Advertisement

Image compressed sensing recovery via nonconvex garrote regularization

  • Razieh Keshavarzian
  • Ali AghagolzadehEmail author
  • Tohid Yousefi Rezaii
Article
  • 39 Downloads

Abstract

Sparsity inducing model is one of the most important components of image compressed sensing (CS) recovery methods. These models are built on the image prior knowledge. The model which can reflect the image priors appropriately, yields high quality recovery results. Recent studies have shown that nonlocal low-rank prior based models often lead to superior results in CS recovery. The rank regularization problem resulting from these models is an NP-hard problem and how to solve it has a great impact on the recovery results. In this paper, we propose a new CS recovery method via nonconvex Garrote regularization (NGR) toward better exploiting the nonlocal low-rank prior. In the proposed CS-NGR method, the nonconvex Garrote function is introduced as a suitable surrogate for the rank function. To solve the resulting minimization problem efficiently, we employ the alternating direction method and so-called Garrote singular value shrinkage (GSVS) technique. Extensive experimental results show effectiveness of the proposed method compared with the state-of-the-arts methods in CS image recovery.

Keywords

Alternating direction method Compressed sensing Garrote function Image reconstruction Low-rank regularization Sparsity 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments which were useful to improve the quality of the paper. They also would like to thank the authors of [10, 39] and [8] for sharing the source code of their papers.

