# FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging

arXiv: https://arxiv.org/abs/2008.02683 · HTML: https://mlsanity.com/paper/2008.02683/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2020.

## Built on by (most cited first, 30 of 74)

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- [Patch-Based Denoising Diffusion Probabilistic Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2211.10388/) (2022)
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- [Multi-domain Integrative Swin Transformer network for Sparse-View Tomographic Reconstruction](https://mlsanity.com/paper/2111.14831/) (2021)
- [Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A survey](https://mlsanity.com/paper/2203.15725/) (2022)
- [Diffusion Prior Regularized Iterative Reconstruction for Low-dose CT](https://mlsanity.com/paper/2310.06949/) (2023)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [Optimal MRI Undersampling Patterns for Ultimate Benefit of Medical Vision Tasks](https://mlsanity.com/paper/2108.04914/) (2021)
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- [Parallel Diffusion Model-based Sparse-view Cone-beam Breast CT](https://mlsanity.com/paper/2303.12861/) (2023)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [A Trust-Guided Approach to MR Image Reconstruction with Side Information](https://mlsanity.com/paper/2501.03021/) (2025)
- [Deep Geometric Distillation Network for Compressive Sensing MRI](https://mlsanity.com/paper/2107.04943/) (2021)
- [Robust PCA Unrolling Network for Super-resolution Vessel Extraction in X-ray Coronary Angiography](https://mlsanity.com/paper/2204.08466/) (2022)
- [QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2402.17951/) (2024)
- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)
- [Convergent Data-driven Regularizations for CT Reconstruction](https://mlsanity.com/paper/2212.07786/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [DISTA-Net: Dynamic Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2505.19148/) (2025)
- [Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers](https://mlsanity.com/paper/2504.19000/) (2025)
- [Convolutional Sparse Coding Fast Approximation with Application to Seismic Reflectivity Estimation](https://mlsanity.com/paper/2106.15296/) (2021)
- [ℓ1DecNet+: A new architecture framework by ℓ1 decomposition and iteration unfolding for sparse feature segmentation](https://mlsanity.com/paper/2203.02690/) (2022)
- [Low-Dose CT Using Denoising Diffusion Probabilistic Model for 20× Speedup](https://mlsanity.com/paper/2209.15136/) (2022)
- [Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL](https://mlsanity.com/paper/2304.11238/) (2023)
- [Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems](https://mlsanity.com/paper/2307.16120/) (2023)
- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [Multi-frequency Electrical Impedance Tomography Reconstruction with Multi-Branch Attention Image Prior](https://mlsanity.com/paper/2409.10794/) (2024)
- [An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling](https://mlsanity.com/paper/2412.01051/) (2024)
- [Tomographic Foundation Model -- FORCE: Flow-Oriented Reconstruction Conditioning Engine](https://mlsanity.com/paper/2506.02149/) (2025)
- [SeqCSIST: Sequential Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2507.09556/) (2025)

## Abstract (arXiv)

Inverse problems are essential to imaging applications. In this paper, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.