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

TL;DR

This paper introduces incDG, a hybrid AI and model-based optimization framework that efficiently solves non-convex inverse problems in medical imaging, outperforming traditional methods in accuracy and stability.

Contribution

The paper presents incDG, a novel hybrid approach combining deep learning with incremental model-based optimization for non-convex inverse problems, with no need for ground truth training data.

Findings

incDG outperforms conventional iterative solvers in accuracy.

incDG surpasses deep learning methods in stability and robustness.

Training incDG without ground truth maintains high performance.

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.