Experimental results on both grayscale and color image restoration demonstrate that the proposed method consistently outperforms representative model-based approaches while achieving performance comparable to state-of-the-art DEQ models based on implicit regularization, despite requiring substantially fewer trainable parameters.
Abstract
We propose a deep learning framework for image restoration from images degraded by both multiplicative Gamma noise and blur. Unlike conventional deep equilibrium (DEQ) models that rely on implicit neural regularization, the proposed method learns an explicit and interpretable regularizer parameterized by geometric priors associated with surface area and mean curvature. To minimize the resulting variational model, we develop a mirror descent algorithm tailored to the commonly used Gamma-noise fidelity terms. Leveraging the Kurdyka-Lojasiewicz property for functions defined in $o$-minimal structures, we establish the global convergence of the generated iterates to a critical point. Experimental results on both grayscale and color image restoration demonstrate that the proposed method consistently outperforms representative model-based approaches while achieving performance comparable to state-of-the-art DEQ models based on implicit regularization, despite requiring substantially fewer trainable parameters.
A model-based deep denoising framework that integrates three tightly coupled components, and proves that every limit point of the L-ADMM sequence is a stationary point of the nonconvex objective, and that the iterate sequence itself converges globally.
Abstract.
We describe a practical framework for data-driven regularization in image reconstruction. It combines model expressivity with the guarantees of variational methods. The approach is based on a weakly convex ridge regularizer, defined as the composition of a convolutional filter bank and pointwise potentials constrained to be weakly convex. These potentials are implemented as learnable splines with a strict control of their weak-convexity modulus. The resulting denoisers outperform classic convex regularization techniques as well as competitive benchmarks such as BM3D, while they still correspond to the minimization of a convex energy. The learned regularizers further extend to general inverse problems with provable convergence to critical points. Overall, this framework shows that a controlled relaxation of convexity enables the design of learnable priors that achieve strong empirical performance while preserving mathematical guarantees.
Alexis Goujon, Sebastian Neumayer, Stanislas Ducotterd et al.· SIAM Review· 0 citations
Results demonstrate the effectiveness of empirical reference statistics as a non-parametric prior for image inpainting by showing that the proposed method outperforms Mean Fill, Telea, and Navier-Stokes inpainting in PSNR, SSIM, and visual quality.
All-in-one Image Restoration (AIR) seeks to address diverse degradations using a unified model trained only once. Existing methods often rely on degradation-specific guidance, leading to conflicting gradients during training. In contrast, diffusion models offer a promising alternative by operating in a high-noise space where diverse degradations exhibit a homogeneous Gaussian distribution. This characteristic alleviates gradient conflicts associated with task-specific degradations. However, existing diffusion-based AIR methods often suffer from a lack of direct supervision in the image space, leading to error accumulation during the iterative denoising process and image fidelity compromisation. This highlights a fundamental dilemma for AIR: the optimal space for modeling degradations is inherently suboptimal for preserving image fidelity. To address this issue, we propose a Virtual Consistency Model for AIR (VCMAIR), which restores images in the high-noise space while employing a novel consistency function to enforce accurate supervision in the image space. Extensive experiments demonstrate that the proposed method outperforms existing state-of-the-art methods across a comprehensive benchmark of diverse degradation scenarios, including both standard AIR tasks and challenging real-world image restoration tasks.
Jiawei Wu, Luwei Tu, Zhe Wang et al.· IEEE Transactions on Image P...· 0 citations
We propose a unified variational framework for image segmentation under sparse pixel-level supervision. Our method is based on a simplex-constrained Potts model with a smooth perimeter regularizer, yielding a convex, smooth energy functional that can be used as a training loss in weakly supervised deep learning paradigms or optimized efficiently using iterative methods. Sparse labels are incorporated by constructing a fuzzy membership function via a function extension problem in a Reproducing Kernel Hilbert Space (RKHS), which effectively captures inhomogeneous intensity statistics. The derived discrete loss for training standard networks demonstrates robustness and consistent improvements over non-training and partial cross-entropy (PCE) baselines in experiments, achieving comparable performance without requiring ground-truth segmentation images.
Yin-King Chu, Lingfeng Li, Sung-Hack Kang et al.· Journal of Mathematical Imag...· 0 citations
Experiments on AAPM and DeepLesion under multiple sparse-view and noise settings show that CG-GLORE achieves strong quantitative performance, stable convergence, lower noise power, and improved visual fidelity compared with representative reconstruction methods.
Tran Xuan Hieu Le, D. C. Bui, V. Le et al.· 0 citations
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