DOI QR코드

DOI QR Code

An Improvement Algorithm for the Image Compression Imaging

  • Hu, Kaiqun (Key Laboratory of Manufacturing Equipment Mechanism Design and Control of Chongqing, Chongqing Technology and Business University) ;
  • Feng, Xin (Key Laboratory of Manufacturing Equipment Mechanism Design and Control of Chongqing, Chongqing Technology and Business University)
  • Received : 2018.03.15
  • Accepted : 2018.05.02
  • Published : 2020.02.29

Abstract

Lines and textures are natural properties of the surface of natural objects, and their images can be sparsely represented in suitable frames such as wavelets, curvelets and wave atoms. Based on characteristics that the curvelets framework is good at expressing the line feature and wavesat is good at representing texture features, we propose a model for the weighted sparsity constraints of the two frames. Furtherly, a multi-step iterative fast algorithm for solving the model is also proposed based on the split Bergman method. By introducing auxiliary variables and the Bergman distance, the original problem is transformed into an iterative solution of two simple sub-problems, which greatly reduces the computational complexity. Experiments using standard images show that the split-based Bergman iterative algorithm in hybrid domain defeats the traditional Wavelets framework or curvelets framework both in terms of timeliness and recovery accuracy, which demonstrates the validity of the model and algorithm in this paper.

Keywords

References

  1. D. L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289-1306, 2006. https://doi.org/10.1109/TIT.2006.871582
  2. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 83-91, 2008. https://doi.org/10.1109/MSP.2007.914730
  3. H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries," IEEE Transactions on Information Theory, vol. 54, no. 5, pp. 2210-2219, 2008. https://doi.org/10.1109/TIT.2008.920190
  4. Q. S. Lian and S. Z. Chen, "Sparse image representation using the analytic contourlet transform and its application on compressed sensing," Acta Electronica Sinica, vol. 38, no. 6, pp. 1293-1298, 2010.
  5. V. Kiani, A. Harati, and A. V. Mazloum, "Iterative wedgelet transform: an efficient algorithm for computing wedgelet representation and approximation of images," Journal of Visual Communication and Image Representation, vol. 34, pp. 65-77, 2016. https://doi.org/10.1016/j.jvcir.2015.10.009
  6. J. Liu, Y. Wang, K. Su, and W. He, "Image denoising with multidirectional shrinkage in directionlet domain," Signal Processing, vol. 125, pp. 64-78, 2016. https://doi.org/10.1016/j.sigpro.2016.01.013
  7. Y. Lu, Q. Gao, D. Sun, Y. Xia, and D. Zhang, "SAR speckle reduction using Laplace mixture model and spatial mutual information in the directionlet domain," Neurocomputing, vol. 173, pp. 633-644, 2016. https://doi.org/10.1016/j.neucom.2015.08.010
  8. C. Dossal, E. Le Pennec, and S. Mallat, "Bandlet image estimation with model selection," Signal Processing, vol. 91, no. 12, pp. 2743-2753, 2011. https://doi.org/10.1016/j.sigpro.2011.01.013
  9. P. Amorim, T. Moraes, D. Fazanaro, J. Silva, and H. Pedrini, "Electroencephalogram signal classification based on shearlet and contourlet transforms," Expert Systems with Applications, vol. 67, pp. 140-147, 2017. https://doi.org/10.1016/j.eswa.2016.09.037
  10. T. Goldstein and S. Osher, "The split Bregman method for L1-regularized problems," SIAM Journal on Imaging Sciences, vol. 2, no. 2, pp. 323-343, 2009. https://doi.org/10.1137/080725891
  11. L. Demanet and L. Ying, "Wave atoms and sparsity of oscillatory patterns," Applied and Computational Harmonic Analysis, vol. 23, no. 3, pp. 368-387, 2017. https://doi.org/10.1016/j.acha.2007.03.003
  12. S. Osher, Y. Mao, B. Dong, and W. Yin, "Fast linearized Bregman iteration for compressive sensing and sparse denoising," Communications in Mathematical Sciences, vol. 8, no. 1, pp. 93-111, 2010. https://doi.org/10.4310/CMS.2010.v8.n1.a6
  13. S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variationbased image restoration," Multiscale Modeling & Simulation, vol. 4, no. 2, pp. 460-489, 2005. https://doi.org/10.1137/040605412
  14. J. Ma, "Improved iterative curvelet thresholding for compressed sensing and measurement," IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 1, pp. 126-136, 2010. https://doi.org/10.1109/TIM.2010.2049221
  15. E. Van Den Berg and M. P. Friedlander, "Probing the Pareto frontier for basis pursuit solutions," SIAM Journal on Scientific Computing, vol. 31, no. 2, pp. 890-912, 2009. https://doi.org/10.1137/080714488