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

2025/05/13 by Morotti, Elena
#Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2505.08324

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 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.

Citations

• Deep Guess acceleration for explainable image reconstruction in sparse-view CT
• Ambiguity in solving imaging inverse problems with deep learning based operators
• Bilevel learning of regularization models and their discretization for image deblurring and super-resolution
• Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling
• To be or not to be stable, that is the question: understanding neural networks for inverse problems
• Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging: Theory, algorithms, and applications
• The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks
• Do CNNs solve the CT inverse problem?
• The gap between theory and practice in function approximation with deep neural networks
• Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging
• Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing
• Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing
• ResUNet++: An Advanced Architecture for Medical Image Segmentation
• Plug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery
• Low-Dose CT via Deep CNN with Skip Connection and Network in Network
• Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT
• Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis
• TU-FG-207A-04: Overview of the Low Dose CT Grand Challenge
• U-Net: Convolutional Networks for Biomedical Image Segmentation
• Bilevel approaches for learning of variational imaging models
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
• Sparse Recovery using Smoothed ℓ⁰ (SL0): Convergence Analysis
• A fast approach for overcomplete sparse decomposition based on smoothed L0 norm
• Iteratively re-weighted least squares minimization for sparse recovery
• Iteratively reweighted least squares minimization for sparse recovery
• Enhancing Sparsity by Reweighted L1 Minimization

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