Skip to main content

Satellite Image Time Series: Mathematical Models for Data Mining and Missing Data Restoration

  • Chapter
  • First Online:
  • 2037 Accesses

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

One of the exceptional advantages of spaceborne remote sensors is their regular scanning of the Earth surface, resulting thus in Satellite Image Time Series (SITS), extremely useful to monitor natural or man-made phenomena on the ground. In this chapter, after providing a brief overview of the most recent methods proposed to process and/or analyze time series of remotely sensed data, we describe methods handling two issues: the unsupervised exploration of SITS and the reconstruction of multispectral images. In particular, we first present data mining methods for extracting spatiotemporal patterns in an unsupervised way and illustrate this approach on time series of displacement measurements derived from multitemporal InSAR images. Then we present two methods which aim to reconstruct multispectral images contaminated by the presence of clouds. The first one is based on a linear contextual prediction mode that reproduces the local spectro-temporal relationships characterizing a given time series of images. The second method tackles the image reconstruction problem within a compressive sensing formulation and with different implementation strategies. A rich set of illustrations on real and simulated examples is provided and discussed.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The authors wish to thank the ANR EFIDIR and ANR FOSTER projects for funding the works presented in this chapter.

  2. 2.

    We thank Romain Jolivet (California Institute of Technology-CALTECH, Seismological laboratory) and Cécile Lasserre (Centre National de la Recherche Scientifique-CNRS, ISTerre laboratory) for computing and providing this InSAR time series.

  3. 3.

    We thank the European Space Agency (ESA) for providing this ENVISAT SAR series (Dragon project ID5305).

  4. 4.

    We thank Romain Jolivet (California Institute of Technology-CALTECH, Seismological laboratory), Cécile Lasserre (Centre National de la Recherche Scientifique-CNRS, ISTerre laboratory), and Catherine Pothier (Institut National des Sciences Appliquées de Lyon-INSA Lyon, LGCIE laboratory) for this interpretation.

  5. 5.

    We thank Romain Jolivet (California Institute of Technology-CALTECH, Seismological laboratory), Cécile Lasserre (Centre National de la Recherche Scientifique-CNRS, ISTerre laboratory) and Catherine Pothier (Institut National des Sciences Appliquées de Lyon-INSA Lyon, LGCIE laboratory) for this interpretation.

References

  1. Lopès, A., Garello, R., Le Hégarat-Mascle, S.: Speckle models. Processing of Synthetic Aperture Radar (SAR) Images. Wiley-ISTE, New York (2008)

    Google Scholar 

  2. Trouvé, E., Chambenoit, Y., Classeau, N., Bolon, P.: Statistical and operational performance assessment of multitemporal SAR image filtering. IEEE Trans. Geosci. Remote Sens. 41(11), 2519–2530 (2003)

    Article  Google Scholar 

  3. Ciuc, M., Bolon, P., Trouvé, E., Buzuloiu, V., Rudant, J.-P.: Adaptive-neighborhood speckle removal in multitemporal synthetic aperture radar images. Appl. Opt. 40(32), 5954–5966 (2001)

    Article  Google Scholar 

  4. Bruniquel, J., Lopès, A.: Multi-variate optimal speckle reduction in SAR imagery. Int. J. Remote Sens. 18(3), 603–627 (1997)

    Article  Google Scholar 

  5. Atto, A.M., Trouvé, E., Nicolas, J.-M., Le, T.T.: Wavelet operators and multiplicative observation models -application to SAR image time series analysis. IEEE Trans. Geosci. Remote Sens. (2016). https://hal.archives-ouvertes.fr/hal-01341064

  6. Le, T.T., Atto, A.M., Trouvé, E., Nicolas, J.-M.: Adaptive multitemporal SAR image filtering based on the change detection matrix. IEEE Geosci. Remote Sens. Lett. 11(10), 5 (2014). https://hal.archives-ouvertes.fr/hal-00975385

  7. Su, X., Deledalle, C.A., Tupin, F., Sun, H.: Two-step multitemporal nonlocal means for synthetic aperture radar images. IEEE Trans. Geosci. Remote Sens. 52(10), 6181–6196 (2014)

