AAM  >> Vol. 3 No. 3 (August 2014)

    A New Method for Signal Reconstruction of lp-Norm Optimization

  • 全文下载: PDF(403KB) HTML    PP.140-148   DOI: 10.12677/AAM.2014.33021  
  • 下载量: 2,463  浏览量: 8,580  


赵 真,陈国庆:内蒙古大学,呼和浩特

压缩感知信号重构非光滑优化极大熵函数Compressed Sensing Signal ReconstructionNonsmooth Optimization Maximum Entropy Function


随着信息科学技术的迅猛发展,信息量越来越大,对信息处理的理论技术的要求也就越高,原有的传统信息处理方法不能够完全满足人们的要求。因此对压缩感知理论的研究是十分必要的。而压缩感知理论中最核心的部分就是信号重构。本文用极大熵函数构造 范数的光滑逼近函数,进而实现信号重构,并提出了基于最小 范数问题的MEFM算法,证明了算法的收敛性。数值实验表明验证了新算法是十分可行有效的信号重构方法。

With the rapid development of information science and technology, the amount of information becomes huge. The demand of technology on information processing will be high and the original traditional information processing methods cannot fully meet the requirements of people. So the study of compression perception theory is very important. The main content of this thesis is the reconstruction algorithm, which has played an important role in the theory of the compressed sensing. In order to overcome the nonsmooth problem in   norm, this paper proposed a new Maximum Entropy Function Method (MEFM) to solve the   optimization problem and proved the convergence of the new algorithm. Numerical experiments demonstrated that the new algorithm is feasible and effective in signal reconstruction.

赵真, 陈国庆. 基于光滑逼近lp范数的重构信号算法[J]. 应用数学进展, 2014, 3(3): 140-148. http://dx.doi.org/10.12677/AAM.2014.33021


[1] Candes, E.J., Romberg, J. and Tao, T. (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52, 489-509.
[2] Donoho, D.L. (2006) Compressed sensing. IEEE Transactions on Information Theory, 52, 1289-1306.
[3] Donoho, D.L. and Tsaig, Y. (2006) Extensions of compressed sensing. Signal Processing, 86, 533-584.
[4] Candes, E. (2006) Compressive sam-pling. Proceedings of the International Congress of Mathematicians, 3, 1433- 1452.
[5] Candes, E. and Romberg, J. (2006) Quantitative robust uncertainty principles and optimally sparse decompositions. Foundations of Computational Mathematics, 6, 227-254.
[6] Chen, S.B., Donoho, D.L. and Saunders, M.A. (1998) Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20, 33-61.
[7] Donoho, D.L., Elad, M. and Temlyakov, V. (2006) Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory, 52, 6-18.
[8] Gribonval, R. and Nielsen, M. (2003) Sparse representation in unions of bases. IEEE Transac-tions on Information Theory, 49, 3320-3325.
[9] Zelinski, A., Wald, L., Setsompop, K., et al. (2008) Sparsity-enforced slice-selective MRI RF excitation pulse design. IEEE Transaction on Medical Imaging, 27, 1213-1229.
[10] Levin, A., Fergus, R., Durand, F. and Freeman, W.T. (2007) Image and depth from a conventional camera with a coded aperture. ACM Transactions on Graphics, 26, 70.
[11] Donoho, D.L. and Elad, M. (2003) Optimally sparse representation in general (nonorthogoinal) dictionaries via L1 minimization. Proceedings of the National Academy of Science of the United States of America, 100, 2197-2202.
[12] Li, X.S. and Fang, S.C. (1997) On the entropic regularization method for solving max-min problems with application. Mathematical Methods of Operations Research, 46, 119-130.