The paper introduces a novel nonlinear diffusion scheme for image denoising, derived from a linear diffusion process applied in a value space tailored to specific application domains such as image compression, still-image acquisition, and medical imaging. It argues that this application-driven linear diffusion in the transformed space outperforms existing nonlinear diffusion techniques.
The paper introduces a tensor‑based functional for targeted image enhancement and denoising, incorporating application‑dependent and contextual information through explicit regularization. It establishes existence of a minimizer and discusses tensor symmetry constraints, convexity, and geometric interpretation. The framework demonstrates strong performance in nonlinear scenarios like gamma correction and targeted value‑range filtering, achieving results comparable to state‑of‑the‑art PDE‑based methods.
This article reviews recent diffusion‑based methods for generative lossy image compression, highlighting how these techniques encode a source into an embedding and use a diffusion model to iteratively refine the reconstruction during decoding. It discusses the role of auxiliary entropy models for transmitting the embedding, explores the use of diffusion models for information transmission via channel simulation, and frames the discussion within rate‑distortion‑perception theory, common randomness, and inverse‑problem connections. The review also identifies open challenges in the field.
arXiv:2608.22302v1 Announce Type: new Abstract: The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data...
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:2608.29172v1 Announce Type: new Abstract: We present a novel variational approach to a tensor-based total variation formulation which is called gradient energy total variation, GETV. We introdu...
arXiv:2605.11585v2 Announce Type: replace Abstract: This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtre...
A blind image denoising framework based on an infinite directional lower semi-frame (DLSF) is introduced for additive white Gaussian noise. The method estimates noise variance directly in the DLSF domain using joint covariance of four directional difference channels, then applies channel‑wise Wiener‑type shrinkage and canonical‑dual synthesis with data‑consistent iterative reconstruction. Experiments on three standard grayscale images show a mean relative noise‑estimation error of 3.28 % and average PSNR gains of 7.45 dB, improving to 8.31 dB at 30/255 noise.
The paper proposes a new covariance model for Denoising Diffusion Probabilistic Models (DDPMs) that captures non‑diagonal correlations and the power‑law frequency spectrum of natural images. Using a Kronecker‑factored DCT (K‑DCT) decomposition, the authors reduce computational complexity from quadratic to log‑linear, enabling efficient sampling with few steps. Experiments on CIFAR‑10, Celeb‑A, ImageNet, and LSUN demonstrate improved FID and likelihoods over previous state‑of‑the‑art samplers.
arXiv:2609.23268v1 Announce Type: new Abstract: Blind image deconvolution (BID) is a prominent research topic in the field of imaging sciences, given its significant practical applications. Most exis...
arXiv:2606. 04299v1 Announce Type: cross Abstract: We consider the problem of generating images whose internal structure -- defined by the distribution of patches across multiple scales -- matches that of a single reference image.
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.