# Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse

@article{Donoho2008FastSO,
title={Fast Solution of \$\ell _\{1\}\$ -Norm Minimization Problems When the Solution May Be Sparse},
author={David L. Donoho and Yaakov Tsaig},
journal={IEEE Transactions on Information Theory},
year={2008},
volume={54},
pages={4789-4812}
}
The minimum lscr1-norm solution to an underdetermined system of linear equations y=Ax is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for lscr1 minimization in many large-scale applications.In this paper, the Homotopy method, originally proposed by Osborne et al. and Efron et al., is applied to the underdetermined lscr1… CONTINUE READING

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