang, Biorthogonal wavelets with 6-fold axial symmetry for hexagonal data and triangle surface multiresolution processing, Int'l J. Wavelets, Multiresolution Info. Proc. 9 (2011), 773-812. bio_wavelet_6sym_dyadic_sqrt3.pdf.

45. Q.T.Jiang, Wavelet bi-frames with uniform symmetry for curve multiresolution processing, J. Comput. Appl. Math. 235 (2011), 1653-1675. frame_1D_uniform_sym.pdf.

44. Q.T.Jiang, Bi-frames with 4-fold axial symmetry for quadrilateral surface multiresolution processing, J. Comput. Appl. Math. 234 (2010), 3303-3325. frame_quad_dyadic_sqrt2_4sym.pdf.

43. Q.T.Jiang, Orthogonal and biorthogonal square-root(3)-refinement wavelets for hexagonal data processing, IEEE Trans. Signal Proc. 57 (2009), 14304-4313. hex_sqrt3_wavelet_3sym.pdf. For an expanded version, click here.

42. Q.T.Jiang, B.B.Li, and W.W.Zhu, Interpolatory quad/triangle subdivision schemes for surface design, Comput. Aided Geom. Design 26 (2009), 904-922. quad_triangle_smoothness.pdf

41. C.K.Chui and Q.T.Jiang, Matrix-valued 4-point spline and 3-point non-spline interpolatory curve subdivision schemes, Comput. Aided Geom. Design 26 (2009), 797-809. curve_interpolatory.pdf

40. Q.T.Jiang, Hexagonal tight frame filter banks with idealized high-pass filters, Adv. Comput. Math. 31 (2009), 215-236. hex_framelet_idealizedHPs.pdf

39. Q.T.Jiang, Orthogonal and biorthogonal FIR hexagonal filter banks with 6-fold symmetry, IEEE Trans. Signal Proc. 52 (2008), 5861-5873. hex_sqrt7_wavelet_6sym.pdf

38. Q.T.Jiang, Compactly supported orthogonal and biorthogonal square-root(5)-refinement wavelets with 4-fold symmetry, IEEE Trans. Image Proc. 17 (2008), 2053-2062. sqrt5_wavelet_4sym.pdf

37. Q.T.Jiang, FIR filter banks for hexagonal data processing, IEEE Trans. Image Proc. 17 (2008), 1512-1521. hex_dyadic_wavelet_3sym.pdf. For an expanded version with more sets of selected parameters, click here.

36. C.K.Chui and Q.T.Jiang, From extension of Loop's approximation scheme to interpolatory subdivisions, Comput. Aided Geom. Design 25 (2008), 96-115. inter_tri_extra.pdf

35. C.K.Chui, Q.T.Jiang, and R.N. Ndao, Triangular sqrt(7) and quadrilateral sqrt(5) subdivision schemes: regular case, J. Math. Anal. Appl. 338 (2008), 1204-1223. sqrt5_7.pdf

34. C.K.Chui, T.X. He, and Q.T.Jiang, Fourier transform of BB polynomials on triangles, J. Math. Anal. Appl. 325 (2006), 294-304. FT_BB.ps, FT_BB.pdf

33. C.K.Chui and Q.T.Jiang, Refinable bivariate quartic and quintic C2-splines for quadrilateral subdivisions, J. Comp. Appl. Math. 196 (2006), 402-424. quad_subd.ps, quad_subd.pdf

32. C.K.Chui and Q.T.Jiang, Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices, Comput. Aided Geom. Design 23 (2006), 419-438. extra_vertex3.ps, extra_vertex3.pdf. For an expanded version, click here.

31. C.K.Chui and Q.T.Jiang, Matrix-valued symmetric templates for interpolatory surface subdivisions, I: Regular vertices, Appl. Comput. Honomic Anal. 19 (2005), 303-339. Interp_I.pdf, Interp_I_nofigures.pdf(no figures for the basis functions)

30. C.K.Chui and Q.T.Jiang, Refinable bivariate Quartic C2-splines for multi-level data representation and surface display, Math. of Computation 74 (2005), 1369-1390. C2quar_mc.ps, C2quar_mc.pdf

29. C.K.Chui and Q.T.Jiang, Balanced multiwavelets in $R^s$ , Math. of Computation 74 (2005), 1323-1344. balance_mc.ps, balance_mc.pdf

28. C.K.Chui and Q.T.Jiang, Surface subdivision schemes generated by refinable bivariate spline function vectors , Appl. Comput. Honomic Anal. 15 (2003), 147-162. subd1.ps, subd1.pdf

27. C.K.Chui and Q.T.Jiang, Multivariate balanced vector-valued refinable functions , in "Modern Development in Multivariate Approximation", ISNM 145, V.W. Haussmann, K. Jetter, M. Reimer, and J. St\"ockler (eds.), Birhh\"auser Verlag, Basel, 2003, 71-102. balan1.ps, balan1.pdf

26. R.Q.Jia and Q.T.Jiang, Spectral analysis of the transition operator and its applications to smoothness analysis of wavelets, SIAM J. of Matrix Anal. and Appl. 24 (2003), 1071-1109. sobsmth.ps, sobsmth.pdf

