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tvdenoise

$ \bigcirc$Name


tvdenoise Image denoising by TV minimization (Rudin-Osher)




$ \bigcirc$Command Synopsis


tvdenoise [-w w] [-s s] [-E eps] [-e e] [-n n] [-r ref] [-v] [-c] in out



-w w : weight on fidelity term (default 0.1)

-s s : initial (and maximal) time step, default 1.

-E eps : epsilon in sqrt(epsilon+ |  Du |   $ \hat{{}}$  2), default 1.

-e e : stop when |  u(n)-u(n-1) |   <  e (L2 error, default 0.1)

-n n : or perform a fixed number of iterations (default: 5)

-r ref : to specify a reference image different from in

-v : verbose : print energy and L2 errors at each iteration

-c : cancel auto step reduction

in : input Fimage

out : output Fimage




$ \bigcirc$Function Summary


Fimage tvdenoise (in , out , s , c , v , e , n , w , ref , eps )

Fimage in , out , ref ;

int *n ;

double *s , *e , *w , *eps ;

char *v , *c ;




$ \bigcirc$Description


This module looks for the image out that minimizes the energy functional proposed by Rudin, Osher and Fatemi [ROF92][RO94],

E(out) = $\displaystyle \int$|$\displaystyle \nabla_{{eps}}^{}$(out)| + w$\displaystyle \int$(out - in)2.

This energy is the combination of a regularity term (the total variation) and a fidelity term (L2 square error). The regularity term is obtained from the local estimate of the gradient norm

|$\displaystyle \nabla_{{eps}}^{}$(u)| = $\displaystyle {\frac{{\displaystyle
\sqrt{eps + (a-b)^2+(c-d)^2+(a-c)^2+(b-d)^2
+ \frac 12 (a-d+b-c)^2
+ \frac 12 (a-d-b+c)^2}}}{{2+\sqrt{2}}}}$,

where the local images values are
a b
c d
.

A gradient descent algorithm is applied, with a initial step s. If the energy does not decrease, then s is multiplied by 0.8 until the stopping criterion is statisfied. Other options are straightforward.




$ \bigcirc$See Also


fnorm.




$ \bigcirc$Version 1.0


Last Modification date : Fri Jan 25 18:14:00 2002


$ \bigcirc$Author


Lionel Moisan






next up previous contents index
Next: fft2d Up: Reference Previous: shock   Contents   Index
mw 2004-05-05