Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organised rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e, there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature

スペクトルの線形性を考慮したハイパースペクトラル画像のノイズ除去とアンミキシングに関する研究

This study aims to generalize color line to M-dimensional spectral line feature (M>3) and introduce methods for denoising and unmixing of hyperspectral images based on the spectral linearity.For denoising, we propose a local spectral component decomposition method based on the spectral line. We first calculate the spectral line of an M-channel image, then using the line, we decompose the image into three components: a single M-channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, thus the algorithm needs to denoise only two grayscale images, regardless of the number of channels. For unmixing, we propose an algorithm that exploits the low-rank local abundance by applying the unclear norm to the abundance matrix for local regions of spatial and abundance domains. In optimization problem, the local abundance regularizer is collaborated with the L2, 1 norm and the total variation.北九州市立大

Hyperspectral unmixing with material variability using social sparsity

International audienceWe apply social-norms for the first time to the problem of hyperspectral unmixing while modeling spectral variability. These norms are built with inter-group penalties which are combined in a global intra-group penalization that can enforce selection of entire endmember bundles; this results in the selection of a few representative materials even in the presence of large endmembers bundles capturing each material's variability. We demonstrate improvements quantitatively on synthetic data and qualitatively on real data for three cases of social norms: group, elitist, and a fractional social norm, respectively. We find that the greatest improvements arise from using either the group or fractional flavor

A Comprehensive Survey of Deep Learning in Remote Sensing: Theories, Tools and Challenges for the Community

In recent years, deep learning (DL), a re-branding of neural networks (NNs), has risen to the top in numerous areas, namely computer vision (CV), speech recognition, natural language processing, etc. Whereas remote sensing (RS) possesses a number of unique challenges, primarily related to sensors and applications, inevitably RS draws from many of the same theories as CV; e.g., statistics, fusion, and machine learning, to name a few. This means that the RS community should be aware of, if not at the leading edge of, of advancements like DL. Herein, we provide the most comprehensive survey of state-of-the-art RS DL research. We also review recent new developments in the DL field that can be used in DL for RS. Namely, we focus on theories, tools and challenges for the RS community. Specifically, we focus on unsolved challenges and opportunities as it relates to (i) inadequate data sets, (ii) human-understandable solutions for modelling physical phenomena, (iii) Big Data, (iv) non-traditional heterogeneous data sources, (v) DL architectures and learning algorithms for spectral, spatial and temporal data, (vi) transfer learning, (vii) an improved theoretical understanding of DL systems, (viii) high barriers to entry, and (ix) training and optimizing the DL.Comment: 64 pages, 411 references. To appear in Journal of Applied Remote Sensin

Topics in High-Dimensional Statistics and the Analysis of Large Hyperspectral Images.

Advancement in imaging technology has made hyperspectral images gathered from remote sensing much more common. The high-dimensional nature of these large scale data coupled with wavelength and spatial dependency necessitates high-dimensional and efficient computation methods to address these issues while producing results that are concise and easy to understand. The thesis addresses these issues by examining high-dimensional methods in the context of hyperspectral image classification, unmixing and wavelength correlation estimation. Chapter 2 re-examines the sparse Bayesian learning (SBL) of linear models in a high-dimensional setting with sparse signal. The hard-thresholded version of the SBL estimator, under orthogonal design, achieves non-asymptotic error rate that is comparable to LASSO. We also establish in the chapter that with high-probability the estimator recovers the sparsity structure of the signal. The ability to recover sparsity structures in high dimensional settings is crucial for unmixing with high-dimensional libraries in the next chapter. In Chapter 3, the thesis investigates the application of SBL on the task of linear/bilinear unmixing and classification of hyperspectral images. The proposed model in this chapter uses latent Markov random fields to classify pixels and account for the spatial dependence between pixels. In the proposed model, the pixels belonging to the same group share the same mixture of pure endmembers. The task of unmixing and classification are performed simultaneously, but this method does not address wavelength dependence. Chapter 4 is a natural extension of the previous chapter that contains the framework to account for both spatial and wavelength dependence in the unmixing of hyperspectral images. The classification of the images are performed using approximate spectral clustering while the unmixing task is performed in tandem with sparse wavelength concentration matrix estimation.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135893/1/chye_1.pd

