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CGU Graduate

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Claremont McKenna College, Mathematics (CMC), Claremont Graduate University, Mathematical Sciences (CGU)

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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.

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© 2016 Needell, Saab, Woolf

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