Stable Image Reconstruction Using Total Variation Minimization

@article{Needell2013StableIR,
  title={Stable Image Reconstruction Using Total Variation Minimization},
  author={Deanna Needell and Rachel Ward},
  journal={ArXiv},
  year={2013},
  volume={abs/1202.6429}
}
  • Deanna Needell, Rachel Ward
  • Published in SIAM J. Imaging Sciences 2013
  • Mathematics, Computer Science
  • ArXiv
  • This paper presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization. In particular, we show that from $O(s\log(N))$ nonadaptive linear measurements, an image can be reconstructed to within the best $s$-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in… CONTINUE READING

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