Publications and Preprints

  1. 1. J. Bryson, H. Zhao and Y. Zhong, Intrinsic Complexity And Scaling Laws: From Random Fields to Random Vectors, submitted. arXiv:1805.00194

  2. 2. H. Zhao and Y. Zhong, A hybrid adaptive phase space method for reflection traveltime tomography, submitted. arXiv:1803.02501

  3. 3. J. Fun, J. Qian, L. Zepeda-Nunez and H. Zhao, An efficient hybrid method for high frequency Helmholtz equation with point source, J. Comp. Phys., accepted.

  4. 4. B. Engquist and H. Zhao, Approximate Separability of Green's Function for High Frequency Helmholtz Equations, Communications on Pure and Applied Mathematics, accepted.

  5. 5. H. Zhao, The fast sweeping method for stationary Hamilton-Jacobi equations, Handbook of Numerical Methods for Hyperbolic Problems, Basics and Fundamental Issues, Vol. 17, Ed. R. Abgrall and C.W. Shu, Elsevier, 2016.

  6. 6.J. Fun, J. Qian, L. Zepeda-Nunez and H. Zhao, Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations, Research in Mathematical Sciences, 4(12), 2017.

  7. 7. H. F. Li, H, Zhao and H. Li, Neural Response Based Extreme Learning Machine for Image Classification, submitted.

  8. 8. L. Zepeda-Nunez and H. Zhao, Fast alternating bi-directional preconditioner for the 2D high frequency Lippmann-Schwinger equation, submitted, SIAM Journal on Scientific Computing, 38(5), 866-888, 2017.

  9. 9. C. Zhang, B. Shahbaba and H. Zhao, Variational Hamiltonian Monte Carlo via score matching, Bayesian Analysis, to appear.

  10. 10. C. Zhang, B. Shahbaba and H. Zhao, Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases, Statistics and Computing, 27(6), 1473-1490, 2017.

  11. 11. M. Wang, S. Leung and H. Zhao, Modified virtual grid difference for discretizing Laplace-Beltrami operator on point clouds,SIAM Journal on Scientific Computing, to appear.

  12. 12. C. Zhang, B. Shahbaba and H. Zhao, Precomputing strategy for Hamiltonian Monte Carlo method based on regularity in parameter space, Computational Statistics, 32(1), 253-279, 2017.

  13. 13. S. Luo and H. Zhao, Convergence analysis of the fast sweeping method for static convex Hamilton-Jacobi equation, Research in Mathematical Sciences, 3:35, 2016.

  14. 14. J. Liu, X. Zhang, X. Zhang, H. Zhao, Y. Gao, D. Thomas, D. Low, and H. Gao, 5D respiratory motion model based image reconstruction algorithm for 4D cone-beam computed tomography, Inverse Problems (Highlights of 2015), 31(11), 2015.

  15. 15. H. Schaeffer, Y. Yang, H. Zhao and S. Osher, Real-time adaptive video compression, SIAM Journal of Scientific Computing, 37(6), 980-1001, 2015.

  16. 16. R. Lai and H. Zhao, Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap, SIAM Journal on Imaging Sciences, 10(2), 449-483, 2017.

  17. 17. L. Xiao, Q. Cai, Z. Li, H. Zhao and R. Luo, A Multi-Scale Method for Dynamics Simulation in Continuum Solvents I: Finite-Difference Algorithm for Navier-Stokes Equation, Chemical Physics Letters, 616, 67-74, 2014.

  18. 18.T. Aslam, S. Luo and H. Zhao, A static PDE approach for multi-dimensional extrapolation using fast sweeping methods, SIAM Journal on Scientific Computing, 36(6), 2014.

  19. 19. T. W. Wong and H. Zhao, Computing Surface Uniformization Using Discrete Beltrami Flow, SIAM SIAM Journal on Scientific Computing, 37(3), 1342-1364, 2015.

  20. 20. A. Wong and H. Zhao, Computation of quasiconformal surface maps using discrete Beltrami flow, SIAM Journal on Imaging Sciences,7(4), 2675–2699, 2014.

  21. 21. Z. Li, Q. Cai, H. Zhao and R. Luo, A semi-implicit augmented IIM for Navier-Stokes equations with open and traction boundary conditions, Journal of Computational Physics, 297, 182-193, 2015.

