2016/12/08 by Charles‐Alban Deledalle, Nicolas Papadakis, Deledalle, Charles-Alban +5
Computer Science · Engineering · Medicine · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Medical Imaging Techniques and Applications #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1612.03080
openalex publication_date 2016/12/08 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dimensional case, that appears reasonably tight in practice. This problem is directly linked to the computation of the pseudo-inverse of the divergence, which can be quickly obtained by performing convolutions in the Fourier domain.