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

Fast and Reliable Noise Estimation for Hyperspectral Subspace Identification

In this letter, we introduce an efficient algorithm to estimate the noise correlation matrix in the initial stage of the hyperspectral signal identification by minimum error (HySime) method, commonly used for signal subspace identification in remotely sensed hyperspectral images. Compared with the current implementations of this stage, the new algorithm for noise estimation relies on the reliable QR factorization, producing correct results even when operating with single-precision arithmetic. Additionally, our algorithm exhibits a lower computational cost, and it is highly parallel. The experiments on a multicore server, using two real hyperspectral scenes, expose that these theoretical advantages carry over to the practical results