A Blind Multiscale Spatial Regularization Framework for Kernel-Based Spectral Unmixing

Abstract

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 lowdimensional 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 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-theart, related strategies.

Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing

“…Model-based approaches rely on prior knowledge about the mixing process, including the bilinear mixing model (BLMM) [35], [36], the post-nonlinear mixing model (PNMM) [37], and Hapke's model [38]. On the other hand, model-free methods attempt to learn the nonlinearity directly from the observed data using, e.g., support vector machines [39], algorithms based on graph geodesic distances [40] and kernel-based methods [9], [41]. Recent approaches have relied on deep learning techniques, reviewed in the following.…”

“…However, due to the complexity of the mixing process, specifying a precise model can be difficult. This has motivated the development of HU method based on nonparametric models where the nonlinearity is learned from the data, such as in kernel-based methods [9], [41] and nonlinear AEC networks [10], [16], [17]. In this work, we consider a decomposition of the nonlinear mixing process as the sum of a linear term (the LMM) and a nonparametric nonlinear component [9], [17], [91], [92]:…”

Online Graph-Based Change Point Detection in Multiband Image Sequences

“…In particular, superpixels are able to group spectrally similar pixels in compact spatial neighborhoods of average size S 2 with excellent preservation of image borders [23]. The superpixel decomposition has been sucesfully applied to construct multiscale transformations used in spectral unmixing applications [26]- [28]. In this paper, we consider the superpixel decomposition in order to divide the pixels n = 1, .…”

Online multi-resolution fusion of space-borne multispectral images

“…Unmixing-based methods make use of the linear mixing model (LMM), which assumes that each pixel in the low resolution image can be represented as a convex combination of the reflectance of a small number of pure spectral signatures, called endmembers [18][19][20]. The LMM has been used for multimodal image fusion by assuming the proportions of each material in a low resolution pixel to be stable/constant over time [21][22][23].…”