A PRIMAL-DUAL ALGORITHM for ROBUST FRACTAL IMAGE CODING

Chen Xu, Yuting Ye, Zhenwei Hu, Yuru Zou, Lixin Shen, Xiaoxia Liu, Jian Lu

Research output: Contribution to journalArticle

Abstract

The essence of Huber fractal image coding (HFIC) is to predict the fractal code of a noiseless image as accurately as possible from its corrupted observation with outliers by adopting Huber M-estimation technique. However, the traditional HFIC is not quite satisfactory mainly due to the absence of contractivity restriction for the estimate of the fractal parameters (actually, it is a fundamental requirement in the theory of fractal image coding). In this paper, we introduce a primal-dual algorithm for robust fractal image coding (PD-RFIC), which formulates the problem of robust prediction of the fractal parameters with contractivity condition as a constrained optimization model and then adopts a primal-dual algorithm to solve it. Furthermore, in order to relieve using the corrupted domain block as the independent variable in the proposed method, instead of using the mean operation on a 2 × 2 subblock in the traditional HFIC, we apply a median operation on a larger subblock to obtain the contracted domain blocks for achieving the robustness against outliers. The effectiveness of the proposed method is experimentally illustrated on problems of image denoising with impulse noise (specifically, salt & pepper noise and random-valued noise). Remarkable improvements of the proposed method over conventional HFIC are demonstrated in terms of both numerical evaluations and visual quality. In addition, a median-based version of Fisher classification method is also developed to accelerate the encoding speed of the proposed method.

Original languageEnglish (US)
Article number1950119
JournalFractals
Volume27
Issue number7
DOIs
StatePublished - Nov 1 2019

Fingerprint

Fractals
Fractal
Image Coding
Image coding
Contractivity
Primal-dual Algorithm
Outlier
M-estimation
Impulse Noise
Image denoising
Impulse noise
Image Denoising
Constrained optimization
Constrained Optimization
Optimization Model
Salt
Accelerate
Encoding
Salts
Robustness

Keywords

  • Fractal Image Coding
  • Impulse Noise
  • Median-Based Fisher's Classification
  • Primal-Dual Algorithm

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics

Cite this

Xu, C., Ye, Y., Hu, Z., Zou, Y., Shen, L., Liu, X., & Lu, J. (2019). A PRIMAL-DUAL ALGORITHM for ROBUST FRACTAL IMAGE CODING. Fractals, 27(7), [1950119]. https://doi.org/10.1142/S0218348X19501196

A PRIMAL-DUAL ALGORITHM for ROBUST FRACTAL IMAGE CODING. / Xu, Chen; Ye, Yuting; Hu, Zhenwei; Zou, Yuru; Shen, Lixin; Liu, Xiaoxia; Lu, Jian.

In: Fractals, Vol. 27, No. 7, 1950119, 01.11.2019.

Research output: Contribution to journalArticle

Xu, C, Ye, Y, Hu, Z, Zou, Y, Shen, L, Liu, X & Lu, J 2019, 'A PRIMAL-DUAL ALGORITHM for ROBUST FRACTAL IMAGE CODING', Fractals, vol. 27, no. 7, 1950119. https://doi.org/10.1142/S0218348X19501196
Xu, Chen ; Ye, Yuting ; Hu, Zhenwei ; Zou, Yuru ; Shen, Lixin ; Liu, Xiaoxia ; Lu, Jian. / A PRIMAL-DUAL ALGORITHM for ROBUST FRACTAL IMAGE CODING. In: Fractals. 2019 ; Vol. 27, No. 7.
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