Synthesis and analysis in total variation regularization

Abstract

We generalize the bridge between analysis and synthesis estimators by Elad, Milanfar and Rubinstein (2007) to rank deficient cases. This is a starting point for the study of the connection between analysis and synthesis for total variation regularized estimators. In particular, the case of first order total variation regularized estimators over general graphs and their synthesis form are studied. We give a definition of the discrete graph derivative operator based on the notion of line graph and provide examples of the synthesis form of $k^{\text{th}}$ order total variation regularized estimators over a range of graphs.

References in corpus (4)

• On the Prediction Performance of the Lasso
• Optimal rates for total variation denoising
• The DFS Fused Lasso: Linear-Time Denoising over General Graphs
• Sandpile groups and spanning trees of directed line graphs

Cited by in corpus (4)

• Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation
• Hemodynamic Deconvolution Demystified: Sparsity-Driven Regularization at Work
• Oracle inequalities for square root analysis estimators with application to total variation penalties
• A causal fused lasso for interpretable heterogeneous treatment effects estimation