# Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction

arXiv: https://arxiv.org/abs/2104.12939 · HTML: https://mlsanity.com/paper/2104.12939/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 130 references that are in the map.
- First posted on arXiv 27 Apr 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Can Deep Learning Outperform Modern Commercial CT Image Reconstruction Methods?](https://mlsanity.com/paper/1811.03691/) (2018)
- [Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction](https://mlsanity.com/paper/1803.00694/) (2018)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2008.00406/) (2020)
- [What are the Receptive, Effective Receptive, and Projective Fields of Neurons in Convolutional Neural Networks?](https://mlsanity.com/paper/1705.07049/) (2017)
- [PWLS-ULTRA: An Efficient Clustering and Learning-Based Approach for Low-Dose 3D CT Image Reconstruction](https://mlsanity.com/paper/1703.09165/) (2017)
- [Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction](https://mlsanity.com/paper/2007.11245/) (2020)
- [Convolutional Analysis Operator Learning: Acceleration and Convergence](https://mlsanity.com/paper/1802.05584/) (2018)
- [Transfer Learning for Scientific Data Chain Extraction in Small Chemical Corpus with BERT-CRF Model](https://mlsanity.com/paper/1905.05615/) (2019)
- [BCD-Net for Low-dose CT Reconstruction: Acceleration, Convergence, and Generalization](https://mlsanity.com/paper/1908.01287/) (2019)
- [Deep Parallel MRI Reconstruction Network Without Coil Sensitivities](https://mlsanity.com/paper/2008.01410/) (2020)
- [Deep Neural Network for 3D Surface Segmentation based on Contour Tree Hierarchy](https://mlsanity.com/paper/2008.11269/) (2020)
- [Convolutional Dictionary Learning: Acceleration and Convergence](https://mlsanity.com/paper/1707.00389/) (2017)
- [Multiscale Detection of Cancerous Tissue in High Resolution Slide Scans](https://mlsanity.com/paper/2010.00641/) (2020)
- [SPULTRA: Low-Dose CT Image Reconstruction with Joint Statistical and Learned Image Models](https://mlsanity.com/paper/1808.08791/) (2018)
- [Geometrically Matched Multi-source Microscopic Image Synthesis Using Bidirectional Adversarial Networks](https://mlsanity.com/paper/2010.13308/) (2020)
- [Segmentation with Residual Attention U-Net and an Edge-Enhancement Approach Preserves Cell Shape Features](https://mlsanity.com/paper/2001.05548/) (2020)
- [Momentum-Net for Low-Dose CT Image Reconstruction](https://mlsanity.com/paper/2002.12018/) (2020)

## Built on by (most cited first, 6 of 6)

- [Learned Alternating Minimization Algorithm for Dual-domain Sparse-View CT Reconstruction](https://mlsanity.com/paper/2306.02644/) (2023)
- [DiffKillR: Killing and Recreating Diffeomorphisms for Cell Annotation in Dense Microscopy Images](https://mlsanity.com/paper/2410.03058/) (2024)
- [SafeAug: Safety-Critical Driving Data Augmentation from Naturalistic Datasets](https://mlsanity.com/paper/2501.02143/) (2025)
- [Long Range Constraints for Neural Texture Synthesis Using Sliced Wasserstein Loss](https://mlsanity.com/paper/2211.11137/) (2022)
- [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)
- [Transferable Optimization Network for Cross-Domain Image Reconstruction](https://mlsanity.com/paper/2603.07831/) (2026)

## Abstract (arXiv)

We propose a provably convergent method, called Efficient Learned Descent Algorithm (ELDA), for low-dose CT (LDCT) reconstruction. ELDA is a highly interpretable neural network architecture with learned parameters and meanwhile retains convergence guarantee as classical optimization algorithms. To improve reconstruction quality, the proposed ELDA also employs a new non-local feature mapping and an associated regularizer. We compare ELDA with several state-of-the-art deep image methods, such as RED-CNN and Learned Primal-Dual, on a set of LDCT reconstruction problems. Numerical experiments demonstrate improvement of reconstruction quality using ELDA with merely 19 layers, suggesting the promising performance of ELDA in solution accuracy and parameter efficiency.