Abstract
Sparse unmixing is widely used for hyperspectral imagery to estimate the optimal fraction (abundance) of materials contained in mixed pixels (endmembers) of a hyperspectral scene, by considering the abundance sparsity. This abundance has a unique property, i.e., high spatial correlation in local regions. This is due to the fact that the endmembers existing in the region are highly correlated. This implies the low-rankness of the abundance in terms of the endmember. From this prior knowledge, it is expected that considering the low-rank local abundance to the sparse unmixing problem improves estimation performance. In this study, we propose an algorithm that exploits the low-rank local abundance by applying the nuclear norm to the abundance matrix for local regions of spatial and abundance domains. In our optimization problem, the local abundance regularizer is collaborated with the L 2 , 1 norm and the total variation for sparsity and spatial information, respectively. We conducted experiments for real and simulated hyperspectral data sets assuming with and without the presence of pure pixels. The experiments showed that our algorithm yields competitive results and performs better than the conventional algorithms.
Highlights
The need to extract more detailed information from remote-sensing imagery has expanded from multispectral images to hyperspectral images that enable pixel-constituent-level analysis
We developed an algorithm, which is called joint local abundance sparse unmixing (J-LASU), in which we proposed the local abundance regularizer and implanted it to the sparse unmixing problem using the nuclear norm for 3D local regions and evaluated the effect
We proposed the local abundance regularizer algorithm for the sparse unmixing problem to improve the accuracy of abundance estimation
Summary
The need to extract more detailed information from remote-sensing imagery has expanded from multispectral images to hyperspectral images that enable pixel-constituent-level analysis. In the sparse regression techniques, additional informations are introduced as prior knowledge that are added to the objective functions in the optimization problems and called regularizers, e.g., considering the abundance sparsity [24,25,26], information of endmembers known to exist in the data [22], or total local spatial differences [27]. 2017, 9, 1224 knowledge, there is no sparse unmixing algorithm that takes into account the low-rankness of local spectral signatures (endmembers) in the abundance dimension, whereas the high correlation between the spectral signatures can be guaranteed by the spectral angle (SA), which is a spectral similarity assesment defined as the angle between two spectral vectors. One can observe the linearity of the data distribution in local regions in terms of spatial as well as abundance dimension This priori may lead to a novel approach for the sparse unmixing algorithm.
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