Technology Category
Computer Vision: Learning & Optimization for CVSearch and Optimization: Non-convex OptimizationMachine Learning: Matrix & Tensor Methods
Anisotropic Tensor Deconvolution of Hyperspectral Images
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
Hyperspectral image deconvolution
ill-posed inverse problem
high dimensionality
anisotropic regularization
low-rank decomposition
Innovation
Methods, ideas, or system contributions that make the work stand out.
Canonical Polyadic Decomposition
Anisotropic Total Variation
Hyperspectral Image Deconvolution
Parameter-Parsimonious Modeling
Proximal Alternating Linearized Minimization
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