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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: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...
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.
The paper presents convergence guarantees for Plug-and-Play (PnP) image restoration algorithms that use annealed noise levels, covering both deterministic and stochastic methods. It identifies explicit nonconvex objectives linked to the final denoising level and proves that iterates become asymptotically stationary with respect to these objectives, without requiring a specific noise decay schedule. The authors validate their theory experimentally on tasks such as inpainting, super‑resolution, demosaicing, and tomography.
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 a highly efficient variational approximation for Gaussian Mixture Models (GMMs) with arbitrary covariances, integrated with mixtures of factor analyzers. This method reduces the per‑iteration runtime from ≠O(NCD^2) to a complexity that scales linearly with dimensionality D and sublinearly with the product NC. Experiments demonstrate sublinear scaling across the entire optimization, order‑of‑magnitude speed‑ups on large benchmarks, training of GMMs with over 10 billion parameters in under nine hours on a single CPU, and competitive zero‑shot image denoising performance.