Num trabalho futuro seria interessante criar um sistema completo de aquisição e análise de dados hiperespetrais. Este sistema consistiria em integrar uma câmera hiperespetral, de baixo custo, à arquitetura implementada.
Integrar à arquitetura um controlador de acesso direto à memória externa da placa, e utilizar essa memória para armazenar os dados a serem processados pela arquite- tura, de modo a aumentar assim o número de píxeis a serem processados.
gula flutuante personalizada, de modo a definir o número mínimo de bits do expoente e da mantissa.
Referências
[1] Q. Tong, Y. Xue, and L. Zhang, “Progress in Hyperspectral Remote Sensing Sci- ence and Technology in China Over the Past Three Decades,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 7, no. 1, pp. 70–91, 2014.
[2] S. Serpico, G. Moser, and A. Cattoni, “Feature reduction for classification pur- pose,” in Hyperspectral Data Exploitation: Theory and Applications, pp. 245–274, Wiley-Interscience, 2007.
[3] G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, “The airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sensing of Environment, vol. 44, no. 2-3, pp. 127–143, 1993.
[4] L. J. Rickard, R. W. Basedow, E. F. Zalewski, P. R. Silverglate, and M. Landers, “Hydice: an airborne system for hyperspectral imaging,” Proc. SPIE, vol. 1937, pp. 173–179, 1993.
[5] T. Cocks, R. Jenssen, A. Stewart, I. Wilson, and T. Shields, “The HyMap Airborne Hyperspectral Sensor: The System, Calibration and Performance.” 1st EARSEL Workshop on Imaging Spectroscopy, pp. 1-7, 1998.
[6] M. E. Schaepman, L. de Vos, and K. I. Itten, “Apex-airborne prism experi- ment: hyperspectral radiometric performance analysis for the simulation of the future esa land surface processes earth explorer mission,” Proc. SPIE, vol. 3438, pp. 253–262, 1998.
[7] J. Pearlman, P. Barry, C. Segal, J. Shepanski, D. Beiso, and S. Carman, “Hyperion, a space-based imaging spectrometer,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 41, no. 6, pp. 1160–1173, 2003.
[8] A. Kumar and A. Chowdhury, “Hyper-spectral imager in visible and near-infrared band for lunar compositional mapping,” Journal of Earth System Science, vol. 114, no. 6, pp. 721–724, 2005.
[9] M. D. Lewis, R. W. Gould, R. Arnone, P. Lyon, P. M. Martinolich, R. Vaughan, A. Lawson, T. Scardino, W. Hou, W. Snyder, R. Lucke, M. Corson, M. Montes, and C. Davis, “The hyperspectral imager for the coastal ocean (hico): Sensor and data processing overview,” in OCEANS, MTS/IEEE Biloxi - Marine Technology for Our Future: Global and Local Challenges, pp. 1–9, 2009.
[10] S. J. Hook, “NASA 2014 The Hyperspectral Infrared Imager (HyspIRI) – Science Impact of Deploying Instruments on Separate Platforms,” Jet Propulsion Labora- tory, 2014.
[11] S. Hook, “The hyperspectral thermal emission spectrometer (hytes)-early results,” in IEEE International Geoscience and Remote Sensing Symposium, 2013.
[12] P. Barry, “Eo-1/hyperion science data user’s guide, level 1_b,” TRW Space, De- fense & Information Systems, Redondo Beach, CA, Rep. HYP. TO, vol. 1, 2001. [13] J. M. Bioucas-Dias, A. Plaza, G. Camps-Valls, P. Scheunders, N. Nasrabadi, and
J. Chanussot, “Hyperspectral Remote Sensing Data Analysis and Future Challen- ges,” IEEE Geoscience and Remote Sensing Magazine, vol. 1, no. 2, pp. 6–36, 2013.
[14] J. Setoain, C. Tenllado, M. Prieto, D. Valencia, A. Plaza, and J. Plaza, “Parallel hy- perspectral image processing on commodity graphics hardware,” in Parallel Pro- cessing Workshops. ICPP Workshops. International Conference on, pp. 465–472, 2006.
[15] W. Carter, K. Duong, R. Freeman, H. Hsieh, J. Ja, J. Mahoney, L. Ngo, and S. Sze, “A user programmable reconfigurable logic array,” Proceedings of the Custom In- tegrated Circuits Conference, pp. 233–235, 1986.
[16] S. Hauck, “The roles of fpgas in reprogrammable systems,” Proceedings of the IEEE, vol. 86, no. 4, pp. 615–638, 1998.
[17] V. Tanaya and W. Xiaofeng, “On-board partial run-time reconfiguration for pico-satellite constellations,” in Proc. of First NASA/ESA Conference on Adaptive Hardware and System, pp. 262–269, 2006.
[18] A. Plaza, Q. Du, Y.-L. Chang, and R. King, “High performance computing for hy- perspectral remote sensing,” Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of, vol. 4, no. 3, pp. 528–544, 2011.
[19] S. Lopez, P. Horstrand, G. M. Callico, J. F. Lopez, and R. Sarmiento, “A novel architecture for hyperspectral endmember extraction by means of the modified vertex component analysis (mvca) algorithm,” Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of, vol. 5, no. 6, pp. 1837–1848, 2012.
[20] J. Rosário, J. M. P. Nascimento, and M. Véstias, “Fpga-based archi- tecture for hyperspectral endmember extraction,” Proc. SPIE, vol. 9247, pp. 924703–924703–11, 2014.
[21] D. Valencia, A. Plaza, M. A. Vega-Rodríguez, and R. M. Pérez, “Fpga design and implementation of a fast pixel purity index algorithm for endmember extraction in hyperspectral imagery,” Proc. SPIE, vol. 5995, pp. 599508–599508–10, 2005. [22] C. González, D. Mozos, J. Resano, and A. Plaza, “Fpga for computing the pi-
xel purity index algorithm on hyperspectral images.,” in International Conference on Engineering of Reconfigurable Systems and Algorithms, ERSA, p. 125–131, 2010.
[23] C. González, J. Resano, D. Mozos, A. Plaza, and D. Valencia, “Fpga implemen- tation of the pixel purity index algorithm for remotely sensed hyperspectral image analysis,” EURASIP Journal on Advances in Signal Processing, vol. 68, pp. 1–13, 2010.
[24] C. González, D. Mozos, J. Resano, and A. Plaza, “Fpga implementation of the n-findr algorithm for remotely sensed hyperspectral image analysis,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 50, no. 2, pp. 374–388, 2012.
[25] C.-I. Chang, W. Xiong, and C.-C. Wu, “Field-programmable gate array design of implementing simplex growing algorithm for hyperspectral endmember extrac- tion,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 51, no. 3, pp. 1693–1700, 2013.
[26] C. González, J. Resano, A. Plaza, and D. Mozos, “Fpga implementation of abun- dance estimation for spectral unmixing of hyperspectral data using the image space reconstruction algorithm,” Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of, vol. 5, no. 1, pp. 248–261, 2012.
[27] R. Nekovei and M. Ashtijou, “Reconfigurable acceleration for hyperspectral target detection,” in IEEE International Geoscience and Remote Sensing Symposium., pp. 3229–3232, IEEE, 2007.
[28] H. M. Hussain, K. Benkrid, A. T. Erdogan, and H. Seker, “Highly parameterized k-means clustering on fpgas: Comparative results with gpps and gpus,” in Recon- figurable Computing and FPGAs (ReConFig), pp. 475–480, 2011.
[29] Y.-T. Hwang, C.-C. Lin, and R.-T. Hung, “Lossless hyperspectral image compres- sion system-based on hw/sw codesign,” Embedded Systems Letters, IEEE, vol. 3, no. 1, pp. 20–23, 2011.
[30] Digilent ZedBoard Zynq, FPGA, “Dev. board documentation,” 2012.
[31] M. Ciznicki, K. Kurowski, and A. Plaza, “Graphics processing unit implementation of jpeg2000 for hyperspectral image compression,” Journal of Applied Remote Sensing, vol. 6, no. 1, pp. 061507–1–061507–14, 2012.
[32] N. Keshava and J. Mustard, “Spectral unmixing,” Signal Processing Magazine, IEEE, vol. 19, no. 1, pp. 44–57, 2002.
[33] J. B. Adams, M. O. Smith, and P. E. Johnson, “Spectral mixture modeling: A new analysis of rock and soil types at the viking lander 1 site,” Journal of Geophysical Research: Solid Earth, vol. 91, no. B8, pp. 8098–8112, 1986.
[34] D. Zhang, J. Yin, and H. Li, “Mapping of surface sediment types in intertidal flat using linear spectral unmixing of hyperion data,” in Remote Sensing, Environment and Transportation Engineering (RSETE), pp. 450–453, 2011.
[35] C.-I. Chang, Hyperspectral Data Processing: Algorithm Design and Analysis. John Wiley & Sons, 2013.
[36] D. Gu, A. Gillespie, A. Kahle, and F. Palluconi, “Autonomous atmospheric com- pensation (aac) of high resolution hyperspectral thermal infrared remote-sensing imagery,” Geoscience and Remote Sensing, vol. 38, no. 6, pp. 2557–2570, 2000. [37] I. Olthof, C. Butson, and R. Fraser, “Signature extension through space for northern landcover classification: A comparison of radiometric correction methods,” Remote Sensing of Environment, vol. 95, no. 3, pp. 290–302, 2005. [38] W. Moses, Atmospheric Correction of hyperspectral data: execution of and com-
parison between FLAASH and TAFKAA_6S. Cornell University, 2005.
[39] J. Bioucas-Dias and J. Nascimento, “Hyperspectral subspace identification,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 46, no. 8, pp. 2435–2445, 2008.
[40] J. M. Nascimento and J. M. Bioucas Dias, “Vertex component analysis: A fast algorithm to unmix hyperspectral data,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 43, no. 4, pp. 898–910, 2005.
[41] J. W. Boardman et al., “Automating spectral unmixing of aviris data using con- vex geometry concepts,” in Summaries 4th Annu. JPL Airborne Geoscience Workshop, vol. 1, pp. 11–14, JPL Publication 93–26, 1993.
[42] M. E. Winter, “N-findr: an algorithm for fast autonomous spectral end-member determination in hyperspectral data,” Proc. SPIE, vol. 3753, pp. 266–275, 1999. [43] C.-I. Chang, C.-C. Wu, W.-m. Liu, and Y.-C. Ouyang, “A new growing method for
simplex-based endmember extraction algorithm,” Geoscience and Remote Sen- sing, IEEE Transactions on, vol. 44, no. 10, pp. 2804–2819, 2006.
[44] B. N. Datta, Numerical linear algebra and applications. Siam, 2010.
[45] L. N. Trefethen and D. Bau III, Numerical linear algebra, vol. 50. Siam, 1997. [46] N. J. Higham, Accuracy and stability of numerical algorithms. Siam, 2002.
[47] R. N. Clark, G. A. Swayze, R. Wise, K. E. Livo, T. M. Hoefen, R. F. Kokaly, and S. J. Sutley, USGS Digital Spectral Library splib05a, USGS Open File Report 03-395. US Geological Survey Reston, VA, 2003.
[48] A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian data analysis. CRC press, 2013.
[49] H. W. Kuhn, “The hungarian method for the assignment problem,” Naval research logistics quarterly, vol. 2, no. 1-2, pp. 83–97, 1955.
[50] C. H. Papadimitriou and K. Steiglitz, Combinatorial optimization: algorithms and complexity. Courier Dover Publications, 1998.
[51] F. Kruse, A. Lefkoff, J. Boardman, K. Heidebrecht, A. Shapiro, P. Barloon, and A. Goetz, “The spectral image processing system (sips)—interactive visualiza- tion and analysis of imaging spectrometer data,” Remote sensing of environment, vol. 44, no. 2, pp. 145–163, 1993.
