GSNR: Graph Smooth Null-Space Representation for Inverse Problems

• URL: http://arxiv.org/abs/2602.20328v1
• Date: Mon, 23 Feb 2026 20:24:00 GMT
• Title: GSNR: Graph Smooth Null-Space Representation for Inverse Problems
• Authors: Romario Gualdrón-Hurtado, Roman Jacome, Rafael S. Suarez, Henry Arguello,
• Abstract summary: Inverse problems in imaging are ill-posed, leading to infinitely many solutions consistent with the measurements due to the nontrivial null-space of the sensing matrix.<n>We propose Graph-Smooth Null-Space Representation (GSNR), a mechanism that imposes structure only into the invisible component.
• Score: 24.2377690980591
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inverse problems in imaging are ill-posed, leading to infinitely many solutions consistent with the measurements due to the non-trivial null-space of the sensing matrix. Common image priors promote solutions on the general image manifold, such as sparsity, smoothness, or score function. However, as these priors do not constrain the null-space component, they can bias the reconstruction. Thus, we aim to incorporate meaningful null-space information in the reconstruction framework. Inspired by smooth image representation on graphs, we propose Graph-Smooth Null-Space Representation (GSNR), a mechanism that imposes structure only into the invisible component. Particularly, given a graph Laplacian, we construct a null-restricted Laplacian that encodes similarity between neighboring pixels in the null-space signal, and we design a low-dimensional projection matrix from the $p$-smoothest spectral graph modes (lowest graph frequencies). This approach has strong theoretical and practical implications: i) improved convergence via a null-only graph regularizer, ii) better coverage, how much null-space variance is captured by $p$ modes, and iii) high predictability, how well these modes can be inferred from the measurements. GSNR is incorporated into well-known inverse problem solvers, e.g., PnP, DIP, and diffusion solvers, in four scenarios: image deblurring, compressed sensing, demosaicing, and image super-resolution, providing consistent improvement of up to 4.3 dB over baseline formulations and up to 1 dB compared with end-to-end learned models in terms of PSNR.

Related papers

• Spectral Collapse in Diffusion Inversion [44.781674986581244]
  Conditional diffusion inversion fails when the source domain is spectrally sparse compared to the target domain.<n>We propose Orthogonal Variance Guidance (OVG), an inference-time method that corrects the ODE dynamics to enforce the theoretical Gaussian noise magnitude.<n>OVG effectively restores photorealistic textures while preserving structural fidelity.
  arXiv  Detail & Related papers  (2026-02-09T17:53:21Z)
• STARK denoises spatial transcriptomics images via adaptive regularization [3.8065244182878613]
  We present an approach to denoising transcriptomics images that is particularly effective for uncovering cell identities in the numerical regime of ultra-low sequencing depths.<n>The method -- Spatial Transcriptomics via Adaptive Regularization and Kernel iterations (STARK) -- shows consistent improvement over the competing methods.
  arXiv  Detail & Related papers  (2025-12-10T06:19:13Z)
• VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment [48.147381011235446]
  3D Gaussian Splatting has recently emerged as an efficient solution for real-time novel view synthesis.<n>We propose a novel method that enhances the geometric representation of 3D Gaussians through view alignment.<n>Our method achieves state-of-the-art performance in both surface reconstruction and novel view synthesis.
  arXiv  Detail & Related papers  (2025-10-13T14:44:50Z)
• NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems [25.35772762396095]
  Non-linear Projections of the Null-Space (NPN) is a novel class of regularization.<n>NPN promotes solutions that lie in a low-dimensional projection of the sensing matrix's null-space with a neural network.<n>We provide theoretical guarantees on convergence and reconstruction accuracy when used within plug-and-play methods.
  arXiv  Detail & Related papers  (2025-10-02T02:45:06Z)
• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• Image denoising as a conditional expectation [0.0]
  Most common techniques estimate the true image as a projection to some subspace.<n>We propose an interpretation of a noisy image as a collection of samples drawn from a certain probability space.<n>We present a data-driven denoising method in which the true image is recovered as a conditional expectation.
  arXiv  Detail & Related papers  (2025-05-24T21:30:56Z)
• Point Cloud Denoising With Fine-Granularity Dynamic Graph Convolutional Networks [58.050130177241186]
  Noise perturbations often corrupt 3-D point clouds, hindering downstream tasks such as surface reconstruction, rendering, and further processing. This paper introduces finegranularity dynamic graph convolutional networks called GDGCN, a novel approach to denoising in 3-D point clouds.
  arXiv  Detail & Related papers  (2024-11-21T14:19:32Z)
• No Pose, No Problem: Surprisingly Simple 3D Gaussian Splats from Sparse Unposed Images [100.80376573969045]
  NoPoSplat is a feed-forward model capable of reconstructing 3D scenes parameterized by 3D Gaussians from multi-view images. Our model achieves real-time 3D Gaussian reconstruction during inference. This work makes significant advances in pose-free generalizable 3D reconstruction and demonstrates its applicability to real-world scenarios.
  arXiv  Detail & Related papers  (2024-10-31T17:58:22Z)
• Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data [5.591221518341613]
  Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight. We propose novel NLOS reconstruction models based on curvature regularization. We evaluate the proposed algorithms on both synthetic and real datasets.
  arXiv  Detail & Related papers  (2023-01-01T14:10:43Z)
• Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography [58.60249163402822]
  Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. The proposed OMR is more robust and performs significantly better than the previous state-of-the-art OMR approach.
  arXiv  Detail & Related papers  (2022-07-06T21:40:59Z)
• Hyperspectral Image Super-resolution via Deep Progressive Zero-centric Residual Learning [62.52242684874278]
  Cross-modality distribution of spatial and spectral information makes the problem challenging. We propose a novel textitlightweight deep neural network-based framework, namely PZRes-Net. Our framework learns a high resolution and textitzero-centric residual image, which contains high-frequency spatial details of the scene.
  arXiv  Detail & Related papers  (2020-06-18T06:32:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.