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We address the problem of compressed sensing (CS) with prior information:reconstruct a target CS signal with the aid of a similar signal that is knownbeforehand, our prior information. We integrate the additional knowledge of thesimilar signal into CS via L1-L1 and L1-L2 minimization. We then establishbounds on the number of measurements required by these problems to successfullyreconstruct the original signal. Our bounds and geometrical interpretationsreveal that if the prior information has good enough quality, L1-L1minimization improves the performance of CS dramatically. In contrast, L1-L2minimization has a performance very similar to classical CS and brings nosignificant benefits. All our findings are illustrated with experimentalresults.

Compressed Sensing with Prior Information: Optimal Strategies, Geometry, and Bounds