https://scholars.lib.ntu.edu.tw/handle/123456789/640463
標題: | On the Degrees of Freedom in Total Variation Minimization | 作者: | Xue, Feng THIERRY BLU |
關鍵字: | Degrees of freedom (DOF) | duality | Stein's unbiased risk estimate (SURE) | total variation (TV) regularization | 公開日期: | 1-五月-2020 | 卷: | 2020-May | 來源出版物: | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings | 摘要: | 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 |
顯示於: | 電機工程學系 |
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