# Weighted-{$ell 1$} minimization with multiple weighting sets

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In this paper, we study the support recovery conditions of weighted $\ell 1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from $\ell 1$ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted $\ell 1$ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted, $\ell 1$ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.

Author: Hassan Mansour; Ozgur Yilmaz

Source: https://archive.org/