Anisotropic Tensor Deconvolution of Hyperspectral Images

TL;DR

This paper introduces an anisotropic tensor deconvolution method for hyperspectral images using low-rank CPD and structure-aware TV regularization, significantly reducing parameters while maintaining high reconstruction quality.

Contribution

It proposes a novel low-rank CPD-based framework with anisotropic TV regularization for hyperspectral image deconvolution, improving efficiency and accuracy.

Findings

Parameter reduction of over two orders of magnitude.

Effective preservation of spectral signatures.

Competitive reconstruction accuracy.

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.