On the Degrees of Freedom in Total Variation Minimization
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Journal Volume
2020-May
ISBN
9781509066315
Date Issued
2020-05-01
Author(s)
Xue, Feng
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.
Subjects
Degrees of freedom (DOF) | duality | Stein's unbiased risk estimate (SURE) | total variation (TV) regularization
SDGs
Type
conference paper