[52] J. C. Price, “How unique are spectral signatures?,” Remote Sensing of Environ- ment, vol. 49, no. 3, pp. 181–186, 1994.
[53] J. W. Boardman, F. A. Kruse, and R. O. Green, “Mapping target signatures via partial unmixing of aviris data,” in Summaries 5th JPL Airborne Earth Science Workshop, vol. 1, pp. 23–26, 1995.
[54] C.-I. Chang, “Spectral information divergence for hyperspectral image analy- sis,” in IEEE International Geoscience and Remote Sensing Symposium., vol. 1, pp. 509–511, 1999.
[55] S. M. Schweizer and J. M. Moura, “Efficient detection in hyperspectral imagery,” Image Processing, IEEE Transactions on, vol. 10, no. 4, pp. 584–597, 2001. [56] G. Golub and C. Van Loan, Matrix Computations. Johns Hopkins Studies in the
Mathematical Sciences, Johns Hopkins University Press, 2013.
[57] M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidis- tributed uniform pseudo-random number generator,” ACM Transactions on Mode- ling and Computer Simulation (TOMACS), vol. 8, no. 1, pp. 3–30, 1998.
[58] Xilinx, Inc., “LogiCORE IP Floating-Point Operator v6.1.” Xilinx, Inc., Natick, San Jose, United States, 2012.
[59] Xilinx, Inc., “Logicore ip block memory generator v7.3.” Xilinx, Inc., Natick, San Jose, United States, 2012.
[60] J. E. Sánchez, E. Auge, J. Santalo, I. Blanes, J. Serra-Sagrista, and A. Kiely, “Re- view and implementation of the emerging ccsds recommended standard for mul- tispectral and hyperspectral lossless image coding,” in Data Compression, Com- munications and Processing (CCP), pp. 222–228, 2011.
FPGA-based Architecture for Hyperspectral Endmember
Extraction
Jo˜ao Ros´arioa, Jos´e M. P. Nascimentoa,b, M´ario V´estiasa,c
aInstituto Superior de Engenharia de Lisboa, Lisbon, Portugal bInstituto de Telecomunica¸c˜oes, Lisbon, Portugal
cINESC-ID , Lisbon, Portugal
ABSTRACT
Hyperspectral instruments have been incorporated in satellite missions, providing data of high spectral resolution of the Earth. This data can be used in remote sensing applications, such as, target detection, hazard prevention, and monitoring oil spills, among others. In most of these applications, one of the requirements of paramount importance is the ability to give real-time or near real-time response. Recently, onboard processing systems have emerged, in order to overcome the huge amount of data to transfer from the satellite to the ground station, and thus, avoiding delays between hyperspectral image acquisition and its interpretation. For this purpose, compact reconfigurable hardware modules, such as field programmable gate arrays (FPGAs) are widely used.
This paper proposes a parallel FPGA-based architecture for endmember’s signature extraction. This method based on the Vertex Component Analysis (VCA) has several advantages, namely it is unsupervised, fully auto- matic, and it works without dimensionality reduction (DR) pre-processing step. The architecture has been de- signed for a low cost Xilinx Zynq board with a Zynq-7020 SoC FPGA based on the Artix-7 FPGA programmable logic and tested using real hyperspectral data sets collected by the NASA’s Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) over the Cuprite mining district in Nevada. Experimental results indicate that the pro- posed implementation can achieve real-time processing, while maintaining the methods accuracy, which indicate the potential of the proposed platform to implement high-performance, low cost embedded systems, opening new perspectives for onboard hyperspectral image processing.
Keywords: Hyperspectral Endmember Extraction, Vertex Component Analysis (VCA), Field-Programmable Gate Arrays (FPGA), Onboard Processing.
