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

TL;DR

This work addresses non-convex inverse problems in medical imaging by leveraging a Total $p$-Variation regularizer and an incremental optimization scheme that uses a Chambolle–Pock primal–dual solver with iterative reweighting. It introduces incDG, a hybrid framework that embeds pretrained neural networks to provide high-quality initializations at each incremental step, enabling faster convergence while preserving model-based robustness, and it supports ground-truth-free training. The method demonstrates superior accuracy and stability over traditional MB solvers and pure DL approaches on deblurring and CT reconstruction tasks, with notable speedups in tomographic reconstruction from subsampled data. The results indicate practical viability for clinical workflows, offering fast, reliable image enhancement with reduced dependency on ground-truth data for training.

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.

Figures (9)

• Figure 1: Sketch of the considered incremental approaches, applied to tomographic image reconstruction.
• Figure 2: Plots of the $p$-norm functions $||x||_p$ for different values of $p$. The curves correspond to different values of $p$: $p=0$ (blue), $p=1$ (brown), and intermediate values approaching $p\to 0$. They illustrate the loss of convexity for $p<1$ and the non-differentiability characteristic of the $\ell_0$.
• Figure 3: Scheme of the ResUNet architecture used to define the image-to-image operators $\Psi^{(h)}$ for the Deep Guess step.
• Figure 4: Experiments performed on a COULE test sample for image deblurring and denoising. On the top, from left to right: the ground truth image with a red rectangle depicting the zoomed area, containing a very low contrast ellipse marked by yellow arrows and a subtle line indicated by a blue arrow; the simulated $\boldsymbol{y}$ image, affected by blur and noise; the solutions of the $T{\it p}V$-regularized model with fixed or variable regularization weights. On the bottom: the solutions obtained using inc$T{\it p}V$, incNN and incDG schemes, with the corresponding zoomed regions of interest.
• Figure 5: Experiments performed on COULE test samples for image deblurring and denoising. At the top: one ground truth image and the solutions obtained using inc$T{\it p}V$, incNN and incDG schemes, with the corresponding zoomed regions of interest. At the bottom: boxplot comparisons of the RE metrics (left) and SSIM metrics (right), computed over the entire test set.