Learned Regularization for Inverse Problems: Insights from a Spectral Model
This work offers theoretical insights for researchers in inverse problems, but it is incremental as it builds on existing spectral models without presenting new empirical results.
The authors investigated state-of-the-art learning approaches for inverse problems using a spectral model to analyze regularization properties, bias, and data dependence, providing a theoretical framework for future studies.
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit.