https://scholars.lib.ntu.edu.tw/handle/123456789/640463
Title: | On the Degrees of Freedom in Total Variation Minimization | Authors: | Xue, Feng THIERRY BLU |
Keywords: | Degrees of freedom (DOF) | duality | Stein's unbiased risk estimate (SURE) | total variation (TV) regularization | Issue Date: | 1-May-2020 | Journal Volume: | 2020-May | Source: | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings | Abstract: | In the theory of linear models, the degrees of freedom (DOF) of an estimator play a pivotal role in risk estimation, as it quantifies the complexity of a statistical modeling procedure. Considering the total-variation (TV) regularization, we present a theoretical study of the DOF in Stein's unbiased risk estimate (SURE), under a very mild assumption. First, from the duality perspective, we give an analytic expression of the exact TV solution, with identification of its support. The closed-form expression of the DOF is derived based on the Karush-Kuhn-Tucker (KKT) conditions. It is also shown that the DOF is upper bounded by the nullity of a sub-analysis-matrix. The theoretical analysis is finally validated by the numerical tests on image recovery. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/640463 | ISBN: | 9781509066315 | ISSN: | 15206149 | DOI: | 10.1109/ICASSP40776.2020.9053816 |
Appears in Collections: | 電機工程學系 |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.