χ2 Test for TV regularization parameter selection
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Total Variation (TV) regularization parameter selection can significantly affect the result of an image processing algorithm. The regularization parameter should be large enough so that an estimate an ill-posed problem can be found, but a parameter that is too large may add bias and lead to oversmoothing. Choice of regularization parameter is more difficult than with least squares or Tikhonov regularization because TV functional is nonlinear. In this work we the use residual properties of the data misfit and regularization functional to specify regularization parameter. In particular we identify the effective degrees of freedom of the regularized cost function and use a $\chi^2$ test to identify a regularization parameter. We will show results using the method with examples from digital image reconstruction.