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Efficient Basis Pursuit DeNoising via Active Sets and Homotopy

The Basis Pursuit DeNoising problem is a variant of the well-known lasso method for obtaining sparse least-squares approximations, which can be represented as the minimization problem minβ 1 2 ‖Aβ − y‖ 2 + λ ‖β‖ 1 . In this paper the problem is treated as a parametric quadratic program with parameter λ ≥ 0. By this technique, very large scale problems can be essentially solved exactly for a range of values of λ, as long as the number of non-zero components of β is small to modest.