Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms
This work addresses image reconstruction in medical imaging (CT and MRI) by providing a data-driven method with strong guarantees, though it is incremental in combining learning with convex optimization principles.
The authors tackled the problem of image reconstruction by learning weakly convex regularizers that yield convex energy minimization, resulting in denoisers that outperform convex-regularization methods and BM3D, with fewer than 15,000 parameters and provable convergence for CT and MRI reconstruction.
We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal-processing interpretation as they mimic handcrafted sparsity-promoting regularizers. Through numerical experiments, we show that such denoisers outperform convex-regularization methods as well as the popular BM3D denoiser. Additionally, the learned regularizer can be deployed to solve inverse problems with iterative schemes that provably converge. For both CT and MRI reconstruction, the regularizer generalizes well and offers an excellent tradeoff between performance, number of parameters, guarantees, and interpretability when compared to other data-driven approaches.