Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing

Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by means of seasoned experts. However, with the ever-growing volume of data, the bulk of costs in manpower and material resources poses new challenges on reducing the burden of manual labor and improving efficiency. For this reason, it is, therefore, urgent to develop more intelligent and automatic approaches for various HS RS applications. Machine learning (ML) tools with convex optimization have successfully undertaken the tasks of numerous artificial intelligence (AI)-related applications. However, their ability in handling complex practical problems remains limited, particularly for HS data, due to the effects of various spectral variabilities in the process of HS imaging and the complexity and redundancy of higher dimensional HS signals. Compared to the convex models, non-convex modeling, which is capable of characterizing more complex real scenes and providing the model interpretability technically and theoretically, has been proven to be a feasible solution to reduce the gap between challenging HS vision tasks and currently advanced intelligent data processing models

Graph Regularized Coupled Spectral Unmixing for Change Detection

This paper presents a methodology of coupled spectral unmixing for multitemporal hyperspectral data analysis. Coupled spectral unmixing simultaneously extracts the sets of spectral signatures of endmembers and respective abundance maps from multiple spectral images with differences in observation conditions and sensor characteristics. The problem is formulated in the framework of coupled nonnegative matrix factorization. A graph regularization that reflects spectral correlation between two images on abundance fractions is introduced into the optimization of coupled spectral unmixing to consider temporal changes of the earth’s surface. An alternating optimization algorithm is investigated using the method of Lagrange multipliers to guarantee a stable convergence. The proposed method was applied to dual-temporal Hyperion images taken over the Fukushima Daiichi nuclear power plant. Experimental results showed that the proposed method can extract essential information on the earth’s surface in a data-driven manner beyond multitemporal data modality

Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Nonlinear Spectral Unmixing using Semi-Supervised Standard Fuzzy Clustering

Coarse resolution captured in remote sensing causes the combination of different materials in one pixel, called the mixed pixel. Spectral unmixing estimates the combination of endmembers in mixed pixels and their corresponding abundance maps in the Hyper/Multi spectral image. In this paper, a nonlinear spectral unmixing based on semi-supervised fuzzy clustering is proposed. First, pure pixels (endmembers) using Vertex Component Analysis (VCA) are extracted and those pixels are the labelled pixels where the membership value of each is 1 for the corresponding endmember and 0 for the others. Second, the semi-supervised fuzzy clustering is applied to find the membership matrix defining the fraction of the endmember in each mixed pixel and hence extract the abundance maps. The experiments were conducted on both synthetic data such as the Legendre data and real data such as Jasper Ridge data. The non-linearity of the Legendre data was performed by the Fan model on different signal-tonoise ratio values. The results of the new unmixing model show its significant performance when compared with four state-of the art unmixing algorithm