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.

中文翻译：

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基于核的谱分解的盲多尺度空间正则化框架


在高光谱成像 (HSI) 分析中引入空间先验信息，导致许多应用于去噪、分类和分解的 HSI 方法的性能得到全面提高。将此类方法扩展到非线性设置并不总是简单的，特别是对于分解问题，其中相邻像素之间的空间关系的考虑可能包括其分数丰度和非线性贡献之间复杂的相互作用。在本文中，我们考虑了一种用于核非线性谱解混合的多尺度正则化策略。所提出的方法将分解问题分成两个不同空间尺度的两个子问题：包含低维结构的粗尺度和原始的细尺度。粗略空间域是使用多尺度变换产生的超像素来定义的。然后，谱分解被公式化为二次约束优化问题的解决方案，通过探索其强对偶性并以求根问题的形式重新表述其对偶成本函数，可以有效地解决这些问题。此外，我们采用基于理论的统计框架来设计一致的策略来估计所有所需的参数，包括算法的正则化参数和变换的超像素数量，从而实现真正的盲（从参数设置的角度来看）解混法。实验结果证明了与其他最先进的相关策略相比，所提出的方法具有优越的性能。