Hyperspectral images taken from aircraft or satellites contain information from hundreds of spectral bands, within which lie latent lower-dimensional structures that can be exploited for classifying vegetation and other materials. A disadvantage of working with hyperspectral images is that, due to an inherent trade-off between spectral and spatial resolution, they have a relatively coarse spatial scale, meaning that single pixels may correspond to spatial regions containing multiple materials. This article introduces the Diffusion and Volume maximization-based Image Clustering (D-VIC) algorithm for unsupervised material clustering to address this problem. By directly incorporating pixel purity into its labeling procedure, D-VIC gives greater weight to pixels corresponding to a spatial region containing just a single material. D-VIC is shown to outperform comparable state-of-the-art methods in extensive experiments on a range of hyperspectral images, including land-use maps and highly mixed forest health surveys (in the context of ash dieback disease), implying that it is well-equipped for unsupervised material clustering of spectrally-mixed hyperspectral datasets.

Hyperspectral images, which store a hundred or more spectral bands of reflectance, have become an important data source in natural and social sciences. Hyperspectral images are often generated in large quantities at a relatively coarse spatial resolution. As such, unsupervised machine learning algorithms incorporating known structure in hyperspectral imagery are needed to analyze these images automatically. This work introduces the Spatial-Spectral Image Reconstruction and Clustering with Diffusion Geometry (DSIRC) algorithm for partitioning highly mixed hyperspectral images. DSIRC reduces measurement noise through a shape-adaptive reconstruction procedure. In particular, for each pixel, DSIRC locates spectrally correlated pixels within a data-adaptive spatial neighborhood and reconstructs that pixel's spectral signature using those of its neighbors. DSIRC then locates high-density, high-purity pixels far in diffusion distance (a data-dependent distance metric) from other high-density, high-purity pixels and treats these as cluster exemplars, giving each a unique label. Non-modal pixels are assigned the label of their diffusion distance-nearest neighbor of higher density and purity that is already labeled. Strong numerical results indicate that incorporating spatial information through image reconstruction substantially improves the performance of pixel-wise clustering.

In hyperspectral imaging for remote sensing, learning from unlabeled data by unsupervised methods is very challenging and it is the subject of considerable recent interest since the collection of large datasets by aircraft, UAVs and satellites has become ubiquitous. We experiment with unsupervised endmember extraction and classification of hyperspectral data collected over India by NASA's AVIRIS-NG airborne remote sensor. We have downloaded some of this data from the NASA-JPL portal in Pasadena, CA, for the purpose of studying land cover and land usage, and especially forests, in India. We report on results from our experiments with unsupervised endmember-based methods and clustering methods for classifying images from a mixed forest region that we selected from the Shoolpaneshwar Wildlife Sanctuary in Western In-dia. Randomized numerical methods are used to speed up the large-scale computations.

We consider three-dimensional (3D) localization and imaging of space debris from only one two-dimensional (2D) snapshot image. The technique involves an optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources, with the latter being encoded in the angle of rotation of the PSF. We formulate 3D localization into a large-scale sparse 3D inverse problem in the discretized form. A recently developed penalty called continuous exact l0 (CEL0) is applied in this problem for the Gaussian noise model. Numerical experiments and comparisons illustrate the efficiency of the algorithm.

We propose a novel two-stage method for the classification of hyperspectral images. Pixel-wise classifiers, such as the classical support vector machine (SVM), consider spectral information only. As spatial information is not utilized, the classification results are not optimal and the classified image may appear noisy. Many existing methods, such as morphological profiles, superpixel segmentation, and composite kernels, exploit the spatial information. In this paper, we propose a two-stage approach inspired by image denoising and segmentation to incorporate the spatial information. In the first stage, SVMs are used to estimate the class probability for each pixel. In the second stage, a convex variant of the Mumford–Shah model is applied to each probability map to denoise and segment the image into different classes. Our proposed method effectively utilizes both spectral and spatial information of the data sets and is fast as only convex minimization is needed in addition to the SVMs. Experimental results on three widely utilized real hyperspectral data sets indicate that our method is very competitive in accuracy, timing, and the number of parameters when compared with current state-of-the-art methods, especially when the inter-class spectra are similar or the percentage of training pixels is reasonably high.

