Anisotropic Tensor Deconvolution of Hyperspectral Images
Xinjue Wang, Xiuheng Wang, Esa Ollila, Sergiy A. Vorobyov
TL;DR
This work addresses ill-posed hyperspectral image deconvolution by modeling the latent HSI $\mathcal{X} \in \mathbb{R}^{P\times Q\times N}$ with a low-rank Canonical Polyadic Decomposition, reducing the parameter burden from $PQN$ to $(P+Q+N)R$. Anisotropic Total Variation is applied to the spatial factor maps, preserving sharp spatial structures while maintaining smooth spectral signatures, and nonnegativity constraints reflect physical abundances and spectra. The optimization is solved via a PALM-based algorithm that uses separable 1D TV proximal operators and FFT-accelerated Gradients for the smooth part, with backtracking to guarantee convergence. Experiments on the CAVE dataset demonstrate an order-of-magnitude reduction in model parameters (to about $3\times 10^4$) while achieving competitive reconstruction quality, with an observation of an optimal CPD rank around $R=20$, illustrating a strong low-rank structure. The method offers a scalable, structure-aware alternative for resource-constrained HSI restoration and provides a public implementation for broader use.
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.