# An incremental algorithm for non-convex AI-enhanced medical image processing

arXiv: https://arxiv.org/abs/2505.08324 · HTML: https://mlsanity.com/paper/2505.08324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 82 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 26 of 26)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [MAXIM: Multi-Axis MLP for Image Processing](https://mlsanity.com/paper/2201.02973/) (2022)
- [ResUNet++: An Advanced Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1911.07067/) (2019)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [The gap between theory and practice in function approximation with deep neural networks](https://mlsanity.com/paper/2001.07523/) (2020)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis](https://mlsanity.com/paper/1611.06391/) (2016)
- [Bilevel approaches for learning of variational imaging models](https://mlsanity.com/paper/1505.02120/) (2015)
- [The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks](https://mlsanity.com/paper/2109.06098/) (2021)
- [Low-Dose CT via Deep CNN with Skip Connection and Network in Network](https://mlsanity.com/paper/1811.10564/) (2018)
- [Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging](https://mlsanity.com/paper/2001.01432/) (2020)
- [Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A survey](https://mlsanity.com/paper/2203.15725/) (2022)
- [Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling](https://mlsanity.com/paper/2301.05888/) (2023)
- [Do CNNs solve the CT inverse problem?](https://mlsanity.com/paper/2005.10755/) (2020)
- [To be or not to be stable, that is the question: understanding neural networks for inverse problems](https://mlsanity.com/paper/2211.13692/) (2022)
- [Ambiguity in solving imaging inverse problems with deep learning based operators](https://mlsanity.com/paper/2305.19774/) (2023)
- [Hybrid Skip: A Biologically Inspired Skip Connection for the UNet Architecture](https://mlsanity.com/paper/2207.04721/) (2022)
- [Bilevel learning of regularization models and their discretization for image deblurring and super-resolution](https://mlsanity.com/paper/2302.10056/) (2023)
- [Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization](https://mlsanity.com/paper/1308.5038/) (2013)

## Abstract (arXiv)

Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions, particularly in medical imaging, where the goal is to enhance clinically relevant features rather than merely minimizing global error. We propose incDG, a hybrid framework that integrates deep learning with incremental model-based optimization to efficiently approximate the ℓ0-optimal solution of imaging inverse problems. Built on the Deep Guess strategy, incDG exploits a deep neural network to generate effective initializations for a non-convex variational solver, which refines the reconstruction through regularized incremental iterations. This design combines the efficiency of Artificial Intelligence (AI) tools with the theoretical guarantees of model-based optimization, ensuring robustness and stability. We validate incDG on TpV-regularized optimization tasks, demonstrating its effectiveness in medical image deblurring and tomographic reconstruction across diverse datasets, including synthetic images, brain CT slices, and chest-abdomen scans. Results show that incDG outperforms both conventional iterative solvers and deep learning-based methods, achieving superior accuracy and stability. Moreover, we confirm that training incDG without ground truth does not significantly degrade performance, making it a practical and powerful tool for solving non-convex inverse problems in imaging and beyond.