    Article  Google Scholar 

  8. Bujor, F., Trouvé, E., Valet, L., Nicolas, J.-M., Rudant, J.-P.: Application of log-cumulants to the detection of spatiotemporal discontinuities in multitemporal SAR images. IEEE Trans. Geosci. Remote Sens. 42(10), 2073–2084 (2004)

    Article  Google Scholar 

  9. Ferretti, A., Prati, C., Rocca, F.: Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens. 39(1), 8–20 (2001)

    Article  Google Scholar 

  10. Berardino, P., Fornaro, G., Lanari, R., Sansosti, E.: A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. IEEE Trans. Geosci. Remote Sens. 40, 2375–2382 (2002)

    Article  Google Scholar 

  11. Lu, D., Mausel, P., Brondizio, E., Moran, E.: Change detection techniques. Int. J. Remote Sens. 25(12), 2365–2401 (2004)

    Article  Google Scholar 

  12. Coppin, P., Jonckheere, I., Nackaerts, K., Muys, B., Lambin, E.: Review articledigital change detection methods in ecosystem monitoring: a review. Int. J. Remote Sens. 25(9), 1565–1596 (2004)

    Article  Google Scholar 

  13. Petitjean, F., Inglada, J., Gançarski, P.: Satellite image time series analysis under time warping. IEEE Trans. Geosci. Remote Sens. 50(8), 3081–3095 (2012)

    Article  Google Scholar 

  14. Millward, A.A., Piwowar, J.M., Howarth, P.J.: Time-series analysis of medium-resolution, multisensor satellite data for identifying landscape change. Photogramm. Eng. Remote Sens. 72(6), 653–663 (2006)

    Article  Google Scholar 

  15. Foody, G.: Monitoring the magnitude of land-cover change around the southern limits of the Sahara. Photogramm. Eng. Remote Sens. 67(7), 841–848 (2001)

    Google Scholar 

  16. Melgani, F., Moser, G., Serpico, S.B.: Unsupervised change-detection methods for remote-sensing images. Opt. Eng. 41(12), 3288–3297 (2002)

    Article  Google Scholar 

  17. Inglada, J., Mercier, G.: A new statistical similarity measure for change detection in multitemporal SAR images and its extension to multiscale change analysis. IEEE Trans. Geosci. Remote Sens. 45(5), 1432–1445 (2007)

    Article  Google Scholar 

  18. Lambin, E.F., Strahlers, A.H.: Change-vector analysis in multitemporal space: a tool to detect and categorize land-cover change processes using high temporal-resolution satellite data. Remote Sens. Environ. 48(2), 231–244 (1994)

    Article  Google Scholar 

  19. JHA, C.S., Unni, N.: Digital change detection of forest conversion of a dry tropical indian forest region. Int. J. Remote Sens. 15(13), 2543–2552 (1994)

    Article  Google Scholar 

  20. Julea, A., Méger, N., Bolon, P., Rigotti, C., Doin, M.-P., Lasserre, C., Trouvé, E., Lăzărescu, V.N.: Unsupervised spatiotemporal mining of satellite image time series using grouped frequent sequential patterns. IEEE Trans. Geosci. Remote Sens. 49(4), 1417–1430 (2011)

    Article  Google Scholar 

  21. Celik, T., Ma, K.-K.: Multitemporal image change detection using undecimated discrete wavelet transform and active contours. IEEE Trans. Geosci. Remote Sens. 49(2), 706–716 (2011)

    Article  Google Scholar 

  22. Frawley, W., Piatetsky-Shapiro, G., Matheus, C.: Knowledge discovery in databases: an overview. In: Piatetsky-Shapiro, G., Frawley, W. (eds.) Knowledge in Discovery in Databases, pp. 1–27. AAAI Press, Menlo Park (1991)

    Google Scholar 

  23. Honda, R., Konishi, O.: Temporal rule discovery for time-series satellite images and integration with RDB. In: PKDD ’01: Proceedings of the 5th European Conference on Principles of Data Mining and Knowledge Discovery, pp. 204–215. Springer, London (2001)

    Google Scholar 

  24. Héas, P., Datcu, M.: Modeling trajectory of dynamic clusters in image time-series for spatio-temporal reasoning. IEEE Trans. Geosci. Remote Sens. 43(7), 1635–1647 (2005)

