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A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data

Junfeng Yang Yin Zhang Wotao Yin

Numerical Analysis and Scientific Computing mathscidoc:1912.43772

Selected Topics in Signal Processing, IEEE Journal of, Special Issue on Compressed Sensing, 4, (2), 288-297, 2010.4
Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, we propose the use of the alternating direction method - a classic approach for optimization problems with separable variables (D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite-element approximations, Computer and Mathematics with Applications, vol. 2, pp. 17-40, 1976; R. Glowinski and A. Marrocco, Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires, Rev. Francaise dAut. Inf. Rech. Oper., vol. R-2, pp. 41-76, 1975) - for signal reconstruction from partial Fourier (i.e., incomplete frequency) measurements. Signals are reconstructed as minimizers of
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@inproceedings{junfeng2010a,
  title={A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data},
  author={Junfeng Yang, Yin Zhang, and Wotao Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205707410174336},
  booktitle={Selected Topics in Signal Processing, IEEE Journal of, Special Issue on Compressed Sensing},
  volume={4},
  number={2},
  pages={288-297},
  year={2010},
}
Junfeng Yang, Yin Zhang, and Wotao Yin. A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data. 2010. Vol. 4. In Selected Topics in Signal Processing, IEEE Journal of, Special Issue on Compressed Sensing. pp.288-297. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205707410174336.
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