一种面向基于核的光谱解混的盲多尺度空间正则化框架
A Blind Multiscale Spatial Regularization Framework for Kernel-based Spectral Unmixing
AI总结：
针对非线性高光谱解混中空间关系建模复杂、参数需手动设置的问题，提出基于超像素的多尺度正则化框架，结合对偶理论与统计参数估计实现盲解混，性能优于现有前沿方法。
摘要：
在高光谱成像（HSI）分析中引入空间先验信息，已使众多应用于去噪、分类和解混的HSI方法的性能得到整体提升。将这类方法拓展到非线性场景并非易事，尤其是对于解混问题，考虑相邻像素间的空间关系可能会涉及它们的丰度分数与非线性贡献之间的复杂相互作用。本文提出了一种面向基于核的非线性光谱解混的多尺度正则化策略。所提方法将解混问题分解为两个不同空间尺度下的子问题：包含低维结构的粗尺度，以及原始的细尺度。粗空间域由多尺度变换生成的超像素（superpixel）定义。随后，光谱解混被建模为二次约束优化问题的求解，通过利用其强对偶性，并将对偶代价函数重新表述为求根问题的形式，可高效求解这些优化问题。此外，我们采用基于理论的统计框架，设计了一套一致的策略来估计所有所需参数，既包括算法的正则化参数，也包括变换的超像素数量，从而得到一种真正意义上的盲（从参数设置角度而言）解混方法。实验结果证明，与其他现有前沿相关策略相比，所提方法的性能更优。
英文摘要：
Introducing spatial prior information in hyperspectral imaging (HSI) analysis has led to an overall improvement of the performance of many HSI methods applied for denoising, classification, and unmixing. Extending such methodologies to nonlinear settings is not always straightforward, specially for unmixing problems where the consideration of spatial relationships between neighboring pixels might comprise intricate interactions between their fractional abundances and nonlinear contributions. In this paper, we consider a multiscale regularization strategy for nonlinear spectral unmixing with kernels. The proposed methodology splits the unmixing problem into two sub-problems at two different spatial scales: a coarse scale containing low-dimensional structures, and the original fine scale. The coarse spatial domain is defined using superpixels that result from a multiscale transformation. Spectral unmixing is then formulated as the solution of quadratically constrained optimization problems, which are solved efficiently by exploring their strong duality and a reformulation of their dual cost functions in the form of root-finding problems. Furthermore, we employ a theory-based statistical framework to devise a consistent strategy to estimate all required parameters, including both the regularization parameters of the algorithm and the number of superpixels of the transformation, resulting in a truly blind (from the parameters setting perspective) unmixing method. Experimental results attest the superior performance of the proposed method when comparing with other, state-of-the-art, related strategies.
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