Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question

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

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.