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

2025-05-13

AI Summary

This paper addresses the challenge of solving nonconvex regularized inverse problems in medical image reconstruction, where complex optimization landscapes often trap conventional methods in poor local minima. We propose incDG—a hybrid framework that employs a deep network to generate high-quality initial estimates (“Deep Guess”) and subsequently drives incremental nonconvex variational optimization toward ℓ₀-sparse solutions, augmented by truncated total variation (TpV) regularization to enhance structural preservation. Our approach introduces the novel paradigm of “deep initialization guidance + incremental nonconvex optimization,” enabling training without ground-truth supervision while ensuring theoretical stability and effectively escaping local minima. Evaluated on CT deblurring and tomographic reconstruction tasks, incDG achieves significantly higher accuracy and robustness than both classical iterative algorithms and end-to-end deep models. It further offers strong interpretability, generalizability, and training efficiency.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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 $ell_0$-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.

Problem

• Solving non-convex regularized inverse problems in medical imaging
• Integrating deep learning with incremental optimization for image reconstruction
• Enhancing accuracy and stability in medical image deblurring and tomography

Innovation

• Hybrid deep learning and model-based optimization framework
• Deep neural network initializes non-convex variational solver
• Combines AI efficiency with theoretical optimization guarantees