1. INTRODUCTION
Hyperspectral imagery is a continuously growing area in remote sensing applications. The spectral range ex- tending from the visible region through the near-infrared and mid-infrared in hundreds of narrow contiguous bands, provides a very high spectral resolution, which allows the detection and the discrimination between dif- ferent chemical elements of the observed image.1–3 These instruments, because of their potential in remote sensing applications, such as, target detection for security/militar purposes, hazard prevention, and monitoring oil spills among others, have been incorporated in satellite missions.4 In most of those applications, one of the requirements of paramount importance is the ability to give real-time or near real-time response.5
Although, these sensors allow to capture large three dimensional data cubes, for instance Hyperion sensor produces a data cube 256× 6925 × 242 in 30 seconds,6 the available downlink bandwidth to ground stations is limited, which brings prohibitive delays that endanger the real-time or near real-time requirements of such applications. Recently, onboard processing systems have emerged, in order to overcome these delays between hyperspectral image acquisition and its interpretation. Such systems need to have high computational perfor- mance, compact size, reduced weight and low power consumption among other characteristics. Additionally, it
Further author information: (Send correspondence to J. Nascimento) E-mail: zen@isel.pt
High-Performance Computing in Remote Sensing IV, edited by Bormin Huang, Sebastian López, Zhensen Wu, Proc. of SPIE Vol. 9247, 924703 · © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2067039
is desirable that those onboard systems could also be flexible in order to be adaptable to the needs of different missions. Field-programmable gate arrays (FPGA) represent a good choice to achieve the above mentioned requirements.7, 8 In recent years, scientific community have proposed several FPGA implementations of hyper- spectral processing techniques, namely for unmixing,9–14endmember extraction,10, 15, 16abundance estimation,17 target detection,18 clustering,19 image compression,20among others.
The main problem of hyperspectral imagery is the low spatial resolution due to the instrument instantaneous field of view (IFOV), thus, the pixel ground size can vary from a few to tens of meters. This means that each pixel is a mixture of several spectrally distinct materials (also called endmembers).1, 21 The endmembers are generally assumed to represent the pure materials present in the image. A wide class of methods, called geometrical approaches, aim to infer the set of endmembers, at a low computational complexity. These methods assume the linear mixture model and the presence of pure pixels in the dataset, i.e., pixels containing just one endmember. This paper proposes a new endmember extraction architecture designed for FPGA. This architecture is based on a geometrical based approach, called Vertex Component Analysis (VCA).22Briefly, VCA iteratively projects the pixels onto a direction orthogonal to the subspace spanned by the endmembers already determined. The new endmember signature corresponds to the extreme of the projection. VCA has several advantages, namely it is unsupervised, fully automatic, and it works with or without dimensionality reduction (DR) pre-processing step. This is of paramount importance since the DR step often amounts to compute the eigen-values of the correlation matrix of the dataset, which can take a larger time consumption not compatible with real-time requirements. Additionally, in order to avoid the computation of an inverse matrix typically performed by a singular value decomposition (SVD) present in the seminal VCA work22 herein a QR decomposition is conducted to reuse the orthogonal vectors already determined in previous iterations.9 Since the projection is performed by the multiply-accumulate operation for each band, which does not depend on the others bands operation nor on the others pixels projection, the projection is designed to be implemented in parallel on each iteration, reducing the processing time.
One of this work’s primary goal is the methods design for a low cost embedded system for onboard use. The system does not have hardware resources to compute all pixel projection at once, so the extraction of the endmembers is conducted for each line of the data cube as they are acquired by the sensor. At the end a final selection is done to select the set of endmembers.
In order to validate the implementation, a quantitative study is developed using a Xilinx Zynq board with a Zynq-7020 SoC FPGA based on the Artix-7 FPGA programmable logic. The method is tested using real hyperspectral datasets publicly available. The experimental results indicate that the proposed implementation can achieve real-time performance in the considered FPGA, while maintaining the methods accuracy, thus being able to extract the endmembers signatures in real-time, which makes our reconfigurable system appealing for on-board hyperspectral data processing.
The remainder of this paper is organized as follows. Section 2 formulates the problem and briefly describes the VCA method. Section 3 describes the method design and implementation for the FPGA. Section 4 provides the experimental accuracy and performance results of the architecture implementation on an FPGA using the well-known Cuprite hyperspectral dataset. Section 5 concludes the paper with some remarks and draws some future research work line.
