Lian Qiu-Sheng, Xiao Ying. Image Compressed Sensing Algorithm Based on Wavelet Tree Structure and Iterative Shrinkage[J]. Journal of Electronics & Information Technology, 2011, 33(4): 967-971. doi: 10.3724/SP.J.1146.2010.00684
Citation:
Lian Qiu-Sheng, Xiao Ying. Image Compressed Sensing Algorithm Based on Wavelet Tree Structure and Iterative Shrinkage[J]. Journal of Electronics & Information Technology, 2011, 33(4): 967-971. doi: 10.3724/SP.J.1146.2010.00684
Lian Qiu-Sheng, Xiao Ying. Image Compressed Sensing Algorithm Based on Wavelet Tree Structure and Iterative Shrinkage[J]. Journal of Electronics & Information Technology, 2011, 33(4): 967-971. doi: 10.3724/SP.J.1146.2010.00684
Citation:
Lian Qiu-Sheng, Xiao Ying. Image Compressed Sensing Algorithm Based on Wavelet Tree Structure and Iterative Shrinkage[J]. Journal of Electronics & Information Technology, 2011, 33(4): 967-971. doi: 10.3724/SP.J.1146.2010.00684
Based on the standard compressed sensing, the model-based Compressed Sensing (CS) uses the tree structure priors, and solves the optimal reconstruction problem with two existing tree structure approximation which are greedy tree approximation and optimal tree approximation. Through numerous statistics test of wavelet relationship, a new tree structure which is named reasonable tree structure is proposed, which is based on the relationship between neighbor coefficients, parent coefficients and children coefficients. What is more, combining with the new reasonable tree structure, an improvement is made for the iterative hard threshold reconstruction algorithm and model-based compressed sensing reconstruction algorithm. Comparing with the iterative hard threshold algorithm and model-based compressed sensing algorithm, the proposed algorithm can achieve higher image reconstruction performance.
Donoho D L. Compressed sensing [J].IEEE Transactions on Information Theory.2006, 52(4):1289-1306[2]Candes E J, Romberg J, and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information [J].IEEE Transactions on Information Theory.2006, 52(2):489-509[3]Chen S B, Donoho D L, and Saunders M A. Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing.1998, 20(1):33-61[4]Figueiredo M A T, Nowak R D, and Wright S J. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing.2007, 1(4):586-597[5]Blumensath T and Davies M E. Iterative hard thresholding for compressed sensing [J].Applied and Computational Harmonic Analysis.2009, 27(3):265-274[6]Mallat S and Zhang Z. Matching pursuits with time- frequency dictionaries[J].IEEE Transactions on Signal Processing.1993, 41(12):3397-3415[7]Tropp J A and Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit [J].IEEE Transactions on Information Theory.2007, 53(12):4655-4666[8]Needell D and Vershynin D. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit[J].Foundations of Computational Mathematics.2009, 9(3):317-334[12]Stojnic M, Parvaresh F, and Hassibi B. On the resconstruction of block-sparse signals with an optimal number of measurements [J].IEEE Transactions on Signal Processing.2009, 57(8):3075-3085[13]He L and Carin L. Exploiting structure in wavelet-based Bayesian compressive sensing [J].IEEE Transactions on Signal Processing.2009, 57(9):3488-3497[14]Baraniuk R G, DeVore R A, Kyriazis G, and Yu X M. Near best tree approximation [J].Advances in Computational Mathmatics.2002, 16(4):357-373[16]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