Haomin Zhou's publication page

Wavelets, Signal Analysis, Imaging Science

S.-N. Chow, K. Yin, H. M. Zhou, and A. Behrooz, Solving Inverse Source Problems by the Orthogonal Solution and Kernel Correction Algorithm (OSKCA) with Applications in Fluorescence Tomography, Inverse Problem and Imaging, Vol. 8, No. 1, (2013).
A. Behrooz, H. M. Zhou, A. Eftekhar and A. Adibi, Total Variation Regularization for 3D Reconstruction in Fluorescence Tomography: Experimental Phantom Studies, Applied Optics, Vol. 51, Issue 34, (2012). It has been selected by the Editors for publication in the Virtual Journal for Biomedical Optics (VJBO).
X. Ye and H. M. Zhou, Fast Total Variation Wavelet Inpainting via Approximated Primal-Dual Hybrid Gradient (PDHG), Inverse Problems and Imaging, Vol. 7, No. 3 (2013).
S. Lou, H. M. Zhou, and T. Zhou, An Improved Color Image Demosaicking Algorithm, in the proceeding of 5th International Congress on Image and Signal Processing (CISP), (2012).
T. Chan, Y. Wang and H. M. Zhou, Denoising Natural Color Photos in Digital Photography, submitted to Inverse Problem and Imaging.
A. Behrooz, H. M. Zhou, A. Eftekhar and A. Adibi, Fast Total Variation Regularization for Higher Resolution in Fluorescence Tomography: A Split Bregman Iteration Approach, in the Proceedings of the IEEE Photonics Conference, (2011).
A. Behrooz, H. M. Zhou, A. Eftekhar and A. Adibi, Toward robust high resolution Fluorescence tomography: a hybrid row-action edge preserving regularization, Optical Tomography and Spectroscopy of Tissue IX. in the Proceedings of the SPIE, Volume 7896, (2011).
F. Crosby, Q. Huynh and H. M. Zhou, Total Variation Methods for Three Dimensional Lidar Image Denoising, Photogrammetric Engineering and Remote Sensing, December (2010).
L. Lin, Y. Wang and H. M. Zhou, Iterative Filters As An Alternative Algorithm for Empirical Mode Decomposition, Advances in Adaptive Data Analysis (AADA), Vol. 1, Issue 4 (a special issue on Hilbert-Huang transform and its applications), (2009).
H. M. Zhou, T. Chan and J. Shen, A Quick Tour of Wavelets and PDE Techniques in Image Processing, Encyclopedia of Complexity and Systems Science, Springer, (2009).
T. Chan and H. M. Zhou, Total Variation Wavelet Thresholding, J. of Schientific Computing, Vol. 32, No. 2, August, (2007).
T. Chan, J. Shen and H. M. Zhou, A Total Variation Wavelet Inpainting Model with Multilevel Fitting Parameters, in the Proceedings to the SPIE, Symposium on Advanced Signal Processing: Algorithms, Architectures and Implementations VIII, Ed: F. Luk, Vol. 6313, San Diego, CA, August, (2006).
Y. Wang and H. M. Zhou, A Total Variation Wavelet Algorithm for Medical Image Denoising, the International Journal on Biomedical Imaging, Volume 2006, article ID 89095, (2006).
T. Chan , J. Shen and H. M. Zhou, Total Variation Wavelet Inpainting, Journal of Mathematical Imaging and Vision, Vol 25, Number 1/July, (2006).
T. Chan , H. M. Zhou and T. Zhou, A Recovery Bound for $H^1$ Based Wavelet Interpolations, in the proceeding to the international conference on PDE-Based Image Processing and Related Inverse Problems. Oslo, Norway, Aug 8-12, (2005).
T. Chan and H. M. Zhou, ENO-wavelet Transforms and Some Applications, in the book "Beyond Wavelets", editored by J. Stoeckler and G. V. Welland, Academic Press (2003).
D. Dugatkin, H. M. Zhou, T. Chan and M. Effros, Lagrangian Optimization of a Group Testing for ENO Wavelets Algorithm, in the proceeding to the Conference on Information Sciences and Systems, Princeton University, March 20-22, (2002).
T. Chan and H. M. Zhou, ENO-wavelet Transforms for Piecewise Smooth Functions, SIAM J. Numer. Anal. Vol 40, No. 4 (2002).
T. Chan and H. M. Zhou, Total Variation Improved Wavelet Thresholding in Image Compression, in the Proceedings to the International Conference on Image Processing, Vancouver, BC, Canada, Sept. 10-13, (2000).
T. Chan and H. M. Zhou, Optimal Construction of Wavelet Coefficients Using Total Variation Regularization in Image Compression, CAM report 00-27, Mathematics Department, UCLA, July, (2000).
T. Chan and H. M. Zhou, Adaptive ENO-wavelet Transforms and Its Application in Image Compression, in the Proceedings to the 12th International Conference on Domain Decomposition Methods, Chiba University, Chiba,Japan, Oct. 25-29, (1999).
T. Chan and H. M. Zhou, Adaptive ENO-wavelet Transforms for Discontinuous Functions, CAM report 99-21, Mathematics Department, UCLA, July, (1999).
T. Chan and H. M. Zhou, Feature Preserving Lossy Image Compression Using Nonlinear PDE's, in the Proceedings to the SPIE, Symposium on Advanced Signal Processing: Algorithms, Architectures and Implementations VIII, Ed: F. Luk, Vol. 3461, San Diego, CA, July, (1998).
T. Chan , H. M. Zhou and R. Chan, Continuation Method for Total Variation Denoising Problem, in the Proceedings to the SPIE, Symposium on Advanced Signal Processing: Algorithms, Architectures and Implementations VIII, Ed: F. Luk, Vol. 2563, San Diego, CA, July, (1995).

