The Journal of Supercomputing

, Volume 72, Issue 1, pp 5–23 | Cite as

Optimal filter based on scale-invariance generation of natural images

  • Feng Jiang
  • Bo-Wei Chen
  • Seungmin Rho
  • Wen Ji
  • Liqiang Pan
  • Hongwei Guo
  • Debin Zhao


One of the most striking properties of natural image statistics is the scale invariance. Some earlier studies have assumed that the kurtosis of marginal band pass filter response to be constant throughout scales for a natural image. In our study, this assumption is loosened by adaptively estimating an optimal filter computation whose response distributions through scales have the least Kullback–Leibler divergence. The adaptive filter and its responses characterize the scale-invariance property more accurately and effectively and are further utilized to model the statistics scale-invariance prior in this paper. Extensive experiments on image super-resolution and de-noising manifest that the explored natural images scale-invariance prior model achieves significant performance improvements over the current state-of-the-art schemes.


Image restoration Statistical modeling Scale invariance 



This work was supported in part by the Major State Basic Research Development Program of China (973 Program 2015CB351804), the National Natural Science Foundation of China under Grant Nos. 61272386 and 61100096, the National Science Council of the Republic of China under Grant Nos. 103-2917-I-564-058, and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2061978).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Feng Jiang
    • 1
  • Bo-Wei Chen
    • 2
  • Seungmin Rho
    • 3
  • Wen Ji
    • 4
  • Liqiang Pan
    • 1
  • Hongwei Guo
    • 1
  • Debin Zhao
    • 1
  1. 1.Department of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Electrical EngineeringNational Cheng Kung UniversityTainan CityTaiwan
  3. 3.Department of MultimediaSungkyul UniversityAnyang CityKorea
  4. 4.Institute of Computing TechnologyChinese Academy of SciencesBeijingChina

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