Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
This work addresses image reconstruction problems for applications like medical imaging or computer vision, offering a versatile and parameter-efficient method, though it is incremental as it builds on existing optimization and learning techniques.
The paper tackles nonsmooth nonconvex image reconstruction by proposing a learnable descent algorithm that combines a deep convolutional neural network with provable convergence, achieving favorable performance compared to state-of-the-art methods in various image reconstruction tasks.
We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the guaranteed convergence of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice.