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.

翻译：最近引入了分析前深层(ADP)方法,用于理论分析具有特殊网络结构的深层图像前(DIP)方法。在本文中,我们证明ADP实际上等同于传统的变异Ivanov方法,用以解决错误的反向问题。此外,我们提出了一个新的变式,其中纳入了尽早停止进入ADP模式的战略。对于这两种变式,我们展示了在共同假设下如何获得典型的正规化特性(存在、稳定、趋同)。