Sparse signal recovery or compressed sensing (CS) theory has recently received attention in the image compression field. CS has proven that the successful recovery rate of the multiple measurement vectors (MMVs) model is higher than that of the single measurement vector (SMV) case. Most existing algorithms have focused on sparse signal recovery using the MMV model, without considering converting the general SMV model into the MMV model. In this study, a simple transforming model that takes advantage of the correlations among wavelet coefficients is proposed, such that the MMV model can be used for general images rather than only certain special signals. To further enhance the performance of the MMV model, the improved MMV model based on the similarity of image blocks is proposed. Simulation results have shown that the obtained solution matrix can be used in the MMV model, and that the proposed algorithm provides better reconstruction quality than many state-of-the-art algorithms.

References

1. 1)
  - 9. Zdunek, R., Cichocki, A.: ‘Improved M-FOCUSS algorithm with overlapping blocks for locally smooth sparse signals’, IEEE Trans. Signal Process., 2008, 56, (10), pp. 4752–4761.
2. 2)
  - 13. Tropp, J.A., Gilbert, A.C., Strauss, M.J.: ‘Algorithms for simultaneous sparse approximation. Part I: greedy pursuit’, Signal Process.., 2006, 86, (3), pp. 572–588.
3. 3)
  - 15. Wipf, D.P., Rao, B.D.: ‘An empirical Bayesian strategy for solving the simultaneous sparse approximation problem’, IEEE Trans. Signal Process., 2007, 55, (7), pp. 3704–3716.
4. 4)
  - 20. Mun, S., Fowler, J.E.: ‘Block compressed sensing of images using directional transforms’. Proc. Int. Conf. Image Processing, Cario, Egypt, November 2009, pp. 3021–3024.
5. 5)
  - 16. Zhang, Z.L., Rao, B.D.: ‘Sparse signal recovery with temporally correlated source vectors using sparse Bayesi an learning’, IEEE J. Sel. Top. Signal Process., 2011, 5, (5), pp. 912–926.
6. 6)
  - 28. Wang, Z., Bovik, A.C., Sheikh, H.R., et al: ‘Image quality assessment: from error visibility to structural similarity’, IEEE Trans. Image Process., 2004, 13, (4), pp. 600–612.
7. 7)
  - 23. Baraniuk, R.G., Cevher, V., Duarte, M.F., et al: ‘Model-based compressive sensing’, IEEE Trans. Inf. Theory, 2010, 56, (4), pp. 1982–2001.
8. 8)
  - 18. Deng, C., Lin, W., Lee, B.S., et al: ‘Robust image coding based upon compressive sensing’, IEEE Trans. Multimed., 2012, 14, (2), pp. 278–290.
9. 9)
  - 22. He, L., Carin, L.: ‘Exploiting structure in wavelet-based Bayesian compressive sensing’, IEEE Trans. Signal Process., 2009, 57, (9), pp. 3488–3497.
10. 10)
  - 17. Zhang, J., Zhao, D., Zhao, C., et al: ‘Image compressive sensing recovery via collaborative sparsity’, IEEE J. Emerging Sel. Top. Circuits Syst., 2012, 2, (3), pp. 380–391.
11. 11)
  - 3. Candès, E.J.: ‘The restricted isometry property and its implications for compressed sensing’, C. R. Math., 2008, 346, (9), pp. 589–592.
12. 12)
  - 4. Chen, S.S., Donoho, D.L., Saunders, M.A.: ‘Atomic decomposition by basis pursuit’, SIAM J. Sci. Comput., 1998, 20, (1), pp. 33–61.
13. 13)
  - 12. Cotter, S.F., Rao, B.D., Engan, K., et al: ‘Sparse solutions to linear inverse problems with multiple measurement vectors’, IEEE Trans. Signal Process., 2005, 53, (7), pp. 2477–2488.
14. 14)
  - 8. Wipf, D., Rao, B.D.: ‘Sparse Bayesian learning for basis selection’, IEEE Trans. Signal Process., 2004, 52, (8), pp. 2153–2164.
15. 15)
  - 21. Fang, H., Vorobyov, S.A., Jiang, H., et al: ‘Permutation meets parallel compressed sensing how to relax RIP for 2D sparse signals’, IEEE Trans. Signal Process., 2014, 62, (1), pp. 196–210.
16. 16)
  - 19. Gan, L.: ‘Block compressed sensing of natural images’, IEEE Int. Conf. on Digital Signal Processing, Cardiff, UK, 1–4 July 2007, pp. 403–406.
17. 17)
  - 6. Gorodnitsky, I.F., Rao, B.D.: ‘Sparse signal reconstructions from limited data using FOCUSS: a re-weighted minimum norm algorithm’, IEEE Trans. Signal Process., 1997, 45, (3), pp. 600–616.
18. 18)
  - 10. Obozinski, G., Wainwright, M.J., Jordan, M.I.: ‘Support union recovery in high-dimensional multivariate regression’, Ann. Stat., 2011, 39, (1), pp. 1–47.
19. 19)
  - 2. Tsaig, Y., Donoho, D.L.: ‘Extensions of compressed sensing’, Signal Process.., 2006, 86, (3), pp. 549–571.
20. 20)
  - 5. Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.S.: ‘Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition’. IEEE Conf. Record of the 27th Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, November 1993, pp. 40–44.
21. 21)
  - 25. Mallat, S.G.: ‘A theory for multi resolution signal decomposition: the wavelet representation’, IEEE Trans. Pattern Anal. Mach. Intell., 1989, 11, pp. 674–693.
22. 22)
  - 26. Liu, J., Moulin, P.: ‘Information-theoretic analysis of inter-scale and intra-scale dependencies between image wavelet coefficients’, IEEE Trans. Image Process., 2001, 10, (11), pp. 1647–1658.
23. 23)
  - 24. Wu, J., Liu, F., Jiao, L.C., et al: ‘Multivariate compressive sensing for image reconstruction in the wavelet domain: using scale mixture models’, IEEE Trans. Image Process., 2011, 20, (12), pp. 3483–3494.
24. 24)
  - 14. Negahban, S., Wainwright, M.J.: ‘Simultaneous support recovery in high dimensions: benefits and perils of block l1/l∞ -regularization’, IEEE Trans. Inf. Technol., 2011, 57, (6), pp. 3841–3863.
25. 25)
  - 27. Swain, M., Barrard, D.: ‘Color indexing’, Int. J. Comput. Vis., 1991, 7, (1), pp. 11–32.
26. 26)
  - 11. Tang, G., Nehorai, A.: ‘Performance analysis for sparse support recovery’, IEEE Trans. Inf. Theory, 2010, 56, (3), pp. 1383–1399.
27. 27)
  - 1. Donoho, D.L.: ‘Compressed sensing’, IEEE Trans. Inf. Theory, 2006, 52, (4), pp. 1289–1306.
28. 28)
  - 7. Candes, E.J., Wakin, M.B., Boyd, S.P.: ‘Enhancing sparsity by reweighted l1 minimization’, J. Fourier Anal. Appl., 2008, 14, (5–6), pp. 877–905.

Transforming the SMV model into MMV model based on the characteristics of wavelet coefficients

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