DOI: 10.3724/SP.J.1146.2009.01153

Journal of Electronics & Information Technology (电子与信息学报) 2010/32:10 PP.2301-2306

Image Compressed Sensing Based on Universal HMT of the Dual-tree Wavelets

The standard Compressed Sensing (CS) reconstructions of image exploit simply the sparse priors of the wavelet coefficients, ignoring the structural information of the wavelet coefficients. In this paper, the Hidden Markov Tree ( HMT ) model is integrated in the compressed sensing,which has been found successful in capturing the key features of the joint probability density of the wavelet coefficients of real-world image. An optimization issue which is similar to the standard compressed sensing is derived from the MAP reconstructions for the image based on HMT model, and an alternating convex projection algorithm based on Bayesian optimization is proposed. What’s more, a universal HMT (uHMT) model based on the dual-tree wavelet transform and its improved form are integrated to improve the reconstruction performance further, instead of the HMT model of the orthogonal wavelet transform. As the experiments show, the average Peak Signal-to-Noise Ratio (PSNR) of the reconstructed image based on the improved uHMT (iuHMT) model in the dual-tree wavelets domain outperforms uHMT model 0.97 dB.

Key words:Compressed Sensing (CS),Model-based CS,Dual-tree wavelet,uHMT model,Alternating convex projection

ReleaseDate:2014-07-21 15:29:13

[1] Donoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

[2] Candes E J nd Romberg J T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

[3] Blumensath T and Davies M E. Iterative thresholding for sparse approximations[J]. Journal of Fourier Analysis and Applications, 2008, 14(5): 629-654.

[4] Bregman L M. The method of successive projection for finding a common point of convex sets [J]. Soviet Math, 1965, 6(3): 688-692.

[5] Chartrand R and Yin Wotao. Iteratively reweighted algorithms for compressive sensing[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, USA, 2008: 3869-3872.

[6] Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization [J]. IEEE Signal Processing Letters, 2007, 14(10): 707-710.

[7] Mohimani G H, Babaie-Zadeh M, and Jutten C. A fast sparse approach for overcomplete sparse decomposition based on smoothed l0 norm [J]. IEEE Transactions on Signal Processing, 2009, 57(1): 289-301.

[8] Needell D and Tropp J A. CoSaMP: Iiterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2008, 26(3): 301-321.

[9] Needell D and Vershynin R. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit[J]. Foundations of Computational Mathematics, 2009, 9(3): 317-334.

[10] Baraniuk R G, Cevher Volkan, and Marco T D, et al. Model-Based compressive sensing [J]. IEEE Transactions on Information Theory, 2010, 56(4): 1982-2001.

[11] Duarte M F. Fast reconstruction from random incoherent projections[R]. Rice ECE Department Technical Report Tree, 2005.

[12] Yonina C E and Helmut B. Block-sparsity:coherence and efficient recovery[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, Taiwan, 2009: 2885-2888.

[13] Kivinen J J, Sudderth E B, and Jordan M I. Image denoising with nonparametric Hidden Markov trees[C]. IEEE International Conference on Image Processing, San Antonio, Texas, 2007, 3: 121-124.

[14] 赵书斌,彭思龙. 基于小波域HMT模型的图像超分辨率重构[J]. 计算机辅助设计与图形学学报,2003, 15(11): 1347-1352. Zhao Shu-bin and Peng Si-long. Wavelet-domain HMT-based image superresolution[J]. Journal of Computer-aided Design & Computer Graphics, 2003, 15(11): 1347-1352.

[15] Marco F D, Wakin M B, and Baraniuk R G. Wavelet-domain compressive signal reconstruction using a hidden markov tree model[C]. IEEE International Conference on Acoutics, Speech and Signal Processing, Las Vegas, NV, USA, 2008: 5137-5140.

[16] Crouse Matthew S, Nowak R D, and Baraniuk R G. Wavelet-based statistical signal processing using Hidden Markov Models[J]. IEEE Transactions on Signal Processing, 1996, 3(6): 1029-1035.

[17] Romberg J K, Hyeokho C, and Baraniuk R G. Bayesian tree-structured image modeling using wavelet-domain hidden markov models [J]. IEEE Transactions on Image Processing, 2001, 10(7): 1056-1068.

[18] Selesnick I W and Baraniuk R G. The dual-tree complex wavelet transform[J]. IEEE Signal Processing Magazine, 2005, 22(6): 123-151.