    Article  Google Scholar 

  25. Nezry, E., Genovese, G., Solaas, G., Rémondière, S.: ERS - Based early estimation of crop areas in Europe during winter 1994–95. In: Guyenne, T.-D. (ed.) ERS Application, Proceedings of the Second International Workshop held 6–8 December 1995 in London, vol. 383, p. 13–20. ESA Special Publication (1996)

    Google Scholar 

  26. Petitjean, F., Inglada, J., Gancarski, P.: Satellite image time series analysis under time warping. IEEE Trans. Geosci. Remote Sens. 50(8), 3081–3095 (2012)

    Article  Google Scholar 

  27. Gueguen, L., Datcu, M.: Image time-series data mining based on the information-bottleneck principle. IEEE Trans. Geosci. Remote Sens. 45(4), 827–838 (2007)

    Article  Google Scholar 

  28. Gallucio, L., Michel, O., Comon, P.: Unsupervised clustering on multi-components datasets: applications on images and astrophysics data. In: 16th European Signal Processing Conference EUSIPCO-2008, Lausanne, Switzerland, August 2008, pp. 25–29 (2008)

    Google Scholar 

  29. Agrawal, R., Srikant, R.: Mining sequential patterns. In: Yu, P.S., Chen, A.S.P. (eds.) Proceedings of the 11th International Conference on Data Engineering (ICDE’95), pp. 3–14. IEEE Computer Society Press, Taipei, Taiwan (1995)

    Google Scholar 

  30. Luo, C., Chung, S.-M.: Efficient mining of maximal sequential patterns using multiple samples. In: Proceedings of the 2005 SIAM International Conference on Data Mining (2005)

    Google Scholar 

  31. Julea, A., Méger, N., Bolon, P., Rigotti, C., Doin, M.-P., Lasserre, C., Trouvé, E., Lăzărescu, V.: Unsupervised spatiotemporal mining of satellite image time series using grouped frequent sequential patterns. IEEE Trans. Geosci. Remote Sens. 49(4), 1417–1430 (2011)

    Article  Google Scholar 

  32. Julea, A., Méger, N., Rigotti, C., Trouvé, R., Jolivet, Emmanuel, Bolon, P.: Efficient spatiotemporal mining of satellite image time series for agricultural monitoring. Trans. Mach. Learn. Data Min. 5(1), 23–44 (2012)

    Google Scholar 

  33. Meger, N., Jolivet, R., Lasserre, C., Trouve, E., Rigotti, C., Lodge, F., Doin, M.-P., Guillaso, S., Julea, A., Bolon, P.: Spatiotemporal mining of ENVISAT SAR interferogram time series over the Haiyuan fault in China. In: 2011 6th International Workshop on the Analysis of Multi-temporal Remote Sensing Images (Multi-Temp), pp. 137–140 (2011)

    Google Scholar 

  34. Rigotti, C., Lodge, F., Meger, N., Pothier, C., Jolivet, R., Lasserre, C.: Monitoring of tectonic deformation by mining satellite image time series. In: 19th National Conference Reconnaissance de Formes et Intelligence Artificielle (RFIA’14), July 2014, pp. 1–6 (2014)

    Google Scholar 

  35. Good, P.: Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses. Springer Series in Statistics. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  36. Cobb, G.W., Chen, Y.-P.: An application of Markov chain Monte Carlo to community ecology. Am. Math. Monthly 110(4), 265–288 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  37. Gionis, A., Mannila, H., Mielikäinen, T., Tsaparas, P.: Assessing data mining results via swap randomization. ACM Trans. Knowl. Discov. Data 1(3) (2007)

    Google Scholar 

  38. Méger, N., Rigotti, C., Pothier, C.: Swap randomization of bases of sequences for mining satellite image times series. Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2015, Porto, Portugal, 7–11 September 2015, Proceedings, Part II, pp. 190–205. Springer International Publishing, Berlin (2015)

    Chapter  Google Scholar 

  39. Cover, T., Thomas, J.: Elements of Information Theory. Wiley, New York (1991)

    Book  MATH  Google Scholar 

  40. Lodge, F., Meger, N., Rigotti, C., Pothier, C., Doin, M.-P.: Iterative summarization of satellite image time series. In: IEEE International Geoscience and Remote Sensing Symposium, July 2014, pp. 1–4 (2014)

