Compressed sensing with side information: Geometrical interpretation and performance bounds

We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via ℓ₁-ℓ₁ and ℓ₁-ℓ₂ minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced via ℓ₁-ℓ₁ minimization, but not so much via ℓ₁-ℓ₂ minimization. We provide geometrical interpretations and experimental results illustrating our findings.