Latent Fused Lasso

Fused lasso norm is classically adopted to model sparse piecewise constant signals, however it is not the convex hull of the best representation of such simultaneously structured signal. In this paper, we propose a convex variational norm for better modeling sparse piecewise constant signals. The norm is based on (1) promoting sparsity in first-order difference with total variation norm and (2) exploiting latent group structure in first-order difference with simple linear constraints. We demonstrate the proposed norm outperforms fused lasso norm in a denoising setup with numerical experiments.