  22. 22. S. Y. Hon, S. Leung and H. Zhao, A cell based particle method for modeling dynamic interfaces, Journal of Computational Physics,  272, 279-306, 2014.

  23. 23. J.-F. Cai, X. Jia, H. Gao, S.B. Jiang, Z. Shen and H. Zhao, Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study, IEEE Transactions on Medical Imaging, 33(8):1581--1591, 2014.

  24. 24.H. Liu, H. Zhao and C. Zou, Determining Scattering Support of Anisotropic Acoustic Mediums and Obstacles, Communications in Mathematical Sciences,13, no. 4, 987--1000, 2015.

  25. 25. Y. Lou, E. Esser, H. Zhao and J. Xin, Partially Blind Deblurring of Barcode from Out-of-Focus Blur, SIAM Journal on Imaging Sciences 7 (2), 740-760, 2014.

  26. 26. G. Bao, K. Huang, P. Li, and H. Zhao, A direct imaging method for inverse scattering using the generalized Foldy-Lax formulation, Contemp. Math., 615, 49-70, 2014.

  27. 27. C. Wang, J. Wang, Q. Cai, Z. Li, H. Zhao and R. Luo, Exploring Accurate Poisson-Boltzmann Methods for Biomolecular Simulations, Computational and Theoretical Chemistry, 1022:34–44, 2013.

  28. 28.K. Ren and H. Zhao, Quantitative fluorescence photoacoustic tomography, SIAM Journal on Imaging Sciences, 6 (4), 2404-2429, 2013.

  29. 29. R. Lai, J. Liang and H. Zhao, A local mesh method for solving PDEs on point clouds, Inverse Problem and Imaging, 7(3), 2013.

  30. 30. J. Liang and H. Zhao, Solving partial differential equations on point clouds, SIAM Journal on Scientific Computing, Vol. 35(3), pp 1461-1486, 2013.

  31. 31. W. M. Botello-Smith, X. Liu, Q. Cai, Z. Li, H. Zhao, and R. Luo, Numerical Poisson--Boltzmann Model for Continuum Membrane Systems, Chem. Phys. Lett., 555:274–281, 2013.

  32. 32. X. Liu, J. Wang, Z. Li, H. Zhao, and R. Luo, Exploring a Charge-Central Strategy in the Solution of Poisson Equation for Biomolecular Applications, Phys. Chem. Chem. Phys., 15:129-141, 2013.

  33. 33. K. Ren, H. Gao, and H. Zhao, A hybrid reconstruction method for quantitative photo-acoustic tomography, SIAM Journal on Imaging Sciences, Vol. 6 (1), pp 32-55, 2013.

  34. 34. R. Lai, J. Liang, A. Wong, and H. Zhao, Geometric Understanding of Point Clouds Using Laplace-Beltrami Operator, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012.

  35. 35. K. Huang, P. Li, and H. Zhao, An efficient algorithm for the generalized Foldy-Lax formulation, J. Comp. Phys., Vol. 234, pp 376-398, 2013.

  36. 36. S. Hou, P. Song, L. Wang, and H. Zhao, A weak formulation for solving elliptic interface problems without body fitted grid, J. Comp. Phys., Vol. 249, pp 80-95, 2013.

  37. 37. E. Castillo, J. Liang, and H. Zhao, Point cloud segmentation and denoising via constrained least squares normal estimates, Book Chapter, Innovations for Shape Analysis: Models and Algorithms, Springer, 2012.

  38. 38. H. Gao, S. Osher, and H. Zhao,  Quantitative photoacoustic tomography, Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographies, Lecture Notes in Mathematics: Mathematical Biosciences Subseries, Volume 2035, Springer-Verlag, Berlin, 2011.

  39. 39. J. Liang, F. Park and H. Zhao, Robust and efficient implicit surface reconstruction of point clouds based on convexified image segmentation, Journal of Scientific Computing, Vol. 54 (2-3), pp 577-602, 2013.

  40. 40. S. Luo, J. Qian and H. Zhao,  Higher-order schemes for 3-D traveltimes and amplitudes, Geophysics, Vol 77 (2), pp 47-56, 2012.

  41. 41.J. Qian, P. Stefanov, G. Uhlmann and H. Zhao, An efficient Neumann-series based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed, SIAM Journal on Imaging Sciences, Vol 4 (3), pp 850-883, 2011.

