A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements

@article{Adcock2016ANO,
  title={A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements},
  author={Ben Adcock and Anders C. Hansen and Bogdan Roman},
  journal={IEEE Signal Processing Letters},
  year={2016},
  volume={23},
  pages={732-736}
}
We consider signal recovery from Fourier measurements using compressed sensing (CS) with wavelets. For discrete signals with structured sparse Haar wavelet coefficients, we give the first proof of near-optimal recovery from discrete Fourier samples taken according to an appropriate variable density sampling scheme. Crucially, in taking into account such structured sparsity-known as sparsity in levels-as opposed to just sparsity, this result yields recovery guarantees that agree with the… 
Compressed sensing with local structure: uniform recovery guarantees for the sparsity in levels class
  • Chen Li, B. Adcock
  • Computer Science
    Applied and Computational Harmonic Analysis
  • 2019
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