One-dimensional total variation denoising (${\hat{\mu }}_{\lambda }=\arg {\min }_{\mu }\{\Vert Y-\mu {\Vert }_2^2/(2n)+\lambda {\sum }_i|{\mu }_{i+1}-{\mu }_i|\}$)

This version of the fused Lasso penalizes only adjacent differences. It estimates a piecewise-constant signal while preserving an unpenalized constant level. Larger penalties generally favour fewer fitted changes.