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2008

Probing the Pareto Frontier for Basis Pursuit Solutions

8 years 12 months ago
Probing the Pareto Frontier for Basis Pursuit Solutions
The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the...
Ewout van den Berg, Michael P. Friedlander
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMSC
Authors Ewout van den Berg, Michael P. Friedlander
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