论文标题
逆问题的正则化：深度平衡模型与双重学习
Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning
论文作者
论文摘要
变分正规化方法通常用于近似反问题的解决方案。近年来，基于模型的变异正则化方法经常被数据驱动的方法（例如Expert模型）取代（Roth and Black，2009）。培训此类数据驱动方法的参数可以作为双层优化问题。在本文中，我们比较了培训数据驱动的变分正规化模型的框架与深度平衡模型的新框架（Bai，Kolter和Koltun，2019年），最近在反问题的背景下引入了（Gileton，Ongie，Ongie和Willett，20211年）。我们表明，使用固定点迭代计算双层公式中的低级优化问题是深度平衡框架的特殊情况。我们将这两种方法都在计算上比较，并与多种数值示例进行了脱氧，内部和反卷积的反相反问题。
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert model (Roth and Black, 2009). Training the parameters of such data-driven methods can be formulated as a bilevel optimization problem. In this paper, we compare the framework of bilevel learning for the training of data-driven variational regularization models with the novel framework of deep equilibrium models (Bai, Kolter, and Koltun, 2019) that has recently been introduced in the context of inverse problems (Gilton, Ongie, and Willett, 2021). We show that computing the lower-level optimization problem within the bilevel formulation with a fixed point iteration is a special case of the deep equilibrium framework. We compare both approaches computationally, with a variety of numerical examples for the inverse problems of denoising, inpainting and deconvolution.
