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One fundamental task of hyperspectral imaging is spectral unmixing. In this case, the conventional pure pixel-based hyperspectral image classification (HSIC) may not work effectively for mixed pixels. This article presents a kernel-based approach to hyperspectral mixed pixel classification (HMPC) which includes two nonlinear mixed pixel classifiers, kernel constrained energy minimization (KCEM) and kernel linearly constrained minimum variance (KLCMV) to replace the widely used pure pixel-based support vector machine (SVM) classifier. Interestingly, what the binary-class and multiclass SVM classifiers are to pure pixel-based HSIC can be similarly derived for what a single-class KCEM detector and a multiclass KLCMV detector are to HMPC. In particular, the commonly used discrete classification map-based hard classification measures, average accuracy (AA) and overall accuracy (OA) for performance evaluation can be further generalized to real-valued mixed class abundance fractional map-based soft classification measures via 3-D receiver operating characteristic (3-D ROC) analysis-derived detection measures. Extensive experiments are conducted to demonstrate the utility of HMPC where KCEM/KLCMV not only significantly improve the classification performance of CEM/LCMV-based classifiers but also outperform many existing spectral-spatial classification methods.

Training sample selection is a great challenge for hyperspectral image classification (HSIC), specifically when only a very limited number of labeled data samples are available for training. Two recently developed concepts for training sample selection are of particular interest. One is active learning (AL), which augments labeled training samples by including unlabeled data samples as new training samples. The other is iterative training sampling (ITS), which expands data cubes by including additional spatial classification information into the training samples. This article combines AL and ITS simultaneously to derive a joint ITS–AL spectral–spatial (SS) classification approach, to be called ITS augmentation by AL spectral–spatial classification, referred to as ITSA-AL-SS, which can improve SS classification using either AL or ITS alone. The novel idea of ITSA-AL-SS is to take advantage of ITS to expand data cubes by incorporating additional spatial classification information iteratively into the AL-augmented unlabeled data samples to update the current training samples iteration by iteration in one-shot operation. As expected, ITSA-AL-SS is benefited from both ITS and AL to not only further improve classification accuracy but also reduce classification inconsistency.

Due to significant inter-band correlation resulting from the use of hundreds of contiguous spectral bands, band selection (BS) is commonly used to reduce data dimensionality for band redundancy removal. A challenge for BS is how to design an effective criterion which can select bands with crucial self-retained spectral information, while also avoiding highly correlated bands to be selected. This article presents a novel approach, referred to as self-mutual information-based band selection (SMI-BS) for hyperspectral image classification (HSIC) to address these two issues. It first constructs a hyperspectral band channel from a hyperspectral image and then takes advantage of such a band channel to coin a new concept of SMI, which is defined as the mutual information (MI) between a selected band, b, and the set of full bands, ${\boldsymbol{\Omega}} $ , $I$ (b; ${\boldsymbol{\Omega}}$ ). As a result, a curve plotted as a function of $I$ (b; ${\boldsymbol{\Omega}}$ ) versus individual band b, called SMI curve, can be used as a BS criterion which selects those bands with large $I$ (b; ${\boldsymbol{\Omega}}$ ) values as desired bands. Since such selected bands may be highly correlated, another new concept, called prominent band (PB), which is defined as a band corresponding to a prominent peak of an SMI curve, is further introduced to avoid selecting highly inter-correlated spectral bands. To validate the utility of SMI-BS in HSIC, experiments are conducted to compare existing state-of-the-art BS methods for performance evaluation. The results demonstrate that SMI-BS is indeed a very effective BS method and also performs better than other test BS methods.

Hyperspectral image classification (HSIC) has generated considerable interests over the past years. However, one of challenging issues arising in HSIC is inconsistent classification, which is mainly caused by random training sampling (RTS) of selecting training data. This is because a different set of training samples may produce a different classification result. A general approach to addressing this problem is the so-called K -fold method which implements RTS K times and takes the average of overall accuracy with respect to standard deviation to describe a confidence level of classification performance. To deal with this issue, this article develops an iterative RTS (IRTS) method as an alternative to the K -fold method to reduce the uncertainty caused by RTS. Its idea is to add the spatial filtered classification maps to the image cube that is currently being processed via feedback loops to augment image cubes iteratively. Then, the training samples will be reselected randomly from the new augmented image cubes iteration-by-iteration. As a result, the training samples selected from each iteration will be updated by new added spatial information captured by spatial filters implemented at the iteration. The experimental results clearly demonstrate that IRTS successfully improves classification accuracy as well as reduces inconsistency in results.