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A new wavelet based efficient image compression algorithm using compressive sensing

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Abstract

We propose a new algorithm for image compression based on compressive sensing (CS). The algorithm starts with a traditional multilevel 2-D Wavelet decomposition, which provides a compact representation of image pixels. We then introduce a new approach for rearranging the wavelet coefficients into a structured manner to formulate sparse vectors. We use a Gaussian random measurement matrix normalized with the weighted average Root Mean Squared energies of different wavelet subbands. Compressed sampling is finally performed using this normalized measurement matrix. At the decoding end, the image is reconstructed using a simple ℓ 1-minimization technique. The proposed wavelet-based CS reconstruction, with the normalized measurement matrix, results in performance increase compared to other conventional CS-based techniques. The proposed approach introduces a completely new framework for using CS in the wavelet domain. The technique was tested on different natural images. We show that the proposed technique outperforms most existing CS-based compression methods.

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References

  1. Ahmed N, Natarajan T, Rao KR (1974) Discrete cosine transform. IEEE Trans Comput 100(1):90–93

    Article  MathSciNet  MATH  Google Scholar 

  2. Baraniuk RG (2007) Compressive sensing [lecture notes]. IEEE Signal Process Mag 24(4):118–121

    Article  Google Scholar 

  3. Baraniuk RG, Candes E, Elad M, Ma Y (2010) Applications of sparse representation and compressive sensing [scanning the issue]. IEEE Proc 98(6):906–909

    Article  Google Scholar 

  4. Becker S, Bobin J, Candès EJ (2011) NESTA: a fast and accurate first-order method for sparse recovery. SIAM J Imag Sci 4(1):1–39

    Article  MathSciNet  MATH  Google Scholar 

  5. Bi X, Chen X-d, Zhang Y, Liu B (2011) Image compressed sensing based on wavelet transform in contourlet domain. Signal Process 91(5):1085–1092

    Article  Google Scholar 

  6. Bobin J, Starck J-L, Ottensamer R (2008) Compressed sensing in astronomy. IEEE J Sel Top Sign Proces 2(5):718–726

    Article  Google Scholar 

  7. Candes E, Romberg J (2007) Sparsity and incoherence in compressive sampling. Inverse Prob 23(3):969

    Article  MathSciNet  MATH  Google Scholar 

  8. Candes EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203–4215

    Article  MathSciNet  MATH  Google Scholar 

  9. Candes EJ, Tao T (2006) Near-optimal signal recovery from random projections: Universal encoding strategies IEEE Trans Inf Theory 52(12):5406–5425

    Article  MathSciNet  MATH  Google Scholar 

  10. Candès EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Process Mag 25(2):21–30

    Article  Google Scholar 

  11. Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509

    Article  MathSciNet  MATH  Google Scholar 

  12. Candes EJ, Romberg JK, Tao T (2006) Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math 59(8):1207–1223

    Article  MathSciNet  MATH  Google Scholar 

  13. Cen Y, Chen X, Cen L, Chen S (2010) Compressed sensing based on the single layer wavelet transform for image processing. J Commun 31(8):53–55

    Google Scholar 

  14. Chartrand R, Yin W (2008) Iteratively reweighted algorithms for compressive sensing. In: IEEE international conference on Acoustics, speech and signal processing (ICASSP). IEEE, pp 3869–3872

  15. Chen C, Huang J (2012) Compressive sensing MRI with wavelet tree sparsity. In: Advances in neural information processing systems, pp 1115–1123

  16. Christopoulos C, Skodras A, Ebrahimi T (2000) The JPEG2000 still image coding system: an overview. IEEE Trans Consum Electron 46(4):1103–1127

    Article  Google Scholar 

  17. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306

    Article  MathSciNet  MATH  Google Scholar 

  18. Du M, Zhao H, Zhao C, Li B (2012) The application of wavelet-based contourlet transform on compressed sensing. In: Multimedia and Signal Processing. Springer, pp 570–577

