Unsupervised spectral sub-feature learning for hyperspectral image classification

Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods

Minimum mean square distance estimation of a subspace

We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace $U$ and its estimate $\hat{U}$ may not be adequate as the MSE is not the natural metric in the Grassmann manifold. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance (MSD) between $U$ and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of $U$ but entails computing the principal eigenvectors of the posterior mean of $U U^{T}$. Derivation of the MMSD estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and a Bingham or von Mises Fisher prior distribution for $U$. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of $U$. An application to hyperspectral imagery is finally investigated

A subpixel target detection algorithm for hyperspectral imagery

The goal of this research is to develop a new algorithm for the detection of subpixel scale target materials on the hyperspectral imagery. The signal decision theory is typically to decide the existence of a target signal embedded in the random noise. This implies that the detection problem can be mathematically formalized by signal decision theory based on the statistical hypothesis test. In particular, since any target signature provided by airborne/spaceborne sensors is embedded in a structured noise such as background or clutter signatures as well as broad band unstructured noise, the problem becomes more complicated, and particularly much more under the unknown noise structure. The approach is based on the statistical hypothesis method known as Generalized Likelihood Ratio Test (GLRT). The use of GLRT requires estimating the unknown parameters, and assumes the prior information of two subspaces describing target variation and background variation respectively. Therefore, this research consists of two parts, the implementation of GLRT and the characterization of two subspaces through new approaches. Results obtained from computer simulation, HYDICE image and AVI RIS image show that this approach is feasible

Hyperspectral image compression : adapting SPIHT and EZW to Anisotropic 3-D Wavelet Coding

Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties

The matched subspace detector with interaction effects

This paper aims to propose a new hyperspectral target-detection method termed the matched subspace detector with interaction effects (MSDinter). The MSDinter introduces “interaction effects” terms into the popular matched subspace detector (MSD), from regression analysis in multivariate statistics and the bilinear mixing model in hyperspectral unmixing. In this way, the interaction between the target and the surrounding background, which should have but not yet been considered by the MSD, is modelled and estimated, such that superior performance of target detection can be achieved. Besides deriving the MSDinter methodologically, we also demonstrate its superiority empirically using two hyperspectral imaging datasets

Linear Unmixing of Hyperspectral Signals via Wavelet Feature Extraction

A pixel in remotely sensed hyperspectral imagery is typically a mixture of multiple electromagnetic radiances from various ground cover materials. Spectral unmixing is a quantitative analysis procedure used to recognize constituent ground cover materials (or endmembers) and obtain their mixing proportions (or abundances) from a mixed pixel. The abundances are typically estimated using the least squares estimation (LSE) method based on the linear mixture model (LMM). This dissertation provides a complete investigation on how the use of appropriate features can improve the LSE of endmember abundances using remotely sensed hyperspectral signals. The dissertation shows how features based on signal classification approaches, such as discrete wavelet transform (DWT), outperform features based on conventional signal representation methods for dimensionality reduction, such as principal component analysis (PCA), for the LSE of endmember abundances. Both experimental and theoretical analyses are reported in the dissertation. A DWT-based linear unmixing system is designed specially for the abundance estimation. The system utilizes the DWT as a pre-processing step for the feature extraction. Based on DWT-based features, the system utilizes the constrained LSE for the abundance estimation. Experimental results show that the use of DWT-based features reduces the abundance estimation deviation by 30-50% on average, as compared to the use of original hyperspectral signals or conventional PCA-based features. Based on the LMM and the LSE method, a series of theoretical analyses are derived to reveal the fundamental reasons why the use of the appropriate features, such as DWT-based features, can improve the LSE of endmember abundances. Under reasonable assumptions, the dissertation derives a generalized mathematical relationship between the abundance estimation error and the endmember separabilty. It is proven that the abundance estimation error can be reduced through increasing the endmember separability. The use of DWT-based features provides a potential to increase the endmember separability, and consequently improves the LSE of endmember abundances. The stability of the LSE of endmember abundances is also analyzed using the concept of the condition number. Analysis results show that the use of DWT-based features not only improves the LSE of endmember abundances, but also improves the LSE stability

Sparse representation based hyperspectral image compression and classification

Abstract This thesis presents a research work on applying sparse representation to lossy hyperspectral image compression and hyperspectral image classification. The proposed lossy hyperspectral image compression framework introduces two types of dictionaries distinguished by the terms sparse representation spectral dictionary (SRSD) and multi-scale spectral dictionary (MSSD), respectively. The former is learnt in the spectral domain to exploit the spectral correlations, and the latter in wavelet multi-scale spectral domain to exploit both spatial and spectral correlations in hyperspectral images. To alleviate the computational demand of dictionary learning, either a base dictionary trained offline or an update of the base dictionary is employed in the compression framework. The proposed compression method is evaluated in terms of different objective metrics, and compared to selected state-of-the-art hyperspectral image compression schemes, including JPEG 2000. The numerical results demonstrate the effectiveness and competitiveness of both SRSD and MSSD approaches. For the proposed hyperspectral image classification method, we utilize the sparse coefficients for training support vector machine (SVM) and k-nearest neighbour (kNN) classifiers. In particular, the discriminative character of the sparse coefficients is enhanced by incorporating contextual information using local mean filters. The classification performance is evaluated and compared to a number of similar or representative methods. The results show that our approach could outperform other approaches based on SVM or sparse representation. This thesis makes the following contributions. It provides a relatively thorough investigation of applying sparse representation to lossy hyperspectral image compression. Specifically, it reveals the effectiveness of sparse representation for the exploitation of spectral correlations in hyperspectral images. In addition, we have shown that the discriminative character of sparse coefficients can lead to superior performance in hyperspectral image classification.EM201

An Image fusion algorithm for spatially enhancing spectral mixture maps

An image fusion algorithm, based upon spectral mixture analysis, is presented. The algorithm combines low spatial resolution multi/hyperspectral data with high spatial resolution sharpening image(s) to create high resolution material maps. Spectral (un)mixing estimates the percentage of each material (called endmembers) within each low resolution pixel. The outputs of unmixing are endmember fraction images (material maps) at the spatial resolution of the multispectral system. This research includes developing an improved unmixing algorithm based upon stepwise regression. In the second stage of the process, the unmixing solution is sharpened with data from another sensor to generate high resolution material maps. Sharpening is implemented as a nonlinear optimization using the same type of model as unmixing. Quantifiable results are obtained through the use of synthetically generated imagery. Without synthetic images, a large amount of ground truth would be required in order to measure the accuracy of the material maps. Multiple band sharpening is easily accommodated by the algorithm, and the results are demonstrated at multiple scales. The analysis includes an examination of the effects of constraints and texture variation on the material maps. The results show stepwise unmixing is an improvement over traditional unmixing algorithms. The results also indicate sharpening improves the material maps. The motivation for this research is to take advantage of the next generation of multi/hyperspectral sensors. Although the hyperspectral images will be of modest to low resolution, fusing them with high resolution sharpening images will produce a higher spatial resolution land cover or material map