Math 285J, Winter 2009

Variational methods in image and information science.

Instructor:                       

Stanley Osher

Lecture Meeting Time: 

MF 3:00PM-4:15PM @ MS 5217

Homework Policy:

HW assigned in week n is due on Friday, week n+1.  Some computational HW problems will be due in week n+2.

Schedule Change:

No class on Friday Feb. 6th

There will be classes on Wednesday, Feb. 11th and 18th, 3-3:50 pm at same room.

 

 

Textbook References:

·         (link) Constrained Optimization and Lagrange Multiplier Methods
D. Bertsekas, Athena Scientific, 1996.

·         (link) Convex Optimization
S. Boyd and L. Vandenberghe, Cambridge University Press, 2004.

·         (link) Oscillating Patterns in Image Processing and Nonlinear Evolution Equations
Y. Meyer, AMS, 2001

·         (link) Convex Analysis and Variational Problems
I. Ekeland and R. Temam, SIAM classics in applied mathematics, 1987

Web References:

·         (link) CAM Reports

Sample Images:

(click right button on the link and choose “save target as ….” to download)

 

Figure

Shape1

Shape2

Shape3

Barbara

Barbara (local)

Satellite

Satellite (local)

Cameraman

Horse

Europe

Size

128×128

128×128

150×150

510×510

200×200

352×352

250×250

256×256

150×230

118×113

 

Some MATLAB sample codes (or you can write these simple codes by yourself):

·         To convert an image to numerical matrix: img2var.m

·         To add noise with given sigma: noiseadd.m

·         To evaluate the SNR: snr.m

 

Related Papers:

·         (link) Convergence Rates of Convex Variational Regularization
Martin Burger and Stanley Osher, 2004

·         (link) An Iterative Regularization Method for Total Variation Based Image Restoration
Stanley Osher, Martin Burger, Donald Goldfarb, Jinjun Xu and Wotao Yin, 2004

·         (link) Nonlinear Inverse Scale Space Methods
Martin Burger, Guy Gilboa, Stanley Osher and Jinjun Xu, 2005

·         (link) Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet Based Denoising
Jinjun Xu and Stanley Osher, 2006

·         (link) Error Estimation for Bregman Iterations and Inverse Scale Space Methods in Image Restoration
Martin Burger, Elena Resmerita and Lin He, 2007

·         (link) Bregman Iterative Algorithms for Compessed Sensing and Related Problems
Wotao Yin, Stanley Osher, Jerome Darbon and Donald Goldfarb, 2007

·         (link) The Split Bregman Algorithm for L1 Regularized Problems
Tom Goldstein and Stanley Osher, 2008

·         (link) Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising
Stanley Osher, Yu Mao, Bin Dong and Wotao Yin, 2008

 

Copyleft David Mao@UCLA 2005-2010(?)