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Abstract
Endmember estimation plays a key role in hyperspectral image unmixing, often requiring an estimation of the number of endmembers and extracting endmembers. However, most of the existing extraction algorithms require prior knowledge regarding the number of endmembers, being a critical process during unmixing. To bridge this, a new maximum distance analysis (MDA) method is proposed that simultaneously estimates the number and spectral signatures of endmembers without any prior information on the experimental data containing pure pixel spectral signatures and no noise, being based on the assumption that endmembers form a simplex with the greatest volume over all pixel combinations. The simplex includes the farthest pixel point from the coordinate origin in the spectral space, which implies that: (1) the farthest pixel point from any other pixel point must be an endmember, (2) the farthest pixel point from any line must be an endmember, and (3) the farthest pixel point from any plane (or affine hull) must be an endmember. Under this scenario, the farthest pixel point from the coordinate origin is the first endmember, being used to create the aforementioned point, line, plane, and affine hull. The remaining endmembers are extracted by repetitively searching for the pixel points that satisfy the above three assumptions. In addition to behaving as an endmember estimation algorithm by itself, the MDA method can co-operate with existing endmember extraction techniques without the pure pixel assumption via generalizing them into more effective schemes. The conducted experiments validate the effectiveness and efficiency of our method on synthetic and real data.
Highlights
Sensed hyperspectral imaging (HSI) [1] provides a significant amount of information regarding different materials on the Earth’s surface, capturing their reflectance behavior in the presence of solar radiation by measuring the degree of absorption along the wavelengths of the electromagnetic spectrum (usually focused on the visible, near infrared (NIR), and shortwave infrared (SWIR) spectrum [2]), in hundreds of narrow and continuous spectral bands [3]
The stopping criterion of endmember extraction is that the maximum distance between all of the pixel points and affine hull formed by the extracted endmember is zero
We have developed a new algorithm for estimating the number of endmembers and the corresponding endmember signatures, which is referred to as maximum distance analysis (MDA)
Summary
Sensed hyperspectral imaging (HSI) [1] provides a significant amount of information regarding different materials on the Earth’s surface, capturing their reflectance behavior in the presence of solar radiation (which depends on their chemical composition and physical structure) by measuring the degree of absorption along the wavelengths of the electromagnetic spectrum (usually focused on the visible, near infrared (NIR), and shortwave infrared (SWIR) spectrum [2]), in hundreds of narrow and continuous spectral bands [3]. Spectral unmixing techniques [15,16,17] have been comprehensively investigated for the purpose of extracting endmembers and estimating their corresponding abundances, allowing for the processing of HSI scenes at the sub-pixel scale [18] These techniques decompose each mixed pixel into a proportional composition of endmembers, where the constituent proportion with respect to different types of materials [19] for each pixel is defined as the abundance. A significant challenge for existing spectral unmixing techniques is how to accurately extract endmembers [20,21,22,23,24] from remotely sensed HSI data This is normally achieved by two seemingly independent, but, highly correlated procedures: (i) determining the number of endmembers, and (ii) extracting their spectral signatures.
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