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Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
- Source :
- SIAM Journal on Imaging Sciences. 14:1532-1564
- Publication Year :
- 2021
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2021.
-
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.
- Subjects :
- FOS: Computer and information sciences
Computer science
business.industry
Computer Vision and Pattern Recognition (cs.CV)
Applied Mathematics
General Mathematics
Deep learning
Computer Science - Computer Vision and Pattern Recognition
Mathematics::Optimization and Control
Iterative reconstruction
Function (mathematics)
Regularization (mathematics)
Statistics::Machine Learning
Norm (mathematics)
Applied mathematics
Learning based
Artificial intelligence
Descent algorithm
business
Subjects
Details
- ISSN :
- 19364954
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Imaging Sciences
- Accession number :
- edsair.doi.dedup.....3faff4e52cd4960de43891573aee39b2