Anisotropic Tensor Deconvolution of Hyperspectral Images

• URL: http://arxiv.org/abs/2601.11694v1
• Date: Fri, 16 Jan 2026 16:29:13 GMT
• Title: Anisotropic Tensor Deconvolution of Hyperspectral Images
• Abstract summary: Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.<n>We propose a framework based on a low-parsimonious parameters of Canonical Poly Decomposition (CPD)<n>This approach recasts the problem from recovering a large-scale image with a latent to estimating the factors with $(P+Q+N)R$ variables.
• Score: 24.509592365283208
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of the entire latent HSI $\mathbf{\mathcal{X}} \in \mathbb{R}^{P\times Q \times N}$.This approach recasts the problem from recovering a large-scale image with $PQN$ variables to estimating the CPD factors with $(P+Q+N)R$ variables.This model also enables a structure-aware, anisotropic Total Variation (TV) regularization applied only to the spatial factors, preserving the smooth spectral signatures.An efficient algorithm based on the Proximal Alternating Linearized Minimization (PALM) framework is developed to solve the resulting non-convex optimization problem.Experiments confirm the model's efficiency, showing a numerous parameter reduction of over two orders of magnitude and a compelling trade-off between model compactness and reconstruction accuracy.

Related papers

• A Cone-Constrained Bilinear Decomposition for Total Scaled-Gradient Variation Models [0.758305251912708]
  The total scaled-gradient variation (TSGV) regularizer has been shown to preserve edges and corners in image restoration.<n>To overcome this, we propose a tailored optimization problem governed by or sphere constraints.<n>In particular, the cone constraint plays a central role in characterizing edge and corner-preserving behavior.
  arXiv  Detail & Related papers  (2026-08-29T08:13:34Z)
• Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometry [0.0]
  This study builds upon works by arXiv:2307.15288v2 and arXiv:2506.11641v1 by extending representation consistency for convolutional layers.<n>We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings.
  arXiv  Detail & Related papers  (2026-07-01T09:16:37Z)
• Parameter Estimation in Stochastic Differential Equations via Wiener Chaos Expansion and Stochastic Gradient Descent [0.0]
  This study addresses the inverse problem of parameter estimation for Differential Equations (SDEs) by minimizing a regularized discrepancy via functional Gradient Descent (SGD)<n>To achieve computational efficiency, we leverage the Wiener Chaos Expansion (WCE), a spectral decomposition technique that projects the solution onto an basis of Hermites.<n>This transformation effectively maps the dynamics into a hierarchical system of functions, termed the textpropagator
  arXiv  Detail & Related papers  (2026-03-27T22:17:27Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization [7.193011407502236]
  We develop a novel primal-dual algorithm based on an augmented Lagrangian formulation, termed primal-dual variational inference (PD-VI)<n>PD-VI jointly updates global and local variational parameters in the evidence lower bound in a scalable manner.<n>We establish convergence guarantees for both PD-VI and P$2$D-VI under properly chosen constant step size.
  arXiv  Detail & Related papers  (2026-02-07T17:24:15Z)
• Analysis of Hessian Scaling for Local and Global Costs in Variational Quantum Algorithm [0.42970700836450487]
  We quantify the entrywise resolvability of the Hessian for Variational Quantum Algorithms.<n>We show two distinct scaling regimes that govern the sample complexity required to resolve Hessian entries against shot noise.
  arXiv  Detail & Related papers  (2026-01-31T15:49:23Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• Quantization through Piecewise-Affine Regularization: Optimization and Statistical Guarantees [13.571671030124604]
  Piecewise regularization (PAR) provides a flexible modelingization based on the statistical perspectives.<n>We show how to use the PAR method to solve problems using gradient, and Alternating Direction Multipliers.
  arXiv  Detail & Related papers  (2025-08-14T23:35:21Z)
• Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance [52.705112811734566]
  A novel diffusion-based framework is introduced for solving inverse problems using a piecewise guidance scheme.<n>The proposed method is problem-agnostic and readily adaptable to a variety of inverse problems.<n>The framework achieves a reduction in inference time of (25%) for inpainting with both random and center masks, and (23%) and (24%) for (4times) and (8times) super-resolution tasks.
  arXiv  Detail & Related papers  (2025-07-22T19:35:14Z)
• 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)
• sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation [8.802387139798808]
  We propose a novel framework for high-order principal component analysis (SHOPCA) that introduces a perspective to tensor-dependent decomposition.<n>We show that sparseGeoHOP supports in high-dimensional image settings and on ImageNet.
  arXiv  Detail & Related papers  (2025-06-10T10:30:48Z)
• Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computation [52.73824786627612]
  This paper establishes new convergence results for textitgeodesic strongly monotone games.<n>Our key result shows that RGD attains last-iterate linear convergence in a textitgeometry-agnostic fashion.<n>Overall, this paper presents the first geometry-agnostic last-iterate convergence analysis for games beyond the Euclidean settings.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR) [0.0]
  We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise-constant objects.
  arXiv  Detail & Related papers  (2022-04-21T00:03:44Z)
• Uncovering the Over-smoothing Challenge in Image Super-Resolution: Entropy-based Quantification and Contrastive Optimization [67.99082021804145]
  We propose an explicit solution to the COO problem, called Detail Enhanced Contrastive Loss (DECLoss) DECLoss utilizes the clustering property of contrastive learning to directly reduce the variance of the potential high-resolution distribution. We evaluate DECLoss on multiple super-resolution benchmarks and demonstrate that it improves the perceptual quality of PSNR-oriented models.
  arXiv  Detail & Related papers  (2022-01-04T08:30:09Z)
• Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descent [15.340540198612823]
  We consider expected risk problems when the range of the estimator is required to be nonnegative. We develop first and second-order variants of approximation mirror descent employing emphpseudo-gradients. Experiments demonstrate favorable performance on ingeneous Process intensity estimation in practice.
  arXiv  Detail & Related papers  (2020-11-13T21:54:28Z)

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.