Abstract
Basis Pursuit and Basis Pursuit Denoising, well established techniques for computing sparse representations, minimize an {ell}{sup 2} data fidelity term subject to an {ell}{sup 1} sparsity constraint or regularization term on the solution by mapping the problem to a linear or quadratic program. Basis Pursuit Denoising with an {ell}{sup 1} data fidelity term has recently been proposed, also implemented via a mapping to a linear program. They introduce an alternative approach via an iteratively Reweighted Least Squares algorithm, providing greater flexibility in the choice of data fidelity term norm, and computational advantages in certain circumstances.
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