    Google Scholar 

  41. Meger, N., Rigotti, C., Gueguen, L., Lodge, F., Pothier, C., Andreoli, R., Datcu, M.: Normalized mutual information-based ranking of spatio-temporal localization maps. In: 8th European Spatial Agency (ESA) - EUSC - JRC Conference on Image Information Mining, October 2012, pp. 11–14 (2012)

    Google Scholar 

  42. SITS-P2MINER: https://int.polytech.univ-smb.fr/fileadmin/polytech_autres_sites/sites/listic/projets/sitsmining/SITSP2MINER.zip (2016). Accessed 12 Apr 2016

  43. Cihlar, J.: Remote sensing of global change: an opportunity for Canada. In: Proceedings of 11th Canadian Symposium on Remote Sensing, pp. 39–48 (1987)

    Google Scholar 

  44. Wang, J.R., Racette, P., Triesky, M., Browell, E., Ismail, S., Chang, L.A.: Profiling of atmospheric water vapor with MIR and LASE. IEEE Trans. Geosci. Remote Sens. 40(6), 1211–1219 (2002)

    Article  Google Scholar 

  45. Vasudevan, B.G., Gohil, B.S., Agarwal, V.K.: Backpropagation neural-network-based retrieval of atmospheric water vapor and cloud liquid water from IRS-P4 MSMR. IEEE Trans. Geosci. Remote Sens. 42(5), 985–990 (2004)

    Article  Google Scholar 

  46. Stowe, L.L., Davis, P.A., McClain, E.P.: Scientific basis and initial evaluation of the CLAVR-1 global clear/cloud classification algorithm for the advanced very high resolution radiometer. J. Atmos. Ocean. Technol. 16(6), 656–681 (1999)

    Article  Google Scholar 

  47. Sea, B., Channel, A.: The cloud and surface parameter retrieval (CASPR) system for polar AVHRR (2002)

    Google Scholar 

  48. Di Vittorio, A.V., Emery, W.J.: An automated, dynamic threshold cloud-masking algorithm for daytime AVHRR images over land. IEEE Trans. Geosci. Remote Sens. 40(8), 1682–1694 (2002)

    Article  Google Scholar 

  49. Logar, A.M., Lloyd, D.E., Corwin, E.M., Penaloza, M.L., Feind, R.E., Berendes, T.A., Kuo, K.-S., Welch, R.M.: The ASTER polar cloud mask. IEEE Trans. Geosci. Remote Sens. 36(4), 1302–1312 (1998)

    Article  Google Scholar 

  50. Murtagh, F., Barreto, D., Marcello, J.: Decision boundaries using Bayes factors: the case of cloud masks. IEEE Trans. Geosci. Remote Sens. 41(12), 2952–2958 (2003)

    Article  Google Scholar 

  51. Demoment, G.: Image reconstruction and restoration: overview of common estimation structures and problems. IEEE Trans. Acoust. Speech Signal Process. 37(12), 2024–2036 (1989)

    Article  Google Scholar 

  52. Banham, M.R., Katsaggelos, A.K.: Digital image restoration. IEEE Signal Process. Mag. 14(2), 24–41 (1997)

    Article  Google Scholar 

  53. Reichenbach, S.E., Koehler, D.E., Strelow, D.W.: Restoration and reconstruction of AVHRR images. IEEE Trans. Geosci. Remote Sens. 33(4), 997–1007 (1995)

    Article  Google Scholar 

  54. Petrovich Bakalov, V., Yuryevich Yerokhin, M.: Removal of uncontrollable phase distortions in synthetic aperture radar signals. IEEE Trans. Geosci. Remote Sens. 38(3), 1298–1302 (2000)

    Article  Google Scholar 

  55. Reichenbach, S.E., Li, J.: Restoration and reconstruction from overlapping images for multi-image fusion. IEEE Trans. Geosci. Remote Sens. 39(4), 769–780 (2001)

    Article  Google Scholar 

  56. Wu, Z., Liu, C.: An image reconstruction method using GPR data. IEEE Trans. Geosci. Remote Sens. 37(1), 327–334 (1999)

