Regularization theory of the analytic deep prior approach. (26th September 2022)

• Record Type: Journal Article
• Authors: Arndt, Clemens
• Is Part Of: Inverse problems. Volume 38:Number 11(2022)
• Publication Date: 2022-09-26
• Subjects: analytic deep prior -- deep image prior -- Tikhonov regularization -- Ivanov regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac9011
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The analytic deep prior (ADP) approach was recently introduced for the theoretical analysis of deep image prior (DIP) methods with special network architectures. In this paper, we prove that ADP is in fact equivalent to classical variational Ivanov methods for solving ill-posed inverse problems. Besides, we propose a new variant which incorporates the strategy of early stopping into the ADP model. For both variants, we show how classical regularization properties (existence, stability, convergence) can be obtained under common assumptions.