Learning optimal nonlinearities for iterative thresholding algorithms
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Abstract (arXiv)
Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Dec 2015.
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Citing papers per year: 2021: 3; 2022: 0; 2023: 1.
4 papers.
- 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
- 2021Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networkscited by 11
- 2021Learning Generative Prior with Latent Space Sparsity Constraintscited by 1
- 2023A statistical perspective on algorithm unrolling models for inverse problemscited by 0
- 2023A statistical perspective on algorithm unrolling models for inverse problems10 Nov 2023
- 2021Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks8 Dec 2021
- 2021Learning Generative Prior with Latent Space Sparsity Constraints25 May 2021
- 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees22 Jan 2021