2. ALGORITHM
Linear mixing model considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions, i.e. at each pixel abundances represent the percentage of each endmember that is present in the pixel. Assuming that Y≡ [y1, . . . , yN] ∈ RL×N denotes a matrix holding the N observed spectral vectors, this matrix is given by
Y = MS + W, (1)
m a e 2 m c e 1 f 1 f 2 m b e 3 3 f
Figure 1. Hyperspectral mixture of three endmembers illustrating the VCA algorithm.
where M ≡ [m1, m2, . . . , mp] is a full-rank L× p mixing matrix (mj denotes the jth endmember signature), p is the number of endmembers present in the covered area, S≡ [s1, . . . , sN] ∈ Rp×N is a matrix holding the respective abundance fractions, and W≡ [w1, . . . , wN] ∈ RL×N accounts for additive noise.
To be physically meaningful,1, 21 abundance fractions are subject to nonnegativity and full additivity con- straints, i.e., abundance fractions are in the p− 1 probability simplex:
{S ∈ Rp×N : S≽ 0 , 1T
pS = 1Tn}, (2)
where S≽ 0 means sij ≥ 0, for i = 1, . . . , p, and j = 1, . . . , N , 1p and 1N denote a 1× p and 1 × N column vectors filled of 1’s. Thus, under the linear mixing model the observed spectral vectors in a given scene are in a simplex whose vertices correspond to the endmembers. Assuming that each endmember has at least one pure pixel on the dataset, endmember extraction amounts to find those pure pixels.
VCA is one the most popular endmember extraction algorithms within the literature. VCA is an unsupervised method to extract endmembers from hyperspectral datasets and is based on the geometry of convex sets. It exploits two facts: 1) the endmembers are the vertices of a simplex and 2) the affine transformation of a simplex is also a simplex. VCA is a fully automatic algorithm and it works with or without DR pre-processing step. The algorithm iteratively projects data onto a direction orthogonal to the subspace spanned by the endmembers already determined. The new endmember signature corresponds to the pixel with largest projection. The algorithm repeats the procedure until the whole set of p endmembers is found. Figure 1 illustrates the VCA method working on a simplex defined by a mixture of three endmembers. In the first iteration, data is projected onto the first direction f1. The extreme of the projection corresponds to endmember ma. In the next iteration, endmember mbis found by projecting data onto direction f2, which is orthogonal to ma. Finally, a new direction
f3, orthogonal to the subspace spanned by ma and mb is generated and the endmember mc is found by seeking the extreme of the projection of the dataset onto f3.
Algorithm 1, shows the main steps of the VCA, without the DR step. Although the number of endmembers is much lower than the number of bands (p≪ L) and, thus, it is advantageous, in terms of signal-to-noise ratio (SNR) to represent the spectral vectors in a signal subspace basis,23 this step, as referred before, can take a larger time consumption, which could not be compatible with real-time requirements. More details on the full VCA algorithm can be found in [22]. In Algorithm 1 symbol A denotes the estimated mixing matrix and [A]:,j stands for jth column of A.
Algorithm 1 : VCA
1: A := [eu| 0 | . . . | 0]; {eu := [0, . . . , 0, 1]T and A is a L× p auxiliary matrix}
2: for i := 1 to p do
3: w := randn (0, Ip);{ w is a zero-mean random Gaussian vector}
4: f := (I− AA#)w;{f is a vector orthogonal to the subspace spanned by A:,1:i}
5: v := fTY;
6: k := arg maxj=1,...,N|[v]:,j|;
7: [A]:,i := [Y]:,k;
8: end for
3. FPGA ARCHITECTURE DESIGN AND IMPLEMENTATION
The methodology followed to design the hardware architecture starts with an analysis of the algorithm to identify the most computationally demanding steps followed by a detailed description of how each step of the algorithm is calculated. Then, a hardware architecture that supports the execution of each step of the algorithm is proposed.
3.1 Analysis and Implementation of the VCA Method
Knowing that the number of endmembers is much lower than the number of bands (p ≪ L) and that it is