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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.

Anyone has any idea about how to deal with it?

Does anyone know if there exists a analytical form for optimal \lambda?

Sparky
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user1943646
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2 Answers2

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Regularization methods. They have a long history in computer vision. A good review to start from (expecially for the references it provides) is this one:

http://yaroslavvb.com/papers/chen-on.pdf

Francesco Callari
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  • Hi, Could you assist in: http://scicomp.stackexchange.com/questions/17528/minimization-of-the-blind-deconvolution-functional Thank You. – Royi Dec 22 '14 at 16:35
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There's not an optimal lambda unless there's some other constraint that you want to satisfy.

Depending on what your application is, simply taking a look at the images and deciding if you like what you see may be a good idea.

Or, if you're really after compression - for performance or storage reasons - tune lambda to leave as much detail as possible while attaining your performance requirement, or perhaps to give you a little bit of wiggle room if necessary.

Phillip Chilton Adkins
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