從基礎數學推廣至研究數學

從基礎數學推廣至研究數學

以高頻譜影像分析為例

Hyperspectral Image Analysis

Sparse demixing of HyperSpectral Images (HSI).

J Greer

In the linear mixture model for hyperspectral images, all the image spectra lie on a high-dimensional simplex with corners called endmembers. Given a set of endmembers, the standard calculation of fractional abundances with constrained least squares typically identifies the spectra as combinations of most, if not all, endmembers. We instead assume that pixels are combinations of only a few endmembers, yielding abundance vectors that are sparse. We introduce Sparse Demixing (SD), a method, similar to Orthogonal Matching Pursuit (OMP), for calculating these sparse abundances. We demonstrate that SD outperforms an existing L1 demixing algorithm, which we prove depends adversely on the angles between endmembers. We combine SD with dictionary learning methods to automatically calculate endmembers for a provided set of spectra. Applying to an AVIRIS image of Cuprite, Nevada yields endmembers that compare favorably with signatures from the USGS spectral library.

Keywords: hyperspectral; demix; hsy; hyperspectral image; image; sparse; omp; abundance; spectra; usg; match pursuit; spectral library; dictionary; mixture model; nevada; 

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