  Weighted $\ell_1$-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 $\ell_1$-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 support estimate set upon which a constant
weight is applied. 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.
