My question goes from the explained in the attached document. It's about image denoising using regularization, with constraints. I used the Lagrange multipliers formulation, but, by obtaining the numerical solution, can't get the regularization parameter (Lagrange multiplier) as should be theoretically expected .
Any suggestion would be much appreciated.
Thanks in advance,
Miguel Tavares
Sorry. On the two last sentences of the attached document, \lambda, should be \lambda^{*} as it refers to the optimal point.
Can you clarify a few things.
-what is X(u)?
-if u is an image, what is the meaning of dL/du?
-how do you define ||u-g||?
I would suggest looking at the gradients that are computed . Miguel , it is certainly not a scalar computation , the inner product results are not equal to zeros hence I am not sure if the optimal point would be exact .
Also , the noise model is stationary then typically Euler -Lagrange is used to solve the PDE.
X(u) is a norm function (total variation norm). dL/du = 0 mean one must find the image u that minimizes X(u)+\lambda*||u-g||^2.
||u-g|| is the Frobenius norm.
The system is solved numerically, so, as Aparna pointed out, is not exact. But I get a close behavior of \lambda* to -dX*/dc, except from a scaling factor, which should not happen (at least if the theoretical derivation is correct).
Thanks
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