Automatic Denoising and Unmixing in Hyperspectral Image Processing

This thesis addresses two important aspects in hyperspectral image processing: automatic hyperspectral image denoising and unmixing. The first part of this thesis is devoted to a novel automatic optimized vector bilateral filter denoising algorithm, while the remainder concerns nonnegative matrix factorization with deterministic annealing for unsupervised unmixing in remote sensing hyperspectral images. The need for automatic hyperspectral image processing has been promoted by the development of potent hyperspectral systems, with hundreds of narrow contiguous bands, spanning the visible to the long wave infrared range of the electromagnetic spectrum. Due to the large volume of raw data generated by such sensors, automatic processing in the hyperspectral images processing chain is preferred to minimize human workload and achieve optimal result. Two of the mostly researched processing for such automatic effort are: hyperspectral image denoising, which is an important preprocessing step for almost all remote sensing tasks, and unsupervised unmixing, which decomposes the pixel spectra into a collection of endmember spectral signatures and their corresponding abundance fractions. Two new methodologies are introduced in this thesis to tackle the automatic processing problems described above. Vector bilateral filtering has been shown to provide good tradeoff between noise removal and edge degradation when applied to multispectral/hyperspectral image denoising. It has also been demonstrated to provide dynamic range enhancement of bands that have impaired signal to noise ratios. Typical vector bilateral filtering usage does not employ parameters that have been determined to satisfy optimality criteria. This thesis also introduces an approach for selection of the parameters of a vector bilateral filter through an optimization procedure rather than by ad hoc means. The approach is based on posing the filtering problem as one of nonlinear estimation and minimizing the Stein\u27s unbiased risk estimate (SURE) of this nonlinear estimator. Along the way, this thesis provides a plausibility argument with an analytical example as to why vector bilateral filtering outperforms band-wise 2D bilateral filtering in enhancing SNR. Experimental results show that the optimized vector bilateral filter provides improved denoising performance on multispectral images when compared to several other approaches. Non-negative matrix factorization (NMF) technique and its extensions were developed to find part based, linear representations of non-negative multivariate data. They have been shown to provide more interpretable results with realistic non-negative constrain in unsupervised learning applications such as hyperspectral imagery unmixing, image feature extraction, and data mining. This thesis extends the NMF method by incorporating deterministic annealing optimization procedure, which will help solve the non-convexity problem in NMF and provide a better choice of sparseness constrain. The approach is based on replacing the difficult non-convex optimization problem of NMF with an easier one by adding an auxiliary convex entropy constrain term and solving this first. Experiment results with hyperspectral unmixing application show that the proposed technique provides improved unmixing performance compared to other state-of-the-art methods

A sparse semi-blind source identification method and its application to Raman spectroscopy for explosives detection

Rapid and reliable detection and identification of unknown chemical substances are critical to homeland security. It is challenging to identify chemical components from a wide range of explosives. There are two key steps involved. One is a non-destructive and informative spectroscopic technique for data acquisition. The other is an associated library of reference features along with a computational method for feature matching and meaningful detection within or beyond the library. In this paper, we develop a new iterative method to identify unknown substances from mixture samples of Raman spectroscopy. In the first step, a constrained least squares method decomposes the data into a sum of linear combination of the known components and a non-negative residual. In the second step, a sparse and convex blind source separation method extracts components geometrically from the residuals. Verification based on the library templates or expert knowledge helps to confirm these components. If necessary, the confirmed meaningful components are fed back into step one to refine the residual and then step two extracts possibly more hidden components. The two steps may be iterated until no more components can be identified. We illustrate the proposed method in processing a set of the so called swept wavelength optical resonant Raman spectroscopy experimental data by a satisfactory blind extraction of a priori unknown chemical explosives from mixture samples. We also test the method on nuclear magnetic resonance (NMR) spectra for chemical compounds identification. © 2013 Published by Elsevier B.V

Bayesian orthogonal component analysis for sparse representation

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin

Tensor-based Hyperspectral Image Processing Methodology and its Applications in Impervious Surface and Land Cover Mapping

The emergence of hyperspectral imaging provides a new perspective for Earth observation, in addition to previously available orthophoto and multispectral imagery. This thesis focused on both the new data and new methodology in the field of hyperspectral imaging. First, the application of the future hyperspectral satellite EnMAP in impervious surface area (ISA) mapping was studied. During the search for the appropriate ISA mapping procedure for the new data, the subpixel classification based on nonnegative matrix factorization (NMF) achieved the best success. The simulated EnMAP image shows great potential in urban ISA mapping with over 85% accuracy. Unfortunately, the NMF based on the linear algebra only considers the spectral information and neglects the spatial information in the original image. The recent wide interest of applying the multilinear algebra in computer vision sheds light on this problem and raised the idea of nonnegative tensor factorization (NTF). This thesis found that the NTF has more advantages over the NMF when work with medium- rather than the high-spatial-resolution hyperspectral image. Furthermore, this thesis proposed to equip the NTF-based subpixel classification methods with the variations adopted from the NMF. By adopting the variations from the NMF, the urban ISA mapping results from the NTF were improved by ~2%. Lastly, the problem known as the curse of dimensionality is an obstacle in hyperspectral image applications. The majority of current dimension reduction (DR) methods are restricted to using only the spectral information, when the spatial information is neglected. To overcome this defect, two spectral-spatial methods: patch-based and tensor-patch-based, were thoroughly studied and compared in this thesis. To date, the popularity of the two solutions remains in computer vision studies and their applications in hyperspectral DR are limited. The patch-based and tensor-patch-based variations greatly improved the quality of dimension-reduced hyperspectral images, which then improved the land cover mapping results from them. In addition, this thesis proposed to use an improved method to produce an important intermediate result in the patch-based and tensor-patch-based DR process, which further improved the land cover mapping results