Fully Smoothed ? 1-TV Models: Bounds for the Minimizers and Parameter Choice
We consider a class of convex functionals that can be seen as \(\mathcal{C}^{1}\) smooth approximations of the ? 1-TV model. The minimizers of such functionals were shown to exhibit a qualitatively different behavior compared to the nonsmooth ? 1-TV model (Nikolova et al. in Exact histogram specification for digital images using a variational approach, 2012). Here we focus on the way the parameters involved in these functionals determine the features of the minimizers\(\hat{u}\). We give explicit relationships between the minimizers and these parameters.
histogram specification parameter estimation for smoothed ? 1-tv model quantisation noise ? ? error convex optimization