All Issue

2024 Vol.12, Issue 2 Preview Page

Research Article

Improving the Convergence Rate of Digital Image Restoration using the PS-PEMG Algorithm

PS-PEMG 알고리즘을 이용한 디지털 화상복원의 수렴률 향상

Mingu Song1

송민구1

1Korea Faculty of Liberal Arts, Yewon Arts University, Professor
1예원예술대학교 교양학부 교수
30 June 2024. pp. 71-83
PDF Citation
Abstract
손상된 디지털 이미지를 복원하는 통계적 방법으로 EM 알고리즘이 있다. 유연한 확률적 모델을 적용할 수 있어 오염이 심한 화상을 복원하는데 유효성이 있지만, 화소 단위로 화상을 복원하기 때문에 알고리즘의 수렴속도가 문제가 있다. 이것을 개선한 것으로 OSL 알고리즘이 있는데, 이 알고리즘은 수렴속도 개선과 함께 초월함수 형태의 복잡한 패널티가 주어져도 로그우도에 수렴하는 장점이 있다. 그러나 이 알고리즘은 평활상수 𝜆가 특정한 영역에서만 수렴하는 제한이 있다. 이러한 문제를 해결하기 위해 저자는 MPEMG 알고리즘을 제안한 바가 있다. 그러나 이것은 평활상수 𝜆가(0<𝜆<∞) 의 영역에서 전역적으로 수렴하는 장점을 갖지만, 페널티 로그 우도를 증가시키는 수렴속도가 통계적 방법의 복원알고리즘이 가지는 한계를 극복하지 못했다. 이러한 문제점을 극복하기 위해서 PS-PEMG 알고리즘을 제안한다. 제안한 알고리즘의 기본 구조는 반복마다 모수들을 동시에 갱신하지 않고 몇 개의 픽셀로 이루어진 그룹들을 순차적으로 갱신하는 방법이다. 따라서 제안한 알고리즘의 수렴 속도가 MPEMG 알고리즘보다 빠르다는 것을 화상 모의실험을 통하여 밝힌다.
The EM algorithm is a statistical method for restoring damaged digital images, utilizing a flexible probabilistic model that can effectively restore highly contaminated images. However, because it restores images pixel by pixel, the convergence speed of the algorithm poses a challenge. The OSL algorithm improves upon this by enhancing the convergence speed and converging to the log-likelihood even with complex transcendental function forms of penalties, but it has limitations as it converges only within specific smoothing constant regions. To address this, the MPEMG algorithm was proposed, which converges globally in the region of the smoothing constants, but it has not overcome the limits of statistical restoration algorithms in terms of increasing the penalty log-likelihood convergence speed. To overcome these issues, the PS-PEMG algorithm is proposed. The core structure of the proposed algorithm does not update the parameters simultaneously at each iteration, but rather updates groups of pixels sequentially. Therefore, the convergence speed of the proposed PS-PEMG algorithm is faster than that of the MPEMG algorithm, as demonstrated through image simulation experiments.
Keywords
Image restoration
Surrogate function
EM algorithm
OSL algorithm
MPEMG algorithm
PS-PEMG algorithm
References

  1. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum Likelihood from Incompelete Data from via the EM algorithm", Journal of Royal Statistical Society B, Vol. 39, No. 2, pp. 1-38, 1997.

     10.1111/j.2517-6161.1977.tb01600.x

  2. P. J. Green, "On use of the EM Algorithm for Penalized Likelihood Estimation", Journal of Royal Statistical Society B, Vol. 52, pp. 443-452, 1990a.

     10.1111/j.2517-6161.1990.tb01798.x

  3. P. J. Green, "Bayesian Reconstruction from Emission Tomography Data using a Modified EM Algorithm", IEEE Transactions on Medical Imaging, Vol. 9, No. 1, pp. 84-93, 1990b.

     10.1109/42.52985 18222753

  4. K. S. Lange, "A Gradient Algorithm Locally Equivalent to the EM Algorithm", Journal of Royal Statistical Society B, Vol. 57, pp. 425-437, 1995.

     10.1111/j.2517-6161.1995.tb02037.x

  5. M. K. Song, "A Study of Penalty EM Gradient Algorithm in Digital Image Restoration", Dongguk University Graduate School Doctoral Thesis, pp. 1-81, 1997.

  6. M. K. Song, "A Study of Digital Image Restoration for Modified PEM Gradient Algorithm", The Transactions of the Korea Information Processing Society, Vol. 7, No. 1, pp. 53-158, 2000.

  7. A. T. Mário, Figueiredo, and R. D. Nowak, "An EM Algorithm for Wavelet-Based Image Restoration", IEEE Transactions on Image Processing, Vol. 12, No. 8, 2003.

     10.1109/TIP.2003.814255 18237964

  8. Bassel Marhaba, "Satellite image restoration by nonlinear statistical filtering techniques", https://theses.hal.science/tel-02094292, 2019.

  9. I. Sadok, A. Masmoudi, and M. Zribi, "Integrating the EM algorithm with particle filter for image restoration with exponential dispersion noise", Communication in Statistics, Vol. 52, No. 2, pp. 445-461. 2023.

     10.1080/03610926.2021.1915336

  10. J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. S. Lange "Grouped-Coordinate Ascent Algorithms for Penalized-Likelihood Transmission Image Reconstruction", IEEE Transactions on Medical Imaging, Vol. 16, No. 2, pp. 166-175, 1997.

     10.1109/42.563662 9101326

  11. M. Abdalla, and J. Kay, "Edge Preserving Image Restoration, Stochastic Models, Statistical Methods, and Algorithm in Image Analysis", Conference Paper, 1-13, 1990.

     10.1007/978-1-4612-2920-9_1

  12. A. S. Vijendran and B. Lukose, "Image Restoration Using Particle Filters By Improving The Scale Of Texture WithMRF" International Journal of Image Processing (IJIP) , Vol. 6, No. 5, 2012.

  13. J. A. Fessler and H. Erdogan, "Fast Monotonic Algorithm for Transmission Tomography", IEEE Transactions on Medical Imaging, Vol. 18, No. 9, pp. 801-814, September 1999.

     10.1109/42.802758 10571385

  14. J. Yu, "Based on Gaussian Filter to Improve the Effect of the Images in Gaussian Noise and Pepper Noise", Journal of Physics: Conference Series, 2023.

     10.1088/1742-6596/2580/1/012062

  15. S. German and D. German, "Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Iimages", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, No. 1, pp. 721-741, 1984.

     10.1109/TPAMI.1984.4767596 22499653

  16. J. K. Mandal and S. Mukhopadhyay, "Image Filtering Using All Neighbor Directional Weighted Pixels: Optimation Using Particles Swarm Optimization", Signal & Image Processing : An International Journal, Vol. 2, No. 4, 2011.

     10.5121/sipij.2011.2416
Information
  • Publisher :The Society of Convergence Knowledge
  • Publisher(Ko) :융복합지식학회
  • Journal Title :The Society of Convergence Knowledge Transactions
  • Journal Title(Ko) :융복합지식학회논문지
  • Volume : 12
  • No :2
  • Pages :71-83
  • DOI :https://doi.org/10.22716/sckt.2024.12.2.007
Journal Informaiton The Society of Convergence Knowledge Transactions The Society of Convergence Knowledge Transactions
Online Submission
  • NRF
  • KISTI Current Status
  • KISTI Cited-by
  • crosscheck
  • orcid
  • open access
  • ccl
Journal Informaiton Journal Informaiton - close