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I am trying to use total variation minimization for an image reconstruction problem. Essentially, I am trying to penalize different in the intensity of the two pixels in the reconstructed image. For this I minimize |Ax-b|+ \lambda |F(X)| where F(x)= (x_i - x_i+1)^2 is a quadratic function that penalizes the difference intensity of two nearest pixels. I am however unable to decide how to fix the value of \lambda (strength of regularization). In literature I found ways to find \lambda for the case of norm regularization using Lagrange multipliers. However, I am unable to find/formulate a method to find optimal \lambda for this case. Any1 has any idea about how to deal with it?

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Usually lambda would be determined by some kind of cross-validation or bootstrapping, i.e. fit random subsets of the data.

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I was searching if one can derive an analytical expression for finding \lambda? it is becoming computationally very expensive to use a bootstrapping method. –  SPB Jan 2 '13 at 16:41

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