Identify Informative Bands for Hyperspectral Target Detection Using the Third-Order Statistic

Constrained energy minimization (CEM) has been proposed and widely researched in the field of hyperspectral target detection. Generally, it selects one of the target spectra as the representative and then keeps its output constant while minimizing the average filter output energy of the data. However, it has been proven that as the number of bands (L) increases, CEM will gradually lower the average filter output energy when keeping the representative’s output constant. Unavoidably, due to the inherent spatial and temporal variation of the spectra, this will lead to an unreasonable phenomenon, i.e., if L is particularly large, when adding more bands, CEM will suppress more and more pixels, even including the target pixels. This means that the optimal solution of CEM may not correspond to the target detection result that we desire. To deal with this, in this paper, we introduce the third-order statistic (skewness) of the CEM model, served as an auxiliary index to determine whether a band is beneficial to target detection or not. Theoretically, we prove that the skewness index can always exclude the noisy bands with Gaussian distribution. In addition, experiments on several widely used remote sensing data indicate that the index can also efficiently identify informative bands for a better target detection performance.