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Bin Dong |
UCLA Mathematics Department Box 951555 Los Angeles, CA 90095-1555 Office: IPAM 1129C |
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I have stopped updating this webpage as of June 30,
2009.
Please go to www.math.ucsd.edu/~b1dong
for the latest updates.
Education
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Ph.D. candidate, University
of California – Los Angeles, Los Angeles, CA, USA, 2005 – 2009.
Advisor: Professor Stanley Osher.
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M.S., National
University of Singapore, Singapore, 2003-2005.
Advisor: Professor Zuowei Shen.
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B.S., Peking
University, Beijing, China, 1999-2003.
Research Interests
1. Numerical PDEs, Level Set Methods.
2. Optimization Problems (e.g. L1-Minimizations
and Compressed Sensing)
3. Wavelets Theory and Applications.
4. Image Processing and 3D Shape Analysis.
My CV: PDF.
My Master Thesis: PDF
My
PhD Thesis: PDF
Current Projects/Working Problems
1. Fast algorithms for L1 minimization and their
applications in signal and image processing.
2. Multiscaled representation (wavelet flavored
but level set and PDE based) for surfaces and its applications.
3. Capturing regions of interests in 3D biological
surfaces via level set and
4. Design fast solvers for nonlinear PDEs via
wavelets/framelets transforms.
5. Ultrasound image processing and analysis
(denoising, segmentation and needle tracking).
6. Level set and
Publications
1. Bin Dong, Nira Dyn
and Kai Hormann, Properties
of dual pseudo-splines, Institut fur Informatik, Technical Report 09-03, 2009.
2. Bin Dong, Aichi
Chien, Zuowei Shen and Stanley Osher, A
new multiscale representation for shapes and its application to blood vessel
recovery, submitted, 2009.
3. Bin Dong, The implicit representation of
biological shapes and forms, Biomedical
Computation Review (issue: Spring 2009), Published by Simbios, the NIH
National Center for Physics-Based Simulation of Biological Structures, 2009.
4. Bin Dong, Eric
Savitsky and Stanley Osher, A Novel
Method for Enhanced Needle Localization Using Ultrasound-Guidance, CAM-Report 08-65, Sep. 2008.
5. Bin Dong, Aichi
Chien, Yu Mao, Jian Ye, Fernando Vinuela and Stanley Osher, Level set based brain aneurysm
capturing in 3D, submitted, 2008.
6. Stanley Osher, Yu Mao, Bin Dong, Wotao Yin, Fast linearized Bregman iterations for
compressive sensing and sparse denoising, accepted by Communications in
Mathematical Sciences, CAM-Report
08-37, Dec. 2008.
7. Bin Dong, Aichi Chien, Yu Mao, Jian Ye and
Stanley Osher, Level set based surface
capturing in 3D medical images, MICCAI
2008, 162-169, 2008.
8. Bin Dong, Jian Ye, Stanley Osher and Ivo
Dinov, Level set based
nonlocal surface restoration, MMS
Vol. 7(2), 589-598 (CAM-Report 07-44), 2008.
9. Bin Dong, Yu Mao, Ivo D. Dinov, Zhuowen Tu,
Yonggang Shi, Yalin Wang and Arthur W. Toga, Wavelet-Based Representation of
Biological Shapes, CAM-Report
07-36 (unpublished manuscript), Sep. 2007.
10.
Bin Dong and Zuowei Shen, Pseudo-splines,
wavelets and framelets, Appl.
Comput. Harmon. Anal., 22,
78-104, 2007.
11.
Bin Dong and Zuowei Shen, Linear
independence of pseudo-splines, Proc.
Amer. Math. Soc., 134, 2685-2694, 2006.
12.
Bin Dong and Zuowei Shen, Construction
of biorthogonal wavelets from pseudo-splines, J.
Approx. Theory, Vol. 138 (2), 211-231, 2006.
Courses Taken at UCLA
1. MATH 266ABC - Ordinary Differential Equations; Applied Partial
Differential Equations (general theories for first order linear, quasilinear
PDEs; parabolic and hyperbolic PDEs; Hamilton-Jacobi equations; scalar
conservation law, shocks and Riemann problems; hyperbolic systems and systems
of conservation laws).
2. MATH 269ABC - Numerical Ordinary Differential Equations; Finite
Difference Methods in Solving Parabolic and Hyperbolic Partial Differential
Equations; Finite Difference, Finite Element Method in Solving Elliptic Partial
Differential Equations.
3. MATH 270C - Iterative Methods in Solving Linear Systems (e.g.
systems obtained from discretizing Poisson equations).
4. MATH 273 (by Luminita Vese) - Optimization, Calculus of
Variations, and Control Theory.
5. MATH 270D&285J (by Stanley Osher) - Mathematical Aspects of
Scientific Computing; given by Professor Stanley Osher. Topics include level
set methods and its applications in image processing: Numerical methods, e.g.
monotone and ENO schemes, for finding viscosity solutions of Hamilton-Jacobi
equations (e.g. motion by mean curvature); ROF model; Snake and Chan-Vese model
in image segmentation; BV$L_1$; Global minimization for snakes and Munford-Shah
models in image segmentation and denoising; Bregman Iterations and Inverse
Scale Space methods for image denoising\&deblurring; Image inpainting).
6. MATH 285J (by Achi Brandt) - A two quarter course about
Multigrid methods (Vcycles and Full Multigrid) in Solving Poisson equations and
Bratu equation (\Delta u+\lambda e^u=0). We also used Full Multigrid method to
solve the parameter \lambda and u of Bratu equation simultaneously with ||u||
being given. The course also includes Algebraic Multigrid method and my final
project is using line integration and Algebraic Multigrid to do image
denoising.
7. EE 236A (by Lieven Vandenberghe) - Linear Programming:
Basic definitions and geometry of linear programming, engineering applications,
duality, the simplex method, interior-point methods, large-scale linear
programming, introduction to network optimization and integer linear
programming.
8. EE 236B (by Lieven Vandenberghe) - Nonlinear Programming:
Convex sets and convex functions, convex optimization problems, duality, approximation
and fitting, statistical estimation, geometric problems, numerical linear
algebra background, unconstrained minimization, equality constrained
minimization, interior-point methods.
Teaching (Winter 2008)
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Math 3B, Calculus for Life
Science Students (Instructor: Prof. Popa).
Office Hour:
1pm-2pm,
Thursday. Location:
1129C@IPAM (Institute for
Pure and Applied Mathematics)
Practice Exams (Note that the practice
exams are only for practice. It does NOT mean the real exams will be of the
same format or difficulty):
1. Midterm1
2. Midterm2
Hobbies:
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Sports: Basketball, Hiking, Diving (only did it twice though…looking for someone
to take a class together), Watching “Man v.s. Wild” on Discovery Channel.
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PC Games: Baldur’s Gate, Neverwinter Nights, The Witcher, Heroes Might and Maggic,
Starcraft/Brood War, Diablo, and pinball on Windows XP.
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Others: Watching TV (favorite TVs: The office, friends, CSI -LV,
south park, six feet under, LOST)
Last
updated: May 2009.