# Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

arXiv: https://arxiv.org/abs/2007.11245 · HTML: https://mlsanity.com/paper/2007.11245/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2020.

## Built on by (most cited first, 15 of 15)

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- [Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2104.12939/) (2021)
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- [DULDA: Dual-domain Unsupervised Learned Descent Algorithm for PET image reconstruction](https://mlsanity.com/paper/2303.04661/) (2023)
- [LAMA: Stable Dual-Domain Deep Reconstruction For Sparse-View CT](https://mlsanity.com/paper/2410.21111/) (2024)
- [A Learned Proximal Alternating Minimization Algorithm and Its Induced Network for a Class of Two-block Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2411.06333/) (2024)
- [LAMA-Net: A Convergent Network Architecture for Dual-Domain Reconstruction](https://mlsanity.com/paper/2507.22316/) (2025)
- [Transferable Optimization Network for Cross-Domain Image Reconstruction](https://mlsanity.com/paper/2603.07831/) (2026)

## Abstract (arXiv)

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 l2,1 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.