 For the numerical realisation of the model, we consider a converging ADMM algorithm. Differently from 1%DIFDELCMD < ]%%% , 2%DIFDELCMD < ]%%% , where approximate graph cuts and dynamic programming techniques were used for solving the non-convex substeps in the case of multivariate data, the proposed splitting allows to compute explicitly their solution by means of hard-thresholding and standard conjugate-gradient solvers.
<clarity>  For the numerical realisation of the model, we consider a converging ADMM algorithm. Differently from 1%DIFDELCMD < ]%%% , 2%DIFDELCMD < ]%%% , where approximate graph cuts and dynamic programming techniques were used for solving the non-convex substeps in the case of multivariate data, the proposed splitting allows to compute explicitly their solution by means of hard-thresholding and standard conjugate-gradient solvers.
 For the numerical realisation of the model, we 1%DIFDELCMD < ]%%% , 2%DIFDELCMD < ]%%% , where approximate graph cuts and dynamic programming techniques were used for solving the non-convex substeps in the case of multivariate data, the proposed splitting allows to compute explicitly their solution by means of hard-thresholding and standard conjugate-gradient solvers.