Deep End-to-End Posterior ENergy (DEEPEN) for image recovery
This work addresses the challenge of efficient and robust image recovery for applications like medical imaging or photography, providing a novel method that combines advantages of existing approaches.
The paper tackles the problem of image reconstruction by introducing the DEEPEN framework, which enables both MAP estimation and sampling from the posterior distribution, offering improved performance over current E2E and PnP models and faster sampling compared to diffusion models.
Current end-to-end (E2E) and plug-and-play (PnP) image reconstruction algorithms approximate the maximum a posteriori (MAP) estimate but cannot offer sampling from the posterior distribution, like diffusion models. By contrast, it is challenging for diffusion models to be trained in an E2E fashion. This paper introduces a Deep End-to-End Posterior ENergy (DEEPEN) framework, which enables MAP estimation as well as sampling. We learn the parameters of the posterior, which is the sum of the data consistency error and the negative log-prior distribution, using maximum likelihood optimization in an E2E fashion. The proposed approach does not require algorithm unrolling, and hence has a smaller computational and memory footprint than current E2E methods, while it does not require contraction constraints typically needed by current PnP methods. Our results demonstrate that DEEPEN offers improved performance than current E2E and PnP models in the MAP setting, while it also offers faster sampling compared to diffusion models. In addition, the learned energy-based model is observed to be more robust to changes in image acquisition settings.