Compressed Sensing With Side Information: Geometