MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model
This work addresses image reconstruction in medical imaging (e.g., MRI) by providing theoretical guarantees, which is important for reliability in clinical applications, though it is incremental as it builds on existing energy models.
The authors tackled the problem of image recovery in inverse problems by proposing a multi-scale deep energy model that is locally convex around the data manifold, ensuring uniqueness, convergence guarantees, and robustness. In parallel MR image reconstruction, their method outperformed state-of-the-art convex regularizers and was competitive with plug-and-play and end-to-end methods.
We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative log-prior as a multi-scale energy model parameterized by a Convolutional Neural Network (CNN). We restrict the gradient of the CNN to be locally monotone, which constrains the model as a Locally Convex Multi-Scale Energy (LC-MuSE). We use the learned energy model in image-based inverse problems, where the formulation offers several desirable properties: i) uniqueness of the solution, ii) convergence guarantees to a minimum of the inverse problem, and iii) robustness to input perturbations. In the context of parallel Magnetic Resonance (MR) image reconstruction, we show that the proposed method performs better than the state-of-the-art convex regularizers, while the performance is comparable to plug-and-play regularizers and end-to-end trained methods.