Abstract
Compressed sensing (CS) has drawn quite an amount of attentions as a joint sampling and compression approach. Its theory shows that if a signal is sparse or compressible in a certain transform domain, it can be decoded from much fewer measurements than suggested by the Nyquist sampling theory. In this paper, we propose an unequal-compressed sensing algorithm which combines the compressed sensing theory with the characteristics of the wavelet coefficients. First, the original signal is decomposed by the multi-scale discrete wavelet transform (DWT) to make it sparse. Secondly, we retain the low frequency coefficients; meanwhile, one of the high frequency sub-band coefficients is measured by random Gaussian matrix. Thirdly, the sparse Bayesian learning (SBL) algorithm is used to reconstruct the high frequency sub-band coefficients. What’s more, other high frequency sub-band coefficients can be recovered according to the high frequency sub-band coefficients and the characteristics of wavelet coefficients. Finally, we use the inverse discrete wavelet transform (IDWT) to reconstruct the original signal. Compared with the original CS algorithms, the proposed algorithm has better reconstructed image quality in the same compression ratio. More importantly, the proposed method has better stability for low compression ratio.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Donoho DL (2006) Compressed sensing. IEEE Trans Inform Theory 52(4):1289–1306
Tsaig Y, Donoho DL (2006) Extensions of compressed sensing. IEEE Trans Signal Process 86(3):549–571
Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 5:489–509
Candès EJ (2008) The restricted isometry property and its implications for compressed sensing. CR Math 346(9):589–592
Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by Basis Pursuit. SIAM J Sci Comput 20(1):33–61
Pati YC, Rezaiifar R, Krishnaprasad PS (1993) Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: IEEE 1993 conference record of the twenty-seventh Asilomar conference on signals, systems and computers, 1–3 Nov 1993, Pacific Grove. IEEE, pp 40–44
Wipf D, Rao BD (2004) Sparse Bayesian learning for basis selection. IEEE Trans Signal Process 52(8):2153–2164
Zhang Y, Mei S, Chen Q, Chen Z (2008) A novel image/video coding method based on compressive sensing theory. In: Proceedings of the international conference on acoustics, speech and signal processing (ICASSP), pp 1361–1364
Sun J, Lian QS (2013) An image compression algorithm combined nonuniform sample and compressed sensing. J Signal Process 29(1):31–37
Cen YG, Chen XF, Cen LH, Chen SM (2010) Compressed sensing based on the single layer wavelet transform for image processing. J Commun 31(8A):52–55
Acknowledgement
This work was supported by National Science Foundation of China (61171176).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Li, W., Jiang, T., Wang, N. (2015). Unequal-Compressed Sensing Based on the Characteristics of Wavelet Coefficients. In: Mu, J., Liang, Q., Wang, W., Zhang, B., Pi, Y. (eds) The Proceedings of the Third International Conference on Communications, Signal Processing, and Systems. Lecture Notes in Electrical Engineering, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-08991-1_73
Download citation
DOI: https://doi.org/10.1007/978-3-319-08991-1_73
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08990-4
Online ISBN: 978-3-319-08991-1
eBook Packages: EngineeringEngineering (R0)