    Article  MathSciNet  Google Scholar 

  57. Holben, B.N.: Characteristics of maximum-value composite images from temporal AVHRR data. Int. J. Remote Sens. 7(11), 1417–1434 (1986)

    Article  Google Scholar 

  58. Lee, S., Crawford, M.: An adaptive reconstruction system for spatially correlated multispectral multitemporal images. IEEE Trans. Geosci. Remote Sens. 29(4), 494–508 (1991)

    Article  Google Scholar 

  59. Lee, S., Crawford, M.M.: Adaptive reconstruction of sequential AVHRR imagery of Texas via dynamic compositing using an exponentially weighted polynomial function. In: IEEE International Geoscience and Remote Sensing Symposium: IGARSS’94, Surface and Atmospheric Remote Sensing: Technologies, Data Analysis and Interpretation, vol. 1, pp. 64–66 (1994)

    Google Scholar 

  60. Cihlar, J., Howarth, J.: Detection and removal of cloud contamination from AVHRR images. IEEE Trans. Geosci. Remote Sens. 32(3), 583–589 (1994)

    Article  Google Scholar 

  61. Choudhury, B., Tucker, C.: Satellite observed seasonal and inter-annual variation of vegetation over the Kalahari, the Great Victoria Desert, and the Great Sandy Desert: 1979–1984. Remote Sens. Environ. 23(2), 233–241 (1987)

    Article  Google Scholar 

  62. Long, D.G., Remund, Q.P., Daum, D.L.: A cloud-removal algorithm for SSM/I data. IEEE Trans. Geosci. Remote Sens. 37(1), 54–62 (1999)

    Article  Google Scholar 

  63. Gao, B.-C., Yang, P., Han, W., Li, R.-R., Wiscombe, W.J.: An algorithm using visible and 1.38-\(\upmu \)m channels to retrieve cirrus cloud reflectances from aircraft and satellite data. IEEE Trans. Geosci. Remote Sens. 40(8), 1659–1668 (2002)

    Article  Google Scholar 

  64. Moody, E.G., King, M.D., Platnick, S., Schaaf, C.B., Gao, F.: Spatially complete global spectral surface albedos: value-added datasets derived from Terra MODIS land products. IEEE Trans. Geosci. Remote Sens. 43(1), 144–158 (2005)

    Article  Google Scholar 

  65. Tseng, D.-C., Tseng, H.-T., Chien, C.-L.: Automatic cloud removal from multi-temporal spot images. Appl. Math. Comput. 205(2), 584–600 (2008)

    MathSciNet  MATH  Google Scholar 

  66. Lin, C.-H., Tsai, P.-H., Lai, K.-H., Chen, J.-Y.: Cloud removal from multitemporal satellite images using information cloning. IEEE Trans. Geosci. Remote Sens. 51(1), 232–241 (2013)

    Article  Google Scholar 

  67. Melgani, F.: Contextual reconstruction of cloud-contaminated multitemporal multispectral images. IEEE Trans. Geosci. Remote Sens. 44(2), 442–455 (2006)

    Article  Google Scholar 

  68. Lorenzi, L., Melgani, F., Mercier, G.: Missing-area reconstruction in multispectral images under a compressive sensing perspective. IEEE Trans. Geosci. Remote Sens. 51(7), 3998–4008 (2013)

    Article  Google Scholar 

  69. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Statis. Soc. Ser. B (Methodol.) 1–38 (1977)

    Google Scholar 

  70. Moon, T.K.: The expectation-maximization algorithm. IEEE Signal Process. Mag. 13(6), 47–60 (1996)

    Article  Google Scholar 

  71. Rissanen, J.: Stochastic Complexity in Statistical Enquiry. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  72. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)

    MATH  Google Scholar 

  73. Kittler, J., Illingworth, J.: Minimum error thresholding. Pattern Recognit. 19(1), 41–47 (1986)

    Article  Google Scholar 

  74. Sezan, M.I.: A peak detection algorithm and its application to histogram-based image data reduction. Comput. Vis. Gr. Image Process. 49(1), 36–51 (1990)

    Article  Google Scholar 

  75. Yen, J.-C., Chang, F.-J., Chang, S.: A new criterion for automatic multilevel thresholding. IEEE Trans. Image Process. 4(3), 370–378 (1995)