References

  1. 1.
    Afonso MV, Bioucas-Dias JM, Figueiredo MAT (2010) Fast Image Recovery Using Variable Splitting and Constrained Optimization. IEEE Trans Image Process 19(9):2345–2356MathSciNetCrossRefGoogle Scholar
  2. 2.
    Breiman L (1995) Better Subset Regression Using the Nonnegative Garrote. Technometrics 37:373–384MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cai JF, Candès EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982MathSciNetCrossRefGoogle Scholar
  4. 4.
    Candes EJ, Romberg J, Tao T (2006) Robust Uncertainlt Principle: Exact Signal Reconstruction From Highly Incomplete Frequency Information. IEEE Trans Inf Theory 52(2):489–509CrossRefGoogle Scholar
  5. 5.
    Candes EJ, Wakin MB, Boyd SP (2008) Enhancing Sparsity by Reweighted l1 Minimization. J Fourier Anal Appl 14(5-6):877–905MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chartrand R (2007) Exact Reconstruction of Sparse Signals via Nonconvex Minimization. IEEE Signal Process Letters 14(10)Google Scholar
  7. 7.
    Chen B, Liu G, Huang Z, Yan S (2011) Multi-task low-rank affinities pursuit for image segmentation. IEEE Int Conf. Computer Vision, BarcelonaGoogle Scholar
  8. 8.
    Dong W, Shi G, Li X, Ma Y, Huang F (2014) Compressive Sensing via Low-Rank Regularization. IEEE Trans Image Process 23(8):3618–3632MathSciNetCrossRefGoogle Scholar
  9. 9.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52:1289–1306MathSciNetCrossRefGoogle Scholar
  10. 10.
    Eslahi N, Aghagolzadeh A (2016) Compressive Sensing Image Restoration Using Adaptive Curvelet Thresholding and Nonlocal Sparse Regularization. IEEE Trans Image Process 25(7):3126–3140MathSciNetCrossRefGoogle Scholar
  11. 11.
    Eslahi N, Aghagolzadeh A, Andargoli SMH (2016) Image/ Video Compressive Sensing Recovery Using Joint Adaptive Sparsity Meature. Neurocomputing 200:88–109CrossRefGoogle Scholar
  12. 12.
    Fei X, Wei Z, Xiao L (2013) Iterative Directional Total Variation Refinement for Compressive Sensing Image Reconstruction. IEEE Signal Process Letters 20(11)Google Scholar
  13. 13.
    Feng L, Sun H, Sun Q, Xia G (2016) Image Compressive Sensing via Truncated Schatten-p Norm Regularization. Signal Process Image Commun 47:28–41CrossRefGoogle Scholar
  14. 14.
    Feng L, Sun H, Sun Q, Xia G (2017) Blind Compressive Sensing Using Block Sparsity and Nonlocal Low-Rank Priors. J Vis Commun Image Represent 42:37–45CrossRefGoogle Scholar
  15. 15.
    Gan L (2007) Block Compressed Sensing of Natural Images. Proc of the 15th Int Conf on Digital Signal Process (DSP 2007), CardiffGoogle Scholar
  16. 16.
    Gao HY (1998) Wavelet Shrinkage Denoising Using the Non-Negative Garrote. J Comput Graph Stat 7(4):469–488MathSciNetGoogle Scholar
  17. 17.
    Gu S, Zhang L, Zuo W, Feng X (2014) Weighted Nuclear Norm Minimization with Application to Image Denoising. Proc of IEEE Conf Computer Vision and Pattern Recognition (CVPR), Columbus, pp 2862–2869Google Scholar
  18. 18.
    Guo Q, Gao S, Zhang X, Yin Y, Zhang C (2017) Patch-Based Image Inpainting via Two-Stage Low Rank Approximation. IEEE Trans Vis Comput Graph 24(6):2023–2036CrossRefGoogle Scholar
  19. 19.
    Guo Q, Zhang C, Zhang Y, Liu H (2016) An Efficient SVD-Based Method for Image Denoising. IEEE Trans Circuits & Sys For Video Tech 26(5):868–880CrossRefGoogle Scholar
  20. 20.
    He N, Wang JB, Zhang LL, Xu GM, Lu K (2016) Nonlocal Sparse Regularization Model with Application to Image Denoising. Multimed Tools Appl 75:2579–2594CrossRefGoogle Scholar
  21. 21.
    Hu Y, Zhang D, Ye J, Li X, He X (2013) Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization. IEEE Trans Pattern Analysis & Machine Intelligence 35(9):2117–2130CrossRefGoogle Scholar
  22. 22.
    Jing P, Su Y, Nie L, Bai X, Liu J, Wang M (2017) Low-Rank Multi-View Embedding Learning for Micro-Video Popularity Prediction. IEEE Trans Knowledge and Data Engineering 30(8):1519–1532CrossRefGoogle Scholar
  23. 23.
    Li S, Qi H (2015) A Douglas-Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low Rank Regularization. IEEE Trans Image Process 24(11):4240–4249MathSciNetCrossRefGoogle Scholar
  24. 24.
    Liu S, Cao J, Liu H, Zhou X, Zhang K, Li Z (2017) MRI Reconstruction via Enhanced Group Sparsity and Nonconvex Regularization. Neurocomputing:1–14
  25. 25.
    Lu C, Tang J, Yan S, Lin Z (2016) Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm. IEEE Trans Image Process 25(2):829–839MathSciNetCrossRefGoogle Scholar
  26. 26.
    Lu C, Zhu C, Xu C, Yan S, Lin Z (2015) Generalized Singular Value Thresholding. in Proc of 29th AAAI Conf on Artificial IntelligenceGoogle Scholar
  27. 27.
    Mun S, Fowler JE (2009) Block Compressed Sensing of Images Using Directional Transforms. 16th IEEE Int Conf on Image Process (ICIP 2009), CairoGoogle Scholar
  28. 28.
    Nie L, Wang M, Zha ZJ, Chua TS (2012) Oracle in Image Search: A Content-Based Approach to Performance Prediction. ACM Trans Inf Syst 30(2)Google Scholar
  29. 29.
    Nie L, Yan S, Wang M, Hong R, Chua TS (2012) Harvesting visual concepts for image search with complex queries. in Proc of the 20th ACM Int Conf on Multimedia 59-68Google Scholar
  30. 30.
    Parekha A, Selesnickb IW (2017) Improved Sparse Low-Rank Matrix Estimation. Signal Process 139:62–69CrossRefGoogle Scholar
  31. 31.
    Selesnick I (2012) Penalty and Shrinkage Functions for Sparse Signal ProcessingGoogle Scholar
  32. 32.
    Sun L, Chen J, Zeng D, Ding X (2015) A Novel Nonlocal MRI Reconstruction Algorithm with Patch-Based Low-Rank regularization. IEEE Global Conf Signal & Inf Process (GlobalSIP), OrlandoGoogle Scholar
  33. 33.
    Wong Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Trans Image Process 13(4):600–612CrossRefGoogle Scholar
  34. 34.
    Xie Y, Gu S, Liu Y, Zuo W, Zhang W, Zhang L (2016) Weighted Schatten p-norm minimization for image Denoising and background subtraction. IEEE Trans Image Process 25(10):4842–4857MathSciNetCrossRefGoogle Scholar
  35. 35.
    Yoon H, Kim KS, Kim D, Bresler Y, Ye JC (2014) Motion Adaptive Patch-Based Low-Rank Approach for Compressed Sensing Cardiac Cine MRI. IEEE Trans Medical Imaging 33(11):2069–2085CrossRefGoogle Scholar
  36. 36.
    Zhang Y, Guo J, Li C (2017) Image Compressed Sensing Based on Nonconvex Low-Rank Approximation. Multimed Tools Appl 77(10):12853–12869CrossRefGoogle Scholar
  37. 37.
    Zhang D, Hu Y, Ye J, Li X, He X (2012) Matrix Completion by Truncated Nuclear Norm Regularization. Proc of IEEE Conf Computer Vision and Pattern Recognition (CVPR), Providence, pp 2192–2199Google Scholar
  38. 38.
    Zhang Z, Li F, Zhao M, Zhang L, Yan S (2016) Joint low-rank and sparse principal feature coding for enhanced robust representation and visual classification. IEEE Trans Image Process 25(6):2429–2443MathSciNetCrossRefGoogle Scholar
  39. 39.
    Zhang J, Zhao D, Gao W (2014) Group-Based Sparse Representation for Image Restoration. IEEE Trans Image Process 23(8):3336–3351MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zhang J, Zhao D, Xiong R, Ma S, Gao W (2014) Image Restoration Using Joint Statistical Modeling in a Space Transform Domain. IEEE Trans Circuits and systems for Video Technology 24(6)Google Scholar
  41. 41.
    Zhang J, Zhao D, Zhao C, Xiong R, Ma S, Gao W (2012) Image Compressive Sensing Recovery via Collaborative Sparsity. IEEE J on Emerging and Selected Topics in Circuits and Systems 2(3)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Electrical and Computer EngineeringBabol Noshirvani University of TechnologyBabolIran
  2. 2.Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran

Personalised recommendations