  42. 42. E. Chung, J. Qian, G. Uhlmann, and H. Zhao, Adaptive phase space method with application to reflection traveltime tomography, Inverse Problem, 27, 2011.

  43. 43. H. Gao, J. Cai, Z. Shen and H. Zhao, Robust principle component analysis based four-dimensional computed tomography, Physics in Medicine and Biology, Vol. 56 (11), pp 3181-3198, 2011. (Featured article \& Editor’s Choice).

  44. 44. Y.-T. Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu, Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations, SIAM Journal on Scientific Computing, 33(4), pp 1873-1896, 2011.

  45. 45. S. Luo, Y. Yu and H. Zhao, A new approximation for effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations, SIAM Journal on Multiscale Modeling and Simulation, 9(2), pp 711-734, 2011.

  46. 46. H. Gao and H. Zhao, Analysis of a fast forward solver for radiative transfer equation, Mathematics of Computation,  Vol. 82, pp 153-172, 2012.

  47. 47. S. Leung, J. Lowengrub and H. Zhao, A grid based particle method for high order geometrical motions and local inextensible flows, J. Comp. Phys.  Vol. 230(7),  pp 2540-2561, 2011.

  48. 48. J. Xu, Z. Li, J. Lowengrub and H. Zhao, Numerical study of surfactant-laden drop-drop interactions, Communications in Computational Physics, Vol. 10 (2), pp. 453-473, 2011.

  49. 49. S. Luo, L. Guibas and H. Zhao, Euclidean Skeletons Using Closest Points, Inverse Problems and Imaging, Vol. 30 (1), pp 95-113, 2011.

  50. 50. H. Gao, H. Zhao, W. Cong and G. Wang, Bioluminescence tomography with Gaussian prior, Biomedical Optics Express, 1, pp 1259-1277, 2010.

  51. 51. Z. Li, M.C. Lai, G. He and H. Zhao, An augmented method for free boundary problems with moving contact lines, Computers & Fluids, 39, 1033-1040, 2010.

  52. 52. H. Gao, Y. Lin, G. Gulsen and H. Zhao, Fully linear reconstruction method for fluorescence yield and lifetime through inverse complex-source formulation, Optics Letters. 35 1899-1901, 2010.

  53. 53. K. Huang, K. Solna and H. Zhao, Generalized Foldy-Lax Formulation, J. Comp. Phys. Vol. 229(12), pp 4544-4553, 2010.

  54. 54. H. Gao and H. Zhao, Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity, Optics Express. 18, 2894-2912, 2010.

  55. 55. H. Gao and H. Zhao, Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization, Optics Express. 18, pp 1854-1871, 2010.

  56. 56. S. Leung and H. Zhao, Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method, Communication in Computational Physics. Vol. 8(4), pp 758-796, 2010.

  57. 57. J. D. Benamou, S. Luo and H. Zhao, A Compact Upwind Second Order Scheme for the Eikonal Equation, Journal of Computational Mathematics, 28, pp 489-516, 2010.

  58. 58. Y. Xi, Y. Duan, and H. Zhao, A Nonparametric Approach for Noisy Point Data Preprocessing, International Journel of CAD/CAM, Vol. 9, No. 1, pages. 31-36, 2009.

  59. 59. H. Gao and H. Zhao, A multilevel and multigrid optical tomography based on radiative transfer equation, Proceedings of the SPIE, Vol. 7369, 73690E-73690E-10, 2009.

  60. 60. S. Leung and H. Zhao, A Grid Based Particle Method for Evolution of Open Curves and Surfaces, J. Comp. Phys. Vol., 228(20), pp 7706-7728, 2009.

  61. 61. H. Gao and H. Zhao, A Fast Forward Solver of Radiative Transfer Equation in Optical Imaging, Transport Theory and Statistical Physics, Vol. 38(3)009 , pp 149-192, 2009.

  62. 62. S. Fomel, S. Luo and H. Zhao, Fast sweeping method for the factored eikonal equation, J. Comp. Phys., Vol. 228(17), pp 6440-6455, 2009.

  63. 63. Q. Cai, J. Wang, H. Zhao, and R. Luo, On Removal of Charge Singularity in Poisson-Boltzmann Equation, Journal of Chemical Physics, 130:145101, 2009.

  64. 64. S. Leung, G. Liang, K. Solna and H. Zhao, Expectation-Maximization algorithm with local adaptivity for image analysis, SIAM Journal on Imaging Sciences, Vol. 2(3), pp 834-857, 2009.

