Plug-and-Play Deep Energy Model for Inverse problems
This work addresses the need for convergence guarantees and more complex priors in PnP methods for image recovery, though it is incremental as it builds on existing PnP frameworks.
The paper tackled the lack of an energy-based formulation in traditional Plug-and-Play (PnP) image recovery methods by introducing a novel energy model that learns image priors via a CNN, resulting in improved performance in magnetic resonance image reconstruction.
We introduce a novel energy formulation for Plug- and-Play (PnP) image recovery. Traditional PnP methods that use a convolutional neural network (CNN) do not have an energy based formulation. The primary focus of this work is to introduce an energy-based PnP formulation, which relies on a CNN that learns the log of the image prior from training data. The score function is evaluated as the gradient of the energy model, which resembles a UNET with shared encoder and decoder weights. The proposed score function is thus constrained to a conservative vector field, which is the key difference with classical PnP models. The energy-based formulation offers algorithms with convergence guarantees, even when the learned score model is not a contraction. The relaxation of the contraction constraint allows the proposed model to learn more complex priors, thus offering improved performance over traditional PnP schemes. Our experiments in magnetic resonance image reconstruction demonstrates the improved performance offered by the proposed energy model over traditional PnP methods.