用低秩分解压缩高光谱图像反卷积模型，显著减少参数量。
Anisotropic Tensor Deconvolution of Hyperspectral Images
- 基于低秩CP分解将图像反卷积转化为小规模因子估计
- 参数量减少超两个数量级，重建精度保持良好
- 仅对空间因子施加方向性总变差正则，适合高光谱图像
高光谱图像（HSI）反卷积是一个因数据高维而困难的不适定逆问题。本文提出一种参数精简框架，基于整个潜在高光谱图像 $/mathbf{/mathcal{X}} imes imes P imes Q imes N$ 的低秩经典多线性分解（CPD）。该方法将恢复 $PQN$ 个变量的大规模图像问题，转化为估计 $(P+Q+N)R$ 个变量的CPD因子问题。该模型还支持仅作用于空间因子的结构感知、各向异性总变差（TV）正则化，保留平滑光谱特征。基于近端交替线性化最小化（PALM）框架设计了高效算法，求解非凸优化问题。实验表明，该模型在参数量减少超过两个数量级的同时，实现了模型紧凑性与重建精度之间的出色权衡。
原文摘要 · Abstract (English)
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.
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