  19. Gan L (2007) Block compressed sensing of natural images. 15th International Conference on Digital Signal Processing

  20. Gao Z, Xiong C, Ding L, Zhou C (2013) Image representation using block compressive sensing for compression applications. J Vis Commun Image Represent 24(7):885–894

    Article  Google Scholar 

  21. Herrmann FJ, Hennenfent G (2008) Non-parametric seismic data recovery with curvelet frames. Geophys J Int 173(1):233–248

    Article  Google Scholar 

  22. Kalra M, Ghosh D (2012) Image compression using wavelet based compressed sensing and vector quantization. In: IEEE 11th International Conference on Signal Processing (ICSP), vol 1. IEEE, pp 640–645

  23. Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med 58(6):1182–1195

    Article  Google Scholar 

  24. Lustig M, Donoho DL, Santos JM, Pauly JM (2008) Compressed sensing MRI. IEEE Signal Process Mag 25(2):72–82

    Article  Google Scholar 

  25. Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693

    Article  MATH  Google Scholar 

  26. Man H, Docef A, Kossentini F (2005) Performance analysis of the JPEG 2000 image coding standard. Multimed Tools Appl 26(1):27–57

    Article  Google Scholar 

  27. Mun S, Fowler JE (2009) Block compressed sensing of images using directional transforms. In: IEEE International Conference on Image Processing (ICIP). IEEE, pp 3021–3024

  28. Rao KR, Yip P, Rao KR (1990) Discrete cosine transform: algorithms, advantages, applications, vol 226. Academic press, Boston

    Book  MATH  Google Scholar 

  29. Romberg J (2008) Imaging via compressive sampling [introduction to compressive sampling and recovery via convex programming]. IEEE Signal Process Mag 25(2):14–20

    Article  Google Scholar 

  30. Sevak MM, Thakkar FN, Kher RK, Modi CK (2012) CT image compression using compressive sensing and wavelet transform. In: IEEE International Conference on Communication Systems and Network Technologies (CSNT). IEEE, pp 138–142

  31. Su L, Huang T, Yang J (2014) A video forgery detection algorithm based on compressive sensing. Multimedia Tools and Applications. pp 1–16

  32. Wallace GK (1991) The JPEG still picture compression standard. ACM Commun 34(4):30–44

    Article  Google Scholar 

  33. Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2009) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227

    Article  Google Scholar 

  34. Yang F, Wang S, Deng C (2010) Compressive sensing of image reconstruction using multi-wavelet transforms. In: IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), vol 1. IEEE, pp 702–705

  35. Yang Y, Au OC, Fang L, Wen X, Tang W (2009) Perceptual compressive sensing for image signals. IEEE International Conference on Multimedia and Expo (ICME). pp 89–92

  36. Yanng Y, Au OC, Fang L, Wen X, Tang W (2009) Reweighted compressive sampling for image compression. In: Picture Coding Symposium (PCS). IEEE, pp 1–4

  37. Yoon Y.-S, Amin M. G (2008) Compressed sensing technique for high-resolution radar imaging. In: SPIE Defense and Security Symposium, International Society for Optics and Photonics, vol 6968, pp 69,681A.1–69,681A.10

  38. Zhang J, Xia L, Huang M, Li G (2014) Image reconstruction in compressed sensing based on single-level DWT. In: IEEE Workshop on Electronics, Computer and Applications. IEEE, pp 941–944

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Acknowledgments

This work was supported in part by the Deanship of Scientific Research at KFUPM under project No. IN121012.

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Authors and Affiliations

  1. Department of Electrical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Muhammad Ali Qureshi & M. Deriche

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  1. Muhammad Ali Qureshi
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  2. M. Deriche
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Correspondence to Muhammad Ali Qureshi.

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Qureshi, M.A., Deriche, M. A new wavelet based efficient image compression algorithm using compressive sensing. Multimed Tools Appl 75, 6737–6754 (2016). https://doi.org/10.1007/s11042-015-2590-9

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  • DOI: https://doi.org/10.1007/s11042-015-2590-9

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