Noise estimation for hyperspectral subspace identification on FPGAs

[EN] We present a reliable and efficient FPGA implementation of a procedure for the computation of the noise estimation matrix, a key stage for subspace identification of hyperspectral images. Our hardware realization is based on numerically stable orthogonal transformations, avoids the numerical difficulties of the normal equations method for the solution of linear least squares problems (LLS), and exploits the special relations between coupled LLS problems arising in the hyperspectral image. Our modular implementation decomposes the QR factorization that comprises a significant part of the cost into a sequence of suboperations, which can be efficiently computed on an FPGA.This work was supported by MINECO Projects TIN2014-53495-R and TIN2013-40968-P.León, G.; González, C.; Mayo Gual, R.; Mozos, D.; Quintana-Ortí, ES. (2019). Noise estimation for hyperspectral subspace identification on FPGAs. The Journal of Supercomputing. 75(3):1323-1335. https://doi.org/10.1007/s11227-018-2425-313231335753Anderson E et al (1999) E LAPACK users’ guide, 3rd edn. SIAM, PhiladelphiaBenner P, Novaković V, Plaza A, Quintana-Ortí ES, Remón A (2015) Fast and reliable noise estimation for Hyperspectral subspace identification. IEEE Geosci Remote Sens Lett 12(6):1199–1203Bioucas-Dias J, Nascimento J (2008) Hyperspectral subspace identification. IEEE Trans Geosci Remote Sens 46:2435–2445Bioucas-Dias J, Plaza A, Dobigeon N, Parente M, Du Q, Gader P, Chanussot J (2012) Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE JSTARS 5(2):354–379Björck A (1996) Numerical methods for least squares problems. Society for Industrial and Applied Mathematics (SIAM), PhiladelphiaGunnels JA, Gustavson FG, Henry GM, van de Geijn RA (2001) FLAME: formal linear algebra methods environment. ACM Trans Math Softw 27(4):422–455. https://doi.org/10.1145/504210.504213Kerekes J, Baum J (2002) Spectral imaging system analytical model for subpixel object detection. IEEE Trans Geosci Remote Sens 40(5):1088–1101León G, González C, Mayo R, Quintana-Ortí ES, Mozos D (2017) Energy-efficient QR factorization on FPGAs. In: Proceedings of 17th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2017), Cádiz, Spai

Spectral Quality Metrics for Terrain Classification

Current image quality approaches are designed to assess the utility of single band images by trained image analysts. While analysts today are certainly involved in the exploitation of spectral imagery, automated tools are generally used as aids in the analysis and offer hope in the future of significantly reducing the analysis timeline and analyst work load. Thus, there is a recognized need for spectral image quality metrics that include the effects of automated algorithms. Previously, we have reported on candidate approaches for spectral quality metrics in the context of unresolved object detection. We have continued these efforts through the use of empirical trade studies in the context of ground cover terrain classification. HYDICE airborne hyperspectral imagery have been analyzed for the effects on scene classification accuracy of spatial resolution, signal-to-noise ratio, and number of spectral channels. Various classification algorithms including Gaussian maximum likelihood, spectral angle mapper, and Euclidean minimum distance have been considered. Performance metrics included classification accuracy, confusion matrices, and the Kappa coefficient. An extension of the previously developed Spectral Quality Equation (SQE) has been developed for the terrain classification application. As expected, the accuracy of terrain classification shows only modest sensitivity to the parameters considered, except at the extreme cases of high noise, few bands, and small ground resolution. However, these results are useful in continuing to develop the quantitative relationships necessary for characterizing the quality of spectral imagery in various applications

A Comparative Evaluation of Spectral Quality Metrics for Hyperspectral Imagery

Quantitative methods to assess or predict the quality of a spectral image are the subject of a number of current research activities. An accepted methodology would be highly desirable to use for data collection tasking or data archive searches in way analogous to the current uses of the National Imagery Interpretation Rating Scale (NIIRS) General Image Quality Equation (GIQE). A number of approaches to the estimation of quality of a spectral image have been published. An issue with many of these approaches is that they tend to be constructed around specific tasks (target detection, background classification, etc.) While this has often been necessary to make the quality assessment tractable, it is desirable to have a method that is more general. One such general approach is presented in a companion paper (Simmons, et al1). This new approach seeks to get at the heart of the general spectral imagery quality analysis problem – assessing the confidence of an image analyst in performing a specified task with a specific spectral image. In this approach the quality from spatial and spectral aspects of the imagery are treated separately and then a fusion concept known as “semantic transformation” is used to combine the utility, or confidence, from these two aspects into an overall quality metric. This paper compares and contrasts the various methods published in the literature with this new General Spectral Utility Metric (GSUM). In particular, the methods are applied to a target detection problem using data from the airborne HYDICE instrument collected at Forest Radiance I. While the GSUM approach is seen to lead to intuitively pleasing results, its sensitivity to image parameters was not seen to be consistent with previously published approaches. However, this likely resulted more from limitations of the previous approaches than with problems with GSUM. Further studies with additional spectral imaging applications are recommended along with efforts to integrate a performance predication capability into the GSUM framework

EXPLORING LIMITS IN HYPERSPECTRAL UNRESOLVED OBJECT DETECTION

ABSTRACT Hyperspectral imaging systems have been shown to enable unresolved object detection through enhanced spectral characteristics of the data. Robust detection performance prediction tools are desirable for many reasons including optimal system design and operation. The research described in this paper explores the general understanding of system factors that limit detection performance. Examples are shown for detectability limits due to target subpixel fill fraction, sensor noise, and scene complexity

The quantization error in a Self-Organizing Map as a contrast and color specific indicator of single-pixel change in large random patterns

The quantization error in a fixed-size Self-Organizing Map (SOM) with unsupervised winner-take-all learning has previously been used successfully to detect, in minimal computation time, highly meaningful changes across images in medical time series and in time series of satellite images. Here, the functional properties of the quantization error in SOM are explored further to show that the metric is capable of reliably discriminating between the finest differences in local contrast intensities and contrast signs. While this capability of the QE is akin to functional characteristics of a specific class of retinal ganglion cells (the so-called Y-cells) in the visual systems of the primate and the cat, the sensitivity of the QE surpasses the capacity limits of human visual detection. Here, the quantization error in the SOM is found to reliably signal changes in contrast or colour when contrast information is removed from or added to the image, but not when the amount and relative weight of contrast information is constant and only the local spatial position of contrast elements in the pattern changes. While the RGB Mean reflects coarser changes in colour or contrast well enough, the SOM-QE is shown to outperform the RGB Mean in the detection of single-pixel changes in images with up to five million pixels. This could have important implications in the context of unsupervised image learning and computational building block approaches to large sets of image data (big data)