Anisotropic Tensor Deconvolution of Hyperspectral Images

2026-01-16

AI Summary

This work addresses the ill-posed inverse problem of hyperspectral image deconvolution, which is exacerbated by high dimensionality and often leads to spectral structure degradation in conventional methods due to parameter redundancy. To overcome these limitations, the authors propose a lightweight approach based on low-rank Canonical Polyadic (CP) decomposition, reformulating high-dimensional latent image recovery as a factor matrix estimation task. For the first time, they incorporate a structure-aware anisotropic total variation (TV) regularization into the spatial factors to preserve spectral smoothness. The resulting non-convex optimization problem is efficiently solved via the Proximal Alternating Linearized Minimization (PALM) framework. The proposed method reduces the number of variables by over two orders of magnitude, achieving highly compact yet structure-preserving representations while maintaining high reconstruction accuracy and significantly lowering model complexity.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Hyperspectral image deconvolution
• ill-posed inverse problem
• high dimensionality
• anisotropic regularization
• low-rank decomposition

Innovation

• Canonical Polyadic Decomposition
• Anisotropic Total Variation
• Hyperspectral Image Deconvolution
• Parameter-Parsimonious Modeling
• Proximal Alternating Linearized Minimization