Matrix Cofactorization for Joint Spatial–Spectral Unmixing of Hyperspectral Images

Abstract

Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often very correlated yielding an ill-conditioned problem. To enrich the model and to reduce ambiguity due to the high correlation, it is common to introduce spatial information to complement the spectral information. The most common way to introduce spatial information is to rely on a spatial regularization of the abundance maps. In this paper, instead of considering a simple but limited regularization process, spatial information is directly incorporated through the newly proposed context of spatial unmixing. Contextual features are extracted for each pixel and this additional set of observations is decomposed according to a linear model. Finally the spatial and spectral observations are unmixed jointly through a cofactorization model. In particular, this model introduces a coupling term used to identify clusters of shared spatial and spectral signatures. An evaluation of the proposed method is conducted on synthetic and real data and shows that results are accurate and also very meaningful since they describe both spatially and spectrally the various areas of the scene.

The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis

“…At this time, it is necessary to distinguish which position measurement data of each sensor comes from the same target. At the same time, we need to combine the position data belonging to the same target to locate the target [7]. This process is also the process of location data association.…”

“… can be obtained by formula (7). We use the distance difference obtained by equation ( 8) and the variance obtained by equation (10).…”

Hyperspectral Unmixing Powered by Deep Image Priors and Denoising Regularization

“…The authors of [25] introduce a spatial group sparsity regularizer generated using image segmentation methods such as SLIC. In [26], a cofactorization model is used to jointly exploit spectral and spatial information, while the work of [27] introduces an adaptive graph to automatically determine the best neighbor points of pixels and assign corresponding weights. However, these methods require handcrafted regularizers, which can be time-consuming when non-standard regularizers are applied to large images.…”

Spectral-Spatial Constrained Nonnegative Matrix Factorization for Spectral Mixture Analysis of Hyperspectral Images

“…commonly found in hyperspectral images [4]- [6]. The presence of mixed pixels seriously affects the performance of many image processing tasks, such as classification and target detection, limiting the quantitative development of hyperspectral remote sensing.…”