Project II (Math Modeling II, Fall 2010)
Image De
‐
Noising via Energy Functional Method
The starting point of this project is the influential paper of Rudin, Osher, and Fameti (can be
downloaded from the course web site (i.e., the one referred to as the ROF paper). The paper has been
cited more than 3000 times (and still counting)! This project will require to study and work out the
details of Section 2 of this classical paper, implement the basic algorithm, and explore the extensions.
Requirements: (i) Must be submitted in research report format (ii) Email programs in a single zipped file
to me (iii) Prepare a 5
‐
8 min presentation (to be presented at a later date) (iv) Must be working in
groups of two.
1.
Problem formulation.
Assume an image is given by a function u(x,y) defined on a two
dimensional region
Ω
, usually a rectangle [a,b]×[c,d]:
u:
Ω →
[0,1].
We can only observe a noisy version of u(x,y), u
0
(x,y) as
u
0
(x,y)=u(x,y)+n(x,y)
where n(x,y) is a noise term with mean zero and variance
σ
2
.
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 Fall '10
 Staff
 Math

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