We address the problem of reference-based compressed sensing: reconstructa sparse signal from few linear measurements using asprior information a reference signal, a signal similar to the signalwe want to reconstruct. Access to reference signals arises in applicationssuch as medical imaging, e.g., through prior images ofthe same patient, and compressive video, where previously reconstructedframes can be used as reference. Our goal is to use thereference signal to reduce the number of required measurements forreconstruction. We achieve this via a reweighted ℓ1-ℓ1 minimizationscheme that updates its weights based on a sample complexitybound. The scheme is simple, intuitive and, as our experimentsshow, outperforms prior algorithms, including reweighted ℓ1 minimization,ℓ1-ℓ1 minimization, and modified CS.