Stochastic Differential Equations

G. Bao, S. N. Chow, P Li and H. M. Zhou, An Inverse Random Source Problem for the Helmholtz Equation, AMS Mathematics of Computation, 83 (2014).
S. N. Chow, T. S. Yang and H. M. Zhou, Global Optimizations by Intermittent Diffusion, Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua, Edited by Adamatzky et al. Published by World Scientific Publishing Co. Ltd., 2013.
S.-N. Chow, W. Li, Z. Liu and H. M. Zhou, A Natural Order in Dynamical Systems Based on Conley-Markov Matrices, Journal of Differential Equations, Vol. 252, Issue 4, (2012).
G. Bao, S. N. Chow, P Li and H. M. Zhou, Numerical Solution of an Inverse Medium Scattering Problem with a Stochastic Source, Inverse Problems Vol. 26 No. 07, 074014, (2010).
C. Y. Lee, B. L. Rozovskii, H. M. Zhou, Randomization of Forcing in Large Systems of PDE for Improvement of Energy Estimates, SIAM Multiscale Modeling and Simulation, Vol 8, No. 4. (2010).
M. Badieirostami, A. Adibi, H. M. Zhou, and S. N. Chow, Wiener Chaos Expansion and Simulation of Electromagnetic Wave Propagation Excited by a Spatially Incoherent Source, SIAM Multiscale Modeling and Simulation, Vol.8, No. 2, (2010).
S. N. Chow , W. X. Shen and H. M. Zhou, Dynamical Order in Systems of Coupled Noisy Oscillators, J. of Dynamics and Differential Equations, Vol. 19, No. 4, Dec (2007).
A. Adibi, M. Badieirostami, H. M. Zhou and S. N. Chow , Efficient Simulation of Diffuse Light for the Analysis of Photonic Crystal Structures, Optics Letter 32 (2007).
M. Badieirostami, A. Adibi, H. M. Zhou and S. N. Chow , Efficient modeling of spatially incoherent sources based on Wiener chaos expansion method for the analysis of photonic crystal spectrometer, in the Proceedings of SPIE , Vol 6480, (2007).
S. N. Chow and H. M. Zhou, An Analysis of Phase Noise and Fokker-Planck Equations, J. of Differential Equations, Vol. 234, Issue 2, (2007).
T. Hou, W. Luo, B. Rozovskii and H. M. Zhou, Wiener Chaos Expansions and Numerical Solutions of Randomly Forced Equations of Fluid Mechanics, J. of Computational Physics, 216 (2006).
T. Hou, H. Kim, B. Rozovskii and H. M. Zhou, Wiener Chaos Expansions and Numerical Solutions of Randomly Forced Equations of Fluid Mechanics, the HERMIS Journal, the international journal of computer mathematics and its applications, vol. 4, (2004).