Regularization approaches to hyperspectral unmixing

We consider a few different approaches to hyperspectral unmixing of remotely sensed imagery which exploit and extend recent advances in sparse statistical regularization, handling of constraints and dictionary reduction. Hyperspectral unmixing methods often use a conventional least-squares based lasso which assumes that the data follows the Gaussian distribution, we use this as a starting point. In addition, we consider a robust approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers. Due to water absorption and atmospheric effects that affect data collection, hyperspectral images are prone to have large outliers. The framework comprises of several well-principled penalties. A non-convex, hyper-Laplacian prior is incorporated to induce sparsity in the number of active pure spectral components, and total variation regularizer is included to exploit the spatial-contextual information of hyperspectral images. Enforcing the sum-to-one and non-negativity constraint on the models parameters is essential for obtaining realistic estimates. We consider two approaches to account for this: an iterative heuristic renormalization and projection onto the positive orthant, and a reparametrization of the coefficients which gives rise to a theoretically founded method. Since the large size of modern spectral libraries cannot only present computational challenges but also introduce collinearities between regressors, we introduce a library reduction step. This uses the multiple signal classi fication (MUSIC) array processing algorithm, which both speeds up unmixing and yields superior results in scenarios where the library size is extensive. We show that although these problems are non-convex, they can be solved by a properly de fined algorithm based on either trust region optimization or iteratively reweighted least squares. The performance of the different approaches is validated in several simulated and real hyperspectral data experiments

From representation learning to thematic classification - Application to hierarchical analysis of hyperspectral images

Numerous frameworks have been developed in order to analyze the increasing amount of available image data. Among those methods, supervised classification has received considerable attention leading to the development of state-of-the-art classification methods. These methods aim at inferring the class of each observation given a specific class nomenclature by exploiting a set of labeled observations. Thanks to extensive research efforts of the community, classification methods have become very efficient. Nevertheless, the results of a classification remains a highlevel interpretation of the scene since it only gives a single class to summarize all information in a given pixel. Contrary to classification methods, representation learning methods are model-based approaches designed especially to handle high-dimensional data and extract meaningful latent variables. By using physic-based models, these methods allow the user to extract very meaningful variables and get a very detailed interpretation of the considered image. The main objective of this thesis is to develop a unified framework for classification and representation learning. These two methods provide complementary approaches allowing to address the problem using a hierarchical modeling approach. The representation learning approach is used to build a low-level model of the data whereas classification is used to incorporate supervised information and may be seen as a high-level interpretation of the data. Two different paradigms, namely Bayesian models and optimization approaches, are explored to set up this hierarchical model. The proposed models are then tested in the specific context of hyperspectral imaging where the representation learning task is specified as a spectral unmixing proble

Hyperspectral unmixing: a theoretical aspect and applications to CRISM data processing

Hyperspectral imaging has been deployed in earth and planetary remote sensing, and has contributed the development of new methods for monitoring the earth environment and new discoveries in planetary science. It has given scientists and engineers a new way to observe the surface of earth and planetary bodies by measuring the spectroscopic spectrum at a pixel scale. Hyperspectal images require complex processing before practical use. One of the important goals of hyperspectral imaging is to obtain the images of reflectance spectrum. A raw image obtained by hyperspectral remote sensing usually undergoes conversion to a physical quantity representing the intensity of light energy, called radiance. In order to obtain the reflectance spectrum of surface, the contribution of atmosphere needs to be addressed and then divided by a spectrum of ``white reference.\u27\u27 Furthermore, the obtained reflectance spectra of image pixels are likely to be the mixtures of multiple species due to limited spatial resolution from orbits around planets. Hyperspectral unmixing is an attempt to unmix those pixels - to identify substantial components and estimate their fractional abundances. Hyperspectral unmixing has been widely explored in the literature, but there are still many aspects yet to be studied. The majority of research focuses on the development of methods to retrieve correct substantial components and accurate fractional abundances. Their theoretical aspects are rarely investigated. Chapter 2 will pursue a theoretical aspect of sparse unmixing, one of the hyperspectral unmixing problems and derive its theoretical conditions that guarantee the correct identification of substantial components. Hyperspectral unmixing can also be used for other stages of hyperspectral data processing. Chapter 3 explores the application of hyperspectral unmixing to the processing of hyperspectral image acquired by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) onboard the Mars Reconnaissance Orbiter (MRO). In particular, new atmospheric correction and de-noising methods for the CRISM data that use a hyperspectral unmixing to model surface spectra, are introduced. The new methods remove most of the problematic systematic artifacts present in CRISM images and significantly improve signal quality. Chapter 4 investigates how hyperspectral images acquired from orbits can be combined with ground exploration. In the recent rush of the launch of many Martian ground rover missions, it is important to effectively integrate knowledge obtained by hyperspectral remote sensing from orbits into ground exploration for facilitating Martian exploration. In specific, this dissertation solves the problem of matching hyperspectral image pixels obtained by the CRISM with ground mega-pixel images acquired by the Mast Camera (Mastcam) installed on the Curiosity rover on Mars. A new systematic methodology to map the CRISM and Mastcam images onto high resolution surface topography is developed