Regular expressionsRegular expressions are a fundamental technique for pattern matching in textual data and for lexical analysis in compiler design. They are ubiquitous in most systems used today, including operating systems (e.g. grep, awk), computer languages (e.g. Perl, Java, Python), and web search engines (e.g. Google). However, this highly useful way of exploring and mining data has thus far eluded non-textual datasets, such as images and 3D geometric data. Shape-based searching of 3D objects continues to be a core problem in computer vision Computer vision . We propose a novel extension of traditional finite-automata-based methods to find multi-dimensional objects in spatial data sets. Our approach extends regular expressions Regular expressions and finite automata to multi-dimensional pattern models. While we demonstrate the effectiveness and efficiency of our approach for finding target objects in 3D LiDAR LiDAR image data sets using an implicit geometry representation of the data, it is important to note that the proposed technique can be applied to any general data set of vertices in 3D space. Non-geometric information, such as material and spectral characteristics from hyperspectral image data can also be discretized and encoded into our approach.

An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved space debris, which can be regarded as a swarm of point sources, can scatter a fraction of laser irradiance back into the imaging sensor. Determining the source locations and fluxes is a large-scale sparse 3D inverse problem, for which we have developed efficient and effective algorithms based on sparse recovery using non-convex optimization. Numerical simulations illustrate the efficiency and stability of the algorithms.

This paper proposes a data-driven approach that derives individual-specific sparse working correlation matrices for generalized estimating equations (GEEs). The approach is motivated by the observation that, in some applications of the GEE, the covariance structure across individuals is heterogeneous and cannot be appropriately captured by a single correlation matrix. The proposed approach enjoys both favorable computational and asymptotic properties. Simulation experiments and analysis of intensively measured longitudinal data on 158 participants collected from a dietary and emotion study are presented.

We solve the l(2)-l(p) sparse recovery problem by transforming the objective function into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Preliminary numerical experiments with simulated compressive sensing 1D data are provided to illustrate that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge in comparison to standard approaches.

This chapter discusses the performance of five different iris segmentation algorithms on challenging periocular images. The goal is to convey some of the difficulties in localizing the iris structure in images of the eye characterized by variations in illumination, eyelid and eyelash occlusion, defocus blur, motion blur, and low resolution. The five algorithms considered in this regard are based on the (a) integrodifferential operator, (b) Hough transform, (c) geodesic active contours, (d) active contours without edges, and (e) directional ray detection method. Experiments on the Face and Ocular Challenge Series (FOCS) database highlight the pros and cons of the individual segmentation algorithms.

We investigate classification from pixel-level fusion of Hyperspectral (HSI) and Light Detection and Ranging (LiDAR) data using convolutional neural networks (CNN). HSI and LiDAR imaging are complementary modalities increasingly used together for geospatial data collection in remote sensing. HSI data is used to glean information about material composition and LiDAR data provides information about the geometry of objects in the scene. Two key questions relative to classification performance are addressed: the effect of merging multi-modal data and the effect of uncertainty in the CNN training data. Two recent co-registered HSI and LiDAR datasets are used here to characterize performance. One was collected, over Houston TX, by the University of Houston National Center for Airborne Laser Mapping with NSF sponsorship, and the other was collected, over Gulfport MS, by Universities of Florida and Missouri with NGA sponsorship.

Summary We present an iterative approach to solve separable nonlinear least squares problems arising in the estimation of wavelength‐dependent point spread function parameters for hyperspectral imaging. A variable projection Gauss–Newton method is used to solve the nonlinear least squares problem. An analysis shows that the Jacobian can be potentially very ill conditioned. To deal with this ill conditioning, we use a combination of subset selection and other regularization techniques. Experimental results related to hyperspectral point spread function parameter identification and star spectrum reconstruction illustrate the effectiveness of the resulting numerical scheme. Copyright © 2015 John Wiley & Sons, Ltd.

In an era of massive data gathering, analysts are facing an increasingly difficult decision regarding the amount of data features to consider for the purpose of target detection and classification. While more data may offer additional information at the cost of potentially prohibitive increase in computation time, it is unclear whether classification accuracy increases accordingly. In this study, we address this question from an information-theoretic standpoint, providing upper and lower bounds of misclassification error, using Chernoff Information (CI) as an upper bound and the resistor-average distance as a lower bound. Our results are applied to the problem of classification from the fusion of real hyperspectral and LiDAR data, using numerical experiments and analysis. The results show that, in principle, adding extra data features does not decrease the CI, or equivalently the classification accuracy. However, empirically this is not the case, and our results show that in fact the indiscriminate inclusion of more data can lead to reduced classification accuracy. We offer a hill-climbing algorithm to incrementally rank and reorder features in such a way that adding an extra feature to any first-k features does not lead to information loss or, equivalently, reduction in classification accuracy. Q. Zhang is with the Department of Biostatistical Sciences, Wake Forest School of Medicine, Winston-Salem, North Carolina. Victor P. Pauca is with the Department of Computer Science, Wake Forest University, Winston-Salem, North Carolina. Robert J. Plemmons is with the Departments of Computer Science and Mathematics, Wake Forest University, Winston-Salem, North Carolina. Robert Rand is with the National Geospatial-Intelligence Agency. Todd C. Torgersen is with the Department of Computer Science, Wake Forest University, Winston-Salem, North Carolina.

