A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization
This work addresses inverse problems in domains like imaging or signal processing where supervised data is limited, offering a novel method that is incremental over existing autoencoder-based approaches.
The paper tackles the problem of solving inverse problems with scarce supervised training pairs by introducing a paired autoencoder framework that learns mappings between latent spaces, achieving improved performance in scenarios with abundant unsupervised data.
In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are used to efficiently represent the input and target spaces separately and optimal mappings are learned between latent spaces, thus enabling forward and inverse surrogate mappings. We focus on interpretations using Bayes risk and empirical Bayes risk minimization, and we provide various theoretical results and connections to existing works on low-rank matrix approximations. Similar to end-to-end approaches, our paired approach creates a surrogate model for forward propagation and regularized inversion. However, our approach outperforms existing approaches in scenarios where training data for unsupervised learning are readily available but training pairs for supervised learning are scarce. Furthermore, we show that cheaply computable evaluation metrics are available through this framework and can be used to predict whether the solution for a new sample should be predicted well.