  65. 65. J. Wang, Q. Cai, Z.-L. Li, H. Zhao, and R. Luo, Achieving Energy Conservation in Poisson-Boltzmann Molecular Dynamics: Accuracy and Precision with Finite-Difference Algorithms, Chemical Physics Letters, 468:112-118, 2009.

  66. 66. S. Leung and H. Zhao, A novel grid based particle method for moving interface problem, J. Comp. Phys., Vol. 228 (8), pp. 2993-3024, 2009.

  67. 67. F. Li, C.-W. Shu, Y.-T. Zhang and  H. Zhao, Second Order discontinuous Galerkin Fast Sweeping Method For Eikonal Equations, J. Comp. Phys., Vol. 227(17), pp. 8191-8208, 2008.

  68. 68. H. Zhao, Time reversal based direct imaging methods, Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Y. Censor, M. Jiang and A.K. Louis (Editors), Edizioni della Normale, pp. 505-521, 2008.

  69. 69. E. Chung, J. Qian, G. Uhlmann, and H. Zhao, A phase space formulation for elastic-wave traveltime tomography, Journal of Physics: Conference Series 124(2008): 012018.

  70. 70. S. Hou, K. Huang, K. Solna, H. Zhao, A phase and space coherent direct imaging algorithm, Journal of the Acoustical Society of America, Vol 125 (1), pp 227-238, 2009.

  71. 71. S. Hou, K. Solna, H. Zhao, A Direct Imaging Method For Far Field Data, Inverse Problem, Vol. 23, 1533-1546, 2007.

  72. 72. E. Chung, J. Qian, G. Uhlmann, H. Zhao, A new phase space method for recovering index of refraction from travel time, Inverse Problems, Vol. 23, No. 1, pp. 309-329, 2007. (highlights of the year)

  73. 73. J. Qian, Y. Zhang, H. Zhao, A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations, Journal of Scientific Computing, Vol. 31, No. 1/2, pp. 237-271, 2007.

  74. 74. H. Zhao, Parallel Implementation of Fast Sweeping Method, Journal of Computational Mathematics, Vol. 25, No. 4, pp. 421-429, 2007.

  75. 75. S. Hou, K. Solna, H. Zhao, A Direct Imaging Algorithm For Extended Targets, Inverse Problem, Vol. 22, 1151-1178, 2006. (highlights of the year)

  76. 76. Y. Zhang, H. Zhao, S. Chen, Fixed-point Iterative Sweeping Methods for Steady-states of Hamilton-Jacob Equations, Methods and Applications of Analysis Vol. 13, pp. 299-320, 2006.

  77. 77. D. Lu, H. Zhao, M. Jiang, S. Zhou, and T. Zhou, A Surface Reconstruction Method for Highly Noisy Point Clouds, N. Paragios et al. (Eds.): VLSM 2005. Lecture Notes in Computer Science, Springer, 3752, pp. 283-294, 2005.

  78. 78. J. Xu, Z. Li, J. Lowengrub, H. Zhao, A Level Set Method for Interfacial Flows with Surfactant, J. Comp. Phys. Vol. 212(2), pp. 590-616, 2006.

  79. 79. J. Qian, Y. Zhang, H. Zhao, Fast sweeping methods for Eikonal equations on triangulated meshes, SIAM Journal on Numerical Analysis, Vol. 45, pp. 83-107, 2007.

  80. 80.K. Huang, G. Papanicolaou, K. Solna, C. Tsogka, H. Zhao,  Efficient Numerical Simulation for Long Range Wave Propagation, J. Comp. Phys. Vol. 215(2), pp. 448-464, 2006.

  81. 81. Y. Xi, G. Heckenberg, Y. Duan and H. Zhao, A New Modeling-Based Algorithm for Implicit Surface Polygonization, Proceedings of Vision Geometry XIII, SPIE 2005, January 2005, San Jose, CA.

  82. 82.M.  Peternell, H.  Pottmann, T. Steiner, H. Zhao,  Swept Volumes, Computer-Aided Design and Applications, Vol. 2, No. 5, 2005.

  83. 83. K. Huang, K. Solna, H. Zhao, Coupled Parabolic Equations for Wave Propagation, Methods and Applications of Analysis, Vol. 11 (3), pp 399-412, 2004.

