Adaptive interpolation of multidimensional signals for differential compression
Maksimov A.I., Gashnikov M.V.

 

Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia

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Abstract:
Algorithms of interpolation of multidimensional signals for differential compression are investigated. We propose an approach for constructing adaptive interpolators based on the automatic selection of an interpolating function at each point of the signal. The selection is made with the use of attributes calculated from the point’s local neighborhood. An adaptive multidimensional interpolator is developed with this approach. It automatically selects an interpolating function at each point of the signal, providing improved contour interpolation accuracy. The choice is made by a decision rule based on a local characteristic of distinctness and direction of the contour. The proposed interpolator is implemented for a three-dimensional case. The interpolator switches between six interpolating functions: an averaging function and functions that take into account contours of five directions. An experimental study of the proposed algorithm is carried out on three-dimensional hyper spectral remote sensing data. The proposed interpolator allows increasing the efficiency of differential compression.

Keywords:
interpolation, multidimensional signal, adaptivity, compression, compression ratio, error.

Citation:
Maksimov AI, Gashnikov MV. Adaptive interpolation of multidimensional signals for differential compression. Computer Optics 2018; 42(4): 679-687. DOI: 10.18287/2412-6179-2018-42-4-679-687.

References:

  1. Woods JW. Multidimensional signal, image, and video processing and coding. 2nd ed. Waltham, Oxford: Academic Press; 2011. ISBN: 978-0-12-381420-3.
  2. Van der Meer FD, van der Werff HM, van Ruitenbeek FJ, Hecker CA, Bakker WH, Noomen MF, van der Meijde M, Carranza EJM, de Smeth JB, Woldai T. Multi- and hyperspectral geologic remote sensing: A review. International Journal of Applied Earth Observation and Geoinformation 2012; 14(1): 112-128. DOI: 10.1016/j.jag.2011.08.002.
  3. Lillesan T, Kiefer RW, Chipman J. Remote sensing and image interpretation. 7th ed. Hoboken, NJ: John Wiley & Sons; 2015. ISBN: 978-1-118-34328-9.
  4. Vapnik VN. Statistical learning theory. New York: John Wiley & Sons; 1998. ISBN: 978-0-471-03003-4.
  5. Bakhvalov YuN. Method of multidimensional interpolation and approximation and its applications [In Russian]. Moscow: “Sputnik+” Publisher; 2007. ISBN: 978-5-364-00728-5.
  6. Vasin YG, Neimark YuI. Recurrent algorithms of adaptive compression using well-adapted local regenerating functions [In Russian]. In Book: Mathematical support of CAD: Intercollegiate collection. Gorky: “GGU” Publisher; 1978; I.13.
  7. Gulakov KV. Selection of neural network architecture for solving the approximation task and regression analysis of experimental data. Vestnik BSTU 2013; 2: 95-105.
  8. Cohen A, Davenport MA, Leviatan D. On the stability and accuracy of least squares approximations. Foundations of Computational Mathematics 2013; 13(5): 819-834. DOI: 10.1007/s10208-013-9142-3.
  9. Blinov AO, Fralenko VP. Multidimensional approximation for modeling and optimization problems. Automation and Remote Control 2009; 70(4): 652-662. DOI: 10.1134/S0005117909040110.
  10. Tchobanou MK, Makarov DV. Image compression by using tensor approximation [In Russian]. Problems of Advanced Micro- and Nanoelectronic Systems Development (MES) 2014; 4: 109-112.
  11. Butyrsky EuYu, Kuvaldin IA, Chalkin VP. Мultidimensional functions’ approximation [In Russian]. Nauchnoe Priborostroenie 2010; 20(2): 82-92.
  12. Caiafa CF, Cichocki A. Computing sparse representations of multidimensional signals using Kronecker bases. Neural Computation 2016; 25(1): 186-220. DOI: 10.1162/NECO_a_00385.
  13. Krapukhinа NV, Brinza BV. New approach to a multi-dimension approximation of technological data on the base of usage of the method of group account of arguments and neuron nets [In Russian]. Non-Ferrous Metals 2007; 5: 19-23.
  14. Sahnoun S, Djermoun EH, Brie D, Comon P. A simultaneous sparse approximation method for multidimensional harmonic retrieval. Signal Processing 2017, 131: 36-48. DOI: 10.1016/j.sigpro.2016.07.029.
  15. Donoho DL. Compressed sensing. IEEE Trans Inform Theory 2006; 52(4): 1289-1306. DOI: 10.1109/TIT.2006.871582.
  16. Bigot J, Boyer C, Weiss P. An analysis of block sampling strategies in compressed sensing. IEEE Trans Inform Theory 2016; 62(4): 2125-2139. DOI: 10.1109/TIT.2016.2524628.
  17. Salomon D. Data compression: The complete reference. 4th ed. London: Springer-Verlag; 2007. ISBN: 978-1-84628-602-5.
  18. Gonsales RC, Woods E. Digital image processing. 3th ed. Upper Saddle River, NJ: Prentice Hall; 2007. ISBN: 978-0-13-168728-8.
  19. Gashnikov MV. Parameterized adaptive predictor for digital image compression based on the differential pulse code modulation. Proc SPIE 2017; 10341: 1034110. DOI: 10.1117/12.2268530.
  20. Gashnikov MV. Minimizing the entropy of post-interpolation residuals for image compression based on hierarchical grid interpolation. Computer Optics 2017; 41(2): 266-275. DOI: 10.18287/2412-6179-2017-41-2-266-275.
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