Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

• URL: http://arxiv.org/abs/2007.11245v5
• Date: Sat, 3 Sep 2022 10:55:02 GMT
• Title: Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
• Authors: Yunmei Chen, Hongcheng Liu, Xiaojing Ye, Qingchao Zhang
• Abstract summary: We propose a general learning based framework for solving nonsmooth non image reconstruction problems. We show that the proposed is-efficient convergence state-of-the-art methods in an image problems in training.
• Score: 4.2476585678737395
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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