Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902698 | Applied Numerical Mathematics | 2018 | 13 Pages |
Abstract
Popular methods for finding regularized solutions to inverse problems include sparsity promoting â1 regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several higher order (HO) methods similar to TV have been proposed, which we generally refer to as HOTV methods. In this letter, we investigate the problem of the often debated selection of λ, the parameter used to carefully balance the interplay between data fitting and regularization terms. We theoretically argue for a scaling of the operators for a uniform parameter selection for all orders of HOTV regularization. In particular, parameter selection for all orders of HOTV may be determined by scaling an initial parameter for TV, which the imaging community may be more familiar with. We also provide several numerical results which justify our theoretical findings.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Toby Sanders,