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Dimensionality reduction is a frequent preprocessing step in hyperspectral image analysis. High-dimensional data will cause the issue of the “curse of dimensionality” in the applications of hyperspectral imagery. In this paper, a dimensionality reduction method of hyperspectral images based on random projection (RP) for target detection was investigated. In the application areas of hyperspectral imagery, e.g. target detection, the high dimensionality of the hyperspectral data would lead to burdensome computations. Random projection is attractive in this area because it is data independent and computationally more efficient than other widely-used hyperspectral dimensionality-reduction methods, such as Principal Component Analysis (PCA) or the maximum-noise-fraction (MNF) transform. In RP, the original highdimensional data is projected onto a low dimensional subspace using a random matrix, which is very simple. Theoretical and experimental results indicated that random projections preserved the structure of the original high-dimensional data quite well without introducing significant distortion. In the experiments, Constrained Energy Minimization (CEM) was adopted as the target detector and a RP-based CEM method for hyperspectral target detection was implemented to reveal that random projections might be a good alternative as a dimensionality reduction tool of hyperspectral images to yield improved target detection with higher detection accuracy and lower computation time than other methods.

A sparse representation based multi-threshold segmentation (SRMTS) algorithm for target detection in hyperspectral images is proposed. Benefiting from the sparse representation, the high-dimensional spectral data can be characterized into a series of sparse feature vectors which has only a few nonzero coefficients. Through setting an appropriate threshold, the noise removed sparse spectral vectors are divided into two subspaces in the sparse domain consistent with the sample spectrum to separate the target from the background. Then a correlation and a vector 1-norm are calculated respectively in the subspaces. The sparse characteristic of the target is used to ext ract the target with a multi -threshold method. Unlike the conventional hyperspectral dimensionality reduction methods used in target detection algorithms, like Principal Components Analysis (PCA) and Maximum Noise Fraction (MNF), this algorithm maintains the spectral characteristics while removing the noise due to the sparse representation. In the experiments, an orthogonal wavelet sparse base is used to sparse the spectral information and a best contraction threshold to remove the hyperspectral image noise according to the noise estimation of the test images. Compared with co mmon algorithms, such as Adaptive Cosine Estimator (ACE), Constrained Energy Minimizat ion (CEM) and the noise removed MNF-CEM algorithm, the proposed algorithm demonstrates higher detection rates and robustness via the ROC curves.

In imaging systems based on compressed sensing, error in the measured data is incurred due to the nonlinear response of the photo-detector, which affects the quality of reconstructed images. Conventionally, the affected measured data will be eliminated in order to obtain the high reconstruction quality. However, when there are too many measured data affected, it is impossible to reject all such data which will certainly degrade the imaging efficiency. Therefore, an algorithm of regionally compensating the non-linear response from the detector is proposed. The nonlinear measured data will be compensated but not rejected in the proposed algorithm. According to the detector response curve, all of the nonlinear measured data will be divided into several parts. The data in the same part will have the same average compensation factor which can be obtained from the response curve after calculation. The affected measured data will be compensated with the compensation factor regionally before used to reconstruct the original image. The theoretical analysis and simulation results show that a reconstructed image with high quality can still be obtained even when over 80% of the measured data are nonlinear. It is impossible to get such a high quality reconstructed image with the conventionally algorithm. The PSNR and the M-rate in the simulation show that the compensation algorithm can greatly deal with the situation of too many nonlinear measured data.