The Lasso is an attractive regularisation method for high dimensional regression. It combines variable selection with an efficient computational procedure. However, the rate of convergence of the Lasso is slow for some sparse high dimensional data, where the number of predictor variables is growing fast with the number of observations. Moreover, many noise variables are selected if the estimato...

Given a bounded open set Ω ⊂ ℝ 2 , we study the relaxation of nonparametric area functional in strict topology BV (Ω; ). and compute it for vortex-type maps, more generally maps W 1,1 (Ω;S 1 ) having finite number topological singularities. We also extend analysis to some specific piecewise constant ), including symmetric triple junction map.