Claremont McKenna College, Mathematics (CMC), Claremont Graduate University, Mathematical Sciences (CGU)
Weighted ℓ1-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In this work, we study the recovery conditions and the associated recovery guarantees of weighted ℓ1-minimization when arbitrarily many distinct weights are permitted. For example, such a setup might be used when one has multiple estimates for the support of a signal, and these estimates have varying degrees of accuracy. Our analysis yields an extension to existing works that assume only a single constant weight is used. We include numerical experiments, with both synthetic signals and real video data, that demonstrate the benefits of allowing non-uniform weights in the reconstruction procedure.
© 2016 Needell, Saab, Woolf
D. Needell, R. Saab, T. Woolf. “Weighted L1-Minimization for Sparse Recovery under Arbitrary Prior Information.” Information and Inference, 2016.