The Shortest Path, Optimal Control Problems

Jun Lu, Yancy Diaz-Mercado, Magnus Egerstedt, Haomin Zhou, and Shui-Nee Chow, Shortest Paths Through 3-Dimensional Cluttered Environments, in the proceeding of International Conference on Robotics and Automation (ICRA), Hong Kong, (2014).
S.-N. Chow, J. Lu, and H. M. Zhou, "Fast Numerical Methods Based on SDEs for Several Problems Related to the Shortest Path",
Methods and Application of Analysis, Vol 20, No. 4, (2013).
S.-N. Chow, J. Lu, and H. M. Zhou, Finding the shortest path by evolving junctions on obstacle boundaries (E-JOB): An initial value ODE's approach, J. Applied and Computational Harmonic Analysis, Vol. 35, Issue 1, July 2013.
R. Goroshin, Q. Huynh and H. M. Zhou, Approximate Solution to Several Visibility Optimization Problems, Communications in Mathematical Sciences, Vol. 9, Issue 2, 2011.
Sachin Jain, Panagiotis Tsiotras and H. M. Zhou, Adaptive Multiresolution Mesh Refinement for the Solution of Evolution PDEs, in the proceedings to the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, December 12-14, 2007.

Differential Equations and Random Processes on Graphs

S.-N. Chow, W. Huang, Y. Li and H. M. Zhou, Fokker-Planck Equations for a Free Energy Functional or Markov Process on a Graph, Archive for Rational Mechanics and Analysis, Volume 203, Issue 3 (2012).
S.-N. Chow, W. Huang, Y. Li and H. M. Zhou, A Free Energy Based Mathematical Study for Molecular Motors, Regular and Chaotic Dynamics, Volume 16, Numbers 1-2 (2011).

Numerical PDEs

A. Shelton, M. Smith and H. M. Zhou, A Multi-Resolution Discontinuous Galerkin Method for Unsteady Compressible Flows, AIAA 2008-4140, 38th Fluid Dynamics Conference and Exhibit, Seattle, Washington, June 23-26, (2008).
S. Jain, P. Tsiotras and H. M. Zhou, Adaptive Multiresolution Mesh Refinement for the Solution of Evolution PDE's, SIAM J. on Scientific Computing, Vol. 31, Issue 2, (2008).

Other Subjects

F. Ghasemi, H. M. Zhou and A. Adibi, "Closed-form Relations for Resonance Detection Error Using Statistical Analysis of Amplitude Noise", accepted by IEEE journal on Selected Topics in Quantum Electronics.
S. Lee, H. M. Zhou and D. Baldwin, A Numerical Study of Void Nucleation and Growth in a Flip Chip Assembly Process, Modeling and Simulation in Materials Science and Engineering, 18 (2010).
R. H. Chan , S. F. Xu, and H. M. Zhou, "On the Convergence Rate of a Quasi-Newton Method for Inverse Eigenvalue Problems", SIAM J. Numer. Anal., 36 (1999), 436--441.
Z. H. Teng and H. M. Zhou, "The L_1 Convergence Rate of Particle Method for Scalar Conservation Laws", Master Thesis, Math Dept., Peking University, China, 1994.

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