A major challenge in astronomical imaging is to characterize objects that are spatially non-resolvable. We consider here an approach for identifying non-resolvable space objects such as satellites or debris using compressive spectro-polarimetric imaging. In particular, deblurring algorithms are described for mitigating the effects of atmospheric turbulence blurring on such images.

Our interest here is spectral imaging for space object identification based upon imaging using simultaneous measurements at different wavelengths. AMOS sensors can collect simultaneous images ranging from visible to LWIR. Multiframe blind deconvolution (MFBD) has demonstrated success by acquiring near-simultaneous multiple images for reconstructing space objects, and another success has been shown through adding phase diversity (PD) by splitting the light beam in channels with different phase functions. So far, most MFBD and PD applications have been focused on monochromatic images, with a few MFBD studies on multispectral images, also called the wavelength diversity. In particular, B. Calef has shown that wavelength-diverse MFBD is a promising technique for combining data from multiple sensors to yield a higher-quality reconstructed image. Here, we present optimization algorithms to blindly deconvolve observed blurred and noisy hyperspectral images with phase diversity at each wavelength channel. We use the facts that at longer wavelengths, turbulence effects on the phase are less severe, while diffraction effects at shorter wavelengths are less severe. Moreover, because the blurring kernels of all wavelength channels essentially share the same optimal path difference (OPD) function, we have greatly reduced the number of parameters in the blurring kernel. We model the true hyperspectral object by a linear spectral unmixing model, which reduces the number of pixels to be recovered. Because the number of known parameters is far greater than the number of unknowns, the method enjoys an enhanced capability of successful reconstruction. We simultaneously reconstruct the true object, estimate the blurring kernels, and separate the object into spectrally homogeneous segments, each characterized by its support and spectral signature, an important step for analyzing the material compositions of space objects.

Due to lack of direct illumination, objects under shadows often reflect significantly less number of photons into a remote hyperspectral imaging (HSI) sensor, leading to low radiance levels near to or below noise. Attempts to perform object classification based on these observed radiances often produce poor results, grouping pixels under shaded areas as being a part of the same class. By fusing LiDAR and HSI data through a physical model, we develop a simple and efficient illumination correction method to remove the direct illumination component of the observed HSI radiance data. This correction then enables accurate object classification, regardless of whether spectral signatures are exposed directly to sunlight. In addition, methods for estimating the area under shadow and geometric parameters such as direct illumination factor and sky-view factor from LiDAR data are presented.

We evaluate recently developed randomized matrix decomposition methods for fast lossless compression and reconstruction of hyperspectral imaging (HSI) data. The simple random projection methods have been shown to be effective for lossy compression without severely affecting the performance of object identification and classification. We build upon these methods to develop a new double-random projection method that may enable security in data transmission of compressed data. For HSI data, the distribution of elements in the resulting residual matrix, i.e., the original data subtracted by its low-rank representation, exhibits a low entropy relative to the original data that favors high-compression ratio. We show both theoretically and empirically that randomized methods combined with residual-coding algorithms can lead to effective lossless compression of HSI data. We conduct numerical tests on real large-scale HSI data that shows promise in this case. In addition, we show that randomized techniques can be applicable for encoding on resource-constrained on-board sensor systems, where the core matrix-vector multiplications can be easily implemented on computing platforms such as graphic processing units or field-programmable gate arrays. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Abstract : The investigators report on their findings, recent publication, and presentations in the areas of lenslet array imaging, wavefront encoding, and non-negative matrix factorization for material component (end-member) identification. Lenslet arrays enable a number of imaging modalities, including amplitude diversity, polarization diversity, wavelength diversity (multi-spectral data) and phase diversity. Each of these techniques extends traditional imaging by modifying the data acquisition to implicitly capture features that would otherwise be undetectable. Post-processing converts implicitly captured or encoded information to a form suitable for human or automated identification tasks. The problem of material identification from multi-spectral image data (blind source separation) can be formulated as a non-negative matrix factorization problem or as a tensor factorization problem. Non-uniqueness and numerical stability are frequently difficult issues. We report here on recent progress on using stochastic constraints for improving the numerical stability of the computation. Current (2009) and prior results relating to pupil phase encoding were adapted to mitigate a frequency-agile pulsed laser attack against CCD-based cameras.