I am struggling with transforming this eq. $$\beta^* = \arg \min_\beta \|\beta \ \ln H -\ln J\|^2_2 +\lambda\|\nabla \beta\|^2_2$$
to standard linear equation. I have looked into several papers that arg min part can be converted to least square problem, but I do not know, what to do with the rest of the formula.
On the other hand some of the solutions derivate a formula and set the equation to zero, but I am not really sure, if it is applicable to this example.
I found this formula in this paper http://www.cse.cuhk.edu.hk/leojia/projects/pencilsketch/npar12_pencil.pdf on the page 6.