  84. 84. Y. Zhang,  H. Zhao, J. Qian, High order fast sweeping methods for static Hamilton-Jacobi equations, Journal of Scientific Computing, Vol. 29, pp. 25-56, 2006.

  85. 85.H. Zhao, Fast Sweeping Method for Eikonal Equations, Mathematics of Computation, Vol. 74, pp 603-627, 2005.

  86. 86. S. Hou, K. Solna, H. Zhao, Imaging of Location and Geometry for Extended Targets Using the Response Matrix, J. Comp. Phys. Vol. 199 (1), pp. 317-338, 2004.

  87. 87. Z.  Li,  X.  Lin,  M. Torres, H. Zhao, Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media, Methods and Applications of Analysis, Vol. 10 (2), 2003.

  88. 88.H. Zhao, Analysis of the Response Matrix for an Extended Target, SIAM Applied Mathematics, Vol. 64 No. 3, pp. 725-745. 2004.

  89. 89. Y.R. Tsai,  L.T. Cheng,  S. Osher, H. Zhao, Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations, SIAM  Journal on Numerical Analysis, Vol 41, No 2, pp. 673-694, 2003.

  90. 90. J. Xu, H. Zhao, An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface, Journal of Scientific Computing, Vol. 19, 2003, pp. 573-594.

  91. 91. H. Zhao and S. Osher, Visualization, Analysis and Shape Reconstruction of Unorganized Data Sets, book chapter in Geometric Level Set Methods in Imaging, Vision and Graphics, S. Osher and N. Paragios Editors, Springer, 2003.

  92. 92. M.J. Gander and H. Zhao, Overlapping Schwarz Waveform Relaxation for the Heat Equation in n-Dimensions, BIT, Vol. 42, No. 4, pp. 779-795, 2002.

  93. 93. J.K. Hunter, Z. Li and H. Zhao, Reactive Autophobic Spreading of Drops, J. Comp. Phys. Vol. 183, 2002, pp. 335-366.

  94. 94. P. Blomgren, G. Papanicolaou, H. Zhao, Super-resolution in Time Reversal Acoustics, Journal of the Acoustical Society of America, Vol 111, 2002, pp. 230-248.

  95. 95. H. Zhao, S. Osher, R. Fedkiw, Fast Surface Reconstruction and Deformation Using the Level Set Method, Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM  2001), July, 2001, Vancouver.

  96. 96. H. Zhao, S. Osher, B. Merriman, M. Kang, Implicit and Non-parametric Shape Reconstruction from Unorganized Points Using Variational Level Set Method, Computer Vision and Image Understanding. Vol. 80, 2000, pp 295-319.

  97. 97. D. Peng, S. Osher, B. Merriman, H. Zhao, The Geometry of Wulff Crystal Shapes and Its Relations with Riemann Problems, Contemporary Mathematics, Vol. 238, AMS, Providence, 1999, pp 251-303, eds G.-Q Chen and E. DiBenedetto.

  98. 98. D. Peng, B. Merriman, S. Osher, H. Zhao, M. Kang, A PDE Based Fast Local Level Set Method, J. Comp. Phys. Vol. 155, 1999, pp 410-438.

  99. 99. Z. Li, H. Zhao, H. Gao, A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid, J. Comp. Phys. Vol. 152, 1999, pp 281-304.

  100. 100.H. Zhao, B. Merriman, S. Osher, L. Wang, Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach, J. Comp. Phys. Vol. 143, 1998, pp 495-518.

  101. 101. A.Q. Li, V. Chalana, H. Zhao, Simultaneous Spatio-Temporal Target Segmentation and Motion Estimation in a Variational Formulation, Proceedings of SPIE on Applied Imagery Pattern Recognition (AIPR), vol 3584, Washington DC, 1998.

  102. 102. B. Engquist, H. Zhao. Absorbing Boundary Conditions for Domain Decomposition, Applied Numerical Mathematics, Vol. 27, 1998, pp341-365.

  103. 103. T.Y. Hou, Z. Li, S. Osher, H. Zhao, A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow, J. Comp. Phys. Vol. 134, 1997, pp 236-252.

  104. 104. H. Zhao, T.F. Chan, B. Merriman, S. Osher,  A Variational Level Set Approach to Multiphase Motion, J. Comp. Phys. Vol. 127, 1996, pp 179-195.