The article reviews how spatially adaptive regularisation weight functions can be incorporated into variational image reconstruction models like Total Variation and Total Generalised Variation. It discusses the regularity properties of these weights—constant, continuous, or piecewise constant—and how they influence edge and detail preservation. The authors highlight recent hybrid methods that learn low‑regularity weights via deep neural networks, demonstrating their effectiveness in image denoising and MRI reconstruction.
arXiv:2608. 04944v1 Announce Type: cross Abstract: We propose a deep learning framework for image restoration from images degraded by both multiplicative Gamma noise and blur.
The paper introduces CM-RED, a fast MRI reconstruction method that combines a pretrained consistency model with the regularization by denoising framework. By integrating controlled noise injection into accelerated proximal gradient updates, CM-RED achieves high‑quality reconstructions on fastMRI knee and brain datasets with only four network function evaluations. It consistently outperforms existing diffusion‑ and consistency‑based approaches in quantitative metrics, visual fidelity, and robustness to hyperparameter changes.
arXiv:2609.25429v1 Announce Type: new Abstract: In this paper, we introduce the Directional Total Variation-Regularized Implicit Neural Representation (DTV-INR), an advanced variational paradigm that...
arXiv:2609.00036v1 Announce Type: new Abstract: The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edges a...
arXiv:2608. 15246v1 Announce Type: cross Abstract: Sparse-view computed tomography (CT) reduces radiation dose by acquiring fewer projection views, but the resulting inverse problem is highly ill-posed and often produces severe streak artifacts.
arXiv:2609.00036v2 Announce Type: replace Abstract: The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edg...
arXiv:2608.29227v1 Announce Type: new Abstract: In this work we propose a novel non-linear diffusion filtering approach for images based on their channel representation. To derive the diffusion updat...
arXiv:2609.22950v1 Announce Type: cross Abstract: While compressed-sensing regularizers enable interpretable reconstruction of 4D Flow CMR through transparent variational objectives, their hand-craft...
The paper introduces a perceptually regularized diffusion framework for image super‑resolution, adding perceptual‑loss based regularization to the standard diffusion training objective. This approach incorporates prior knowledge to improve training convergence and encourages the recovery of meaningful image features. Experiments on benchmark datasets show enhanced perceptual quality while maintaining competitive distortion metrics.
MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations.
Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely used in medical imaging. While sparse-view acquisition can lower radiation exposure, it makes DECT material decomposition even more challenging, as the problem is nonlinear and ill-posed.
arXiv:2606.30159v2 Announce Type: replace Abstract: Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely us...