25. Q.T.Jiang, P. Oswald, and S.D.Riemenschneider, sqrt(3)-subdivision schemes: maximal sum rule orders, Constr. Approx. 19 (2003), 437-463. jor.ps, jor.pdf

24. Q.T.Jiang and P. Oswald, Triangular sqrt(3)-subdivision schemes: the regular case, J. Comp. Appl. Math. 156 (2003), 47-75. sqrt3.ps, sqrt3.pdf

23. Q.T.Jiang, Parameterizations of masks for tight affine frames with two symmetric/antisymmetric generators, Adv. Comput. Math. 18 (2003), 247-268. aicm.ps, aicm.pdf

22. B. Han and Q.T.Jiang, Multiwavelets on the interval, Appl. Comput. Harmonic Anal. 12 (2002), 100-127. inval.ps, inval.pdf

21. R.Q.Jia, Q.T.Jiang, and S.L.Lee, Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets, Numer. Math. 91 (2002), 453-473. jjl.ps, jjl.pdf

20. Q.Jia and Q.T.Jiang, Approximation power of refinable vectors of functions , in "Wavelet Analysis and Applications", Studies Adv. Math. #25, 155-178, Amer. Math. Soc., Providence, RI, 2002. app_power.ps, app_power.pdf

19. Q.T.Jiang, Symmetric paraunitary matrix extension and parametrization of symmetric orthogonal multifilter banks , SIAM J. Matrix Anal. and Appl. 23 (2001), 167-186. exten.ps, exten.pdf

18. R.Q.Jia, Q.T.Jiang, and Z.W.Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001), 415-427. jjs1.ps , jjs1.pdf

17. Q.T.Jiang, Parametrizations of symmetric orthogonal multifilter banks with different filter lengths, Linear Algebra and its Applications 311 (2000), 79-96. para2.ps, para2.pdf

16. R.Q.Jia, Q.T.Jiang, and Z.W.Shen, Distributional solutions of nonhomogeneous discrete and continuous refinement equations, SIAM J. Math. Anal. 32 (2000), 420-434. jjs2.ps, jjs2.pdf

15. S.S.Goh, Q.T.Jiang, and T. Xia, Construction of biorthogonal multiwavelets using the lifting scheme, Appl. Comput. Harmonic Anal. 9 (2000), 336-352. blift.ps , blift.pdf (no figures)

14. Q.T.Jiang, Parameterization of M-channel orthogonal multifilter banks, Adv. Comput. Math. 12 (2000), 189-211. para.ps, para.pdf

13. Q.T.Jiang, Multivariate matrix refinable functions with arbitrary matrix dilation, Trans. Amer. Math. Soc. 351 (1999), 2407-2438. arbireg.ps, arbireg.pdf

12. Q.T.Jiang and Z.W.Shen, On existence and weak stability of matrix refinable functions, Constr. Approx. 15 (1999), 337-353. exist.ps, exist.pdf

11. T.Xia and Q.T.Jiang Optimal multifilter banks: Design, related symmetric extension transform and application to image compression, IEEE Trans. Signal Proc.47 (1999), 1878-1889. compres.ps , compres.pdf

10. Q.T.Jiang, S.S.Goh, and Z.P.Lin, Local discriminant time-frequency atoms for signal classification, Signal Processing 72 (1999), 47-52.

9. Q.T.Jiang, On the regularity of matrix refinable functions, SIAM J. Math. Anal. 29 (1998), 1157-1176. reg.ps, reg.pdf

8. Q.T.Jiang, On the design of multifilter banks and orthonormal multiwavelet bases, IEEE Trans. Signal Proc. 46 (1998), 3292-3303. design.ps, design.pdf

7. Q.T.Jiang, Orthogonal multiwavelets with optimum time-frequency resolution, IEEE Trans. Signal Proc. 46 (1998), 830-844. optwtwoc.ps, optwtwoc.pdf

6. Q.T.Jiang, Rotation invariant ambiguity functions, Proc. Amer. Math. Soc. 126 (1998), 561-567. rot.ps, rot.pdf

5. Q.T.Jiang, S.S.Goh, N.C.Lim, and Z.P.Lin, Selection of initial parameters for signal representation by adaptive wavelets, Optical Engineering 37 (1998), 2613-2619.

4. Q.T.Jiang and L.Z.Peng, Admissible wavelets on the Siegel domain of type one, Sci. China Ser. A 41 (1998), 897-909. bdr.pdf

3. Q.T.Jiang, Wavelet transform and orthogonal decomposition of $L^2$ space on the Cartan domain $BDI(q=2)$, Trans. Amer. Math. Soc. 349 (1997), 2049-2068. BDI.pdf

2. Q.T.Jiang and S.L.Lee, Spectral properties of matrix continuous refinement operators, Adv. Comp. Math. 7 (1997), 383-399.

1. Q.T.Jiang and L.Z.Peng, Toeplitz type operators on wavelet subspaces, J. Math. Anal. Appl. 207 (1997), 462-474.


Old preprint:

Q.T. Jiang, On the construction of biorthogonal multiwavelet bases, preprint, 1999. bwave5.pdf



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