Close Encounters of the Binary Kind: Signal Reconstruction Guarantees for Compressive Hadamard Sampling With Haar Wavelet Basis

@article{Moshtaghpour2019CloseEO,
  title={Close Encounters of the Binary Kind: Signal Reconstruction Guarantees for Compressive Hadamard Sampling With Haar Wavelet Basis},
  author={Amirafshar Moshtaghpour and Jos{\'e} M. Bioucas-Dias and Laurent Jacques},
  journal={IEEE Transactions on Information Theory},
  year={2019},
  volume={66},
  pages={7253-7273}
}
We investigate the problems of 1-D and 2-D signal recovery from subsampled Hadamard measurements using Haar wavelet as a sparsity inducing prior. These problems are of interest in, e.g., computational imaging applications relying on optical multiplexing or single-pixel imaging. However, the realization of such modalities is often hindered by the coherence between the Hadamard and Haar bases. The variable and multilevel density sampling strategies solve this issue by adjusting the subsampling… 

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