A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data

@article{Bourguignon2007ASM,
  title={A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data},
  author={S{\'e}bastien Bourguignon and Herv{\'e} Carfantan and J{\'e}r{\^o}me Idier},
  journal={IEEE Journal of Selected Topics in Signal Processing},
  year={2007},
  volume={1},
  pages={575-585}
}
We address the problem of estimating spectral lines from irregularly sampled data within the framework of sparse representations. Spectral analysis is formulated as a linear inverse problem, which is solved by minimizing an l1-norm penalized cost function. This approach can be viewed as a basis pursuit de-noising (BPDN) problem using a dictionary of cisoids with high frequency resolution. In the studied case, however, usual BPDN characterizations of uniqueness and sparsity do not apply. This… CONTINUE READING
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