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Reseach Article

Processing Hyperspectral Images using Non-Linear Least Square Algorithm as an Optimization Method for Tensor Decomposition Model

by Ankit Gupta, Nishi Goel, Ashish Oberoi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 123 - Number 12
Year of Publication: 2015
Authors: Ankit Gupta, Nishi Goel, Ashish Oberoi
10.5120/ijca2015904872

Ankit Gupta, Nishi Goel, Ashish Oberoi . Processing Hyperspectral Images using Non-Linear Least Square Algorithm as an Optimization Method for Tensor Decomposition Model. International Journal of Computer Applications. 123, 12 ( August 2015), 14-19. DOI=10.5120/ijca2015904872

@article{ 10.5120/ijca2015904872,
author = { Ankit Gupta, Nishi Goel, Ashish Oberoi },
title = { Processing Hyperspectral Images using Non-Linear Least Square Algorithm as an Optimization Method for Tensor Decomposition Model },
journal = { International Journal of Computer Applications },
issue_date = { August 2015 },
volume = { 123 },
number = { 12 },
month = { August },
year = { 2015 },
issn = { 0975-8887 },
pages = { 14-19 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume123/number12/22010-2015904872/ },
doi = { 10.5120/ijca2015904872 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:12:30.350434+05:30
%A Ankit Gupta
%A Nishi Goel
%A Ashish Oberoi
%T Processing Hyperspectral Images using Non-Linear Least Square Algorithm as an Optimization Method for Tensor Decomposition Model
%J International Journal of Computer Applications
%@ 0975-8887
%V 123
%N 12
%P 14-19
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Due to large size and huge availability of unwanted or missing information in hyperspectral image, development of data effective compression and denoising methods is of prior importance. Compression removes unmeaningful information and thereby reducing data which ultimately leads to noise free image. This study deals with execution of two lossless decomposition methods Low Multi-linear Rank Approximation, four types of Block Term Decomposition to the input image cube to make it noise free using non-linear least square method as an optimization method and their performance were assessed. BTD (Lr, Lr, 1) was selected as the best tensor algorithm based on residual error and frobenius norm value with a limitation that the image cube to be processed by the method should have good spatial resolution.

References
  1. Cheng-Chen Lin, Yin-TsungHwang,2011,"Lossless Compression of Hyperspectral Images Using Adaptive Prediction and Backward Search Schemes",Journal Of Information Science And Engineering,Vol.27,pp.419-435.
  2. L. Hitchcock.” ,1927,The expression of a tensor or a polyadic as a sum of products”, Journal of Mathematical Physics, Vol.6, pp.164–189.
  3. Ji Liu, Przemyslaw Musialski, Peter Wonka, and JiepingYe,2012,”Tensor Completion for Estimating Missing Values in Visual Data”, Pattern Analysis and Machine Intelligence, IEEE Transactions, Vol.35, pp.s 208-220, January .
  4. L. R. Tucker,1963, Implications of factor analysis of three-way matrices for measurement of change, in Problems in Measuring Change, C. W. Harris, ed., University of Wiscons in Press, pp. 122–137, 1963.
  5. L. R. Tucker, 1966,” Some mathematical notes on three-mode factor analysis”, Psychometrika, Vol.31, pp.279–311, 1966.
  6. Qiang Zhang , Han Wang, Robert J. Plemmons,V. Pau’l Pauca,2008,"Tensor methods for hyperspectral data analysis: a space object material identification study",J. Opt. Soc. Am. A, Vol.25, (December 2008), pp.3001-3012.
  7. Fang Lia, Michael K. Ngb, Robert Plemmonsc, Sudhakar Prasadd, Qiang Zhang,2010,“Hyperspectral image segmentation, deblurring, and spectral analysis for material identification”, in Proc. SPIE, Visual Information Processing XIX, Vol.7701 770103 (April 2010).
  8. Cichocki, D. Mandic, A-H. Phan, C. Caiafa, G. Zhou, Q. Zhao, and L. De Lathauwer,2015"Tensor Decompositions for Signal Processing Applications: From Two-way to Multi-way Component Analysis", Signal Processing Magazine, IEEE,Vol.32( March 2015)pp.145-163,.
  9. Antonio Plaza, David Valencia, Javier Plaza, Pablo Martinez, 2006,“Commodity cluster-based parallel processing of hyperspectralimagery”, J. Parallel Distrib. Comput. Vol.66 (March 2006),pp. 345 – 358,.
  10. GaryShaw, DimitrisManolakis, 2002,"Signal Processing for Hyperspectral Image Exploitation" ,IEEE signal processing magzine,pp.12-16.
  11. Michael W. Mahoney, Mauro Maggioni, Petros Drineas,2008,"Tensor CUR Decompositions for Tensor Based Data”, SIAM Journal on Matrix Analysis and Applications,Vol.30 (September 2008),pp.957-987.
  12. Tamara G. Kolda,Brett W. Bader,2008,"Tensor Decompositions and Applications", SIAM, Vol.51 (June 2008) ,pp. 455-500.
  13. Z. Pan, G. Healey, M. Prasad, B. Tromberg,2003, "Face recognition in hyperspectral images", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.25 (December 2003), pp.1552-1560.
  14. Laurent Sorber, Marc Van Barel and Lieven De Lathauwer,2014, Tensorlab v2.0, Available online, (January 2014)
  15. Salah Bourennane, Caroline Fossati and Alexis Cailly,2010,"Improvement Of Target Detection Based On Tensorial Modelling",18th European Signal Processing Conference,pp.304-308.
  16. Santiago Velasco-Forero, Jesus Angulo,2013, “Classification of hyperspectral images by tensor modeling and additive morphological decomposition” Pattern Recognition, Elsevier, Vol.46 ( February 2013), pp.566-577.
  17. Xiurui Geng, Kang Sun, Luyan Ji ,Yong chao Zhao,2014,"A High-Order Statistical Tensor Based Algorithm for Anomaly Detection in Hyperspectral Imagery",Scientific reports,,Vol.4.
  18. Chein-I-Chang, 2007," Hyperspectral Data Explotation: Theory and Applications ",Wiley.
  19. Laurent Sorber, Marc Van Barel, Lieven De Lathauwer ,2013,"Optimization-Based Algorithms For Tensor Decompositions: Canonical Polyadic Decomposition,in Rank-(Lr, Lr,1) Terms,And A New Generalization",Siam J. Optim.,Vol.23,pp.695-720.
  20. L. Sorber, M. Van Barel, and L. De Lathauwer, 2012,” Unconstrained optimization of real functions in complex variables”, SIAM J. Optim., Vol.22 , pp. 879–898.
  21. Lieven De Lathauwer,2008,"Decompositions Of A Higher-Order Tensor In BlockTerms—Part Ii: Definitions And Uniqueness",Siam J. Matrix Anal. Appl., Vol.30, pp.1033-1066.
Index Terms

Computer Science
Information Sciences

Keywords

Hyperspectral imaging Data Compression Tensor decomposition models Low Multi-linear Rank Approximation Block Term Decomposition Frobenius Norm.