    Article  MathSciNet  Google Scholar 

  76. Shah-Hosseini, H., Safabakhsh, R.: Automatic multilevel thresholding for image segmentation by the growing time adaptive self-organizing map. IEEE Trans. Pattern Anal. Mach. Intell. 10, 1388–1393 (2002)

    Article  Google Scholar 

  77. McLachlan, G., Peel, D.: Multivariate normal mixtures. Finite Mixture Models, pp. 81–116 (2000)

    Google Scholar 

  78. Rissanen, J.: Complexity in Statistical Inquiry. Teaneck (1989)

    Google Scholar 

  79. Liang, Z., Jaszczak, R.J., Coleman, R.E.: Parameter estimation of finite mixtures using the EM algorithm and information criteria with application to medical image processing. IEEE Trans. Nucl. Sci. 39(4), 1126–1133 (1992)

    Article  Google Scholar 

  80. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  81. Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  82. Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  83. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  84. Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  85. Wang, N., Wang, Y.: An image reconstruction algorithm based on compressed sensing using conjugate gradient. In: IEEE 2010 4th International Universal Communication Symposium (IUCS), pp. 374–377 (2010)

    Google Scholar 

  86. Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: IEEE 1993 Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, pp. 40–44 (1993)

    Google Scholar 

  87. Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  88. Kunis, S., Rauhut, H.: Random sampling of sparse trigonometric polynomials II - orthogonal matching pursuit versus basis pursuit. Found. Comput. Math. 8(6), 737–763 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  89. Goldberg, D.E.: Genetic Algorithms in Search and Machine Learning. Addison Wesley, Reading (1989)

    MATH  Google Scholar 

  90. Chambers, L.D.: Practical Handbook of Genetic Algorithms: Complex Coding Systems, vol. 3. CRC Press, Boca Raton (1998)

    Book  Google Scholar 

  91. Deb, K.: Multi-objective optimization using evolutionary algorithms, vol. 16. Wiley, New York (2001)

    MATH  Google Scholar 

  92. Zitzler, E., Laumanns, M., Thiele, L., Zitzler, E., Zitzler, E., Thiele, L., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm (2001)

    Google Scholar 

  93. Knowles, J., Corne, D.: The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. In: IEEE Proceedings of the 1999 Congress on Evolutionary Computation, CEC 99, vol. 1 (1999)

    Google Scholar 

  94. Srinivas, N., Deb, K.: Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)

    Article  Google Scholar 

  95. Ghoggali, N., Melgani, F., Bazi, Y.: A multiobjective genetic SVM approach for classification problems with limited training samples. IEEE Trans. Geosci. Remote Sens. 47(6), 1707–1718 (2009)

    Article  Google Scholar 

  96. Ghoggali, N., Melgani, F.: Genetic SVM approach to semisupervised multitemporal classification. IEEE Geosci. Remote Sens. Lett. 5(2), 212–216 (2008)

    Article  Google Scholar 

  97. Pasolli, E., Melgani, F., Donelli, M.: Automatic analysis of GPR images: a pattern-recognition approach. IEEE Trans. Geosci. Remote Sens. 47(7), 2206–2217 (2009)

    Article  Google Scholar 

  98. Liu, C.-C.: Processing of FORMOSAT-2 daily revisit imagery for site surveillance. IEEE Trans. Geosci. Remote Sens. 44(11), 3206–3214 (2006)

    Article  Google Scholar 

  99. Baudoin, A.: Mission analysis for spot 5. In: IEEE International Geoscience and Remote Sensing Symposium, IGARSS’93, Better Understanding of Earth Environment., p. 1084 (1993)

    Google Scholar 

  100. Jain, A.K.: Fundamentals of Digital Image Processing. Prentice-Hall Inc., Englewood Cliffs (1989)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Farid Melgani .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Méger, N., Pasolli, E., Rigotti, C., Trouvé, E., Melgani, F. (2018). Satellite Image Time Series: Mathematical Models for Data Mining and Missing Data Restoration. In: Moser, G., Zerubia, J. (eds) Mathematical Models for Remote Sensing Image Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-66330-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66330-2_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66328-9

  • Online ISBN: 978-3-319-66330-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics