Parameter selection for HOTV regularization. (English) Zbl 1379.65032
Summary: Popular methods for finding regularized solutions to inverse problems include sparsity promoting \(\ell_1\) 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 \(\lambda\), 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.
MSC:
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65J22 | Numerical solution to inverse problems in abstract spaces |
| 65J10 | Numerical solutions to equations with linear operators |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
image reconstruction; regularization; inverse problems; higher-order total variation; parameter selection; numerical resultReferences:
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