February  2014, 8(1): 321-337. doi: 10.3934/ipi.2014.8.321

PHLST with adaptive tiling and its application to antarctic remote sensing image approximation

1. 

College of Global Change and Earth System Science, Beijing Normal University, Beijing, 100875, China

2. 

Department of Mathematics, University of California, Davis, California, 95616, United States

Received  July 2011 Revised  March 2012 Published  March 2014

We propose an efficient nonlinear approximation scheme using the Polyharmonic Local Sine Transform (PHLST) of Saito and Remy combined with an algorithm to tile a given image automatically and adaptively according to its local smoothness and singularities. To measure such local smoothness, we introduce the so-called local Besov indices of an image, which is based on the pointwise modulus of smoothness of the image. Such an adaptive tiling of an image is important for image approximation using PHLST because PHLST stores the corner and boundary information of each tile and consequently it is wasteful to divide a smooth region of a given image into a set of smaller tiles. We demonstrate the superiority of the proposed algorithm using Antarctic remote sensing images over the PHLST using the uniform tiling. Analysis of such images including their efficient approximation and compression has gained its importance due to the global climate change.
Citation: Zhihua Zhang, Naoki Saito. PHLST with adaptive tiling and its application to antarctic remote sensing image approximation. Inverse Problems & Imaging, 2014, 8 (1) : 321-337. doi: 10.3934/ipi.2014.8.321
References:
[1]

SIAM J. Sci. Comput., 19 (1998), 933-952. doi: 10.1137/S1064827595288589.  Google Scholar

[2]

J. Comput. Phys., 144 (1998), 109-136. doi: 10.1006/jcph.1998.6001.  Google Scholar

[3]

IEEE Trans. Pattern Anal. Machine Intell., 8 (1986), 679-698. doi: 10.1109/TPAMI.1986.4767851.  Google Scholar

[4]

J. Fourier Anal. Appl., 2 (1995), 29-48. doi: 10.1007/s00041-001-4021-8.  Google Scholar

[5]

Comptes Rendus Acad. Sci. Paris, Serie I, 312 (1991), 259-261.  Google Scholar

[6]

Prentice Hall, Englewood Cliffs, NJ, 1990. Google Scholar

[7]

2nd Ed., Chelsea Pub. Co., New York, 1986. doi: 10.2307/2008020.  Google Scholar

[8]

IEEE Trans. Acoust., Speech, Signal Process., 38 (1990), 969-978. doi: 10.1109/29.56057.  Google Scholar

[9]

IEEE Trans. Acoust., Speech, Signal Process., 37 (1989), 553-559. doi: 10.1109/29.17536.  Google Scholar

[10]

John Wiley & Sons, Inc., New York, 1997. Google Scholar

[11]

Appl. Comput. Harmon. Anal., 20 (2006), 41-73. doi: 10.1016/j.acha.2005.01.005.  Google Scholar

[12]

SIAM Review, 41 (1999), 135-147. doi: 10.1137/S0036144598336745.  Google Scholar

[13]

Macmillan, New York, 1963.  Google Scholar

[14]

3rd Edition, Cambridge University Press, 2003. doi: 10.2307/1989363.  Google Scholar

show all references

References:
[1]

SIAM J. Sci. Comput., 19 (1998), 933-952. doi: 10.1137/S1064827595288589.  Google Scholar

[2]

J. Comput. Phys., 144 (1998), 109-136. doi: 10.1006/jcph.1998.6001.  Google Scholar

[3]

IEEE Trans. Pattern Anal. Machine Intell., 8 (1986), 679-698. doi: 10.1109/TPAMI.1986.4767851.  Google Scholar

[4]

J. Fourier Anal. Appl., 2 (1995), 29-48. doi: 10.1007/s00041-001-4021-8.  Google Scholar

[5]

Comptes Rendus Acad. Sci. Paris, Serie I, 312 (1991), 259-261.  Google Scholar

[6]

Prentice Hall, Englewood Cliffs, NJ, 1990. Google Scholar

[7]

2nd Ed., Chelsea Pub. Co., New York, 1986. doi: 10.2307/2008020.  Google Scholar

[8]

IEEE Trans. Acoust., Speech, Signal Process., 38 (1990), 969-978. doi: 10.1109/29.56057.  Google Scholar

[9]

IEEE Trans. Acoust., Speech, Signal Process., 37 (1989), 553-559. doi: 10.1109/29.17536.  Google Scholar

[10]

John Wiley & Sons, Inc., New York, 1997. Google Scholar

[11]

Appl. Comput. Harmon. Anal., 20 (2006), 41-73. doi: 10.1016/j.acha.2005.01.005.  Google Scholar

[12]

SIAM Review, 41 (1999), 135-147. doi: 10.1137/S0036144598336745.  Google Scholar

[13]

Macmillan, New York, 1963.  Google Scholar

[14]

3rd Edition, Cambridge University Press, 2003. doi: 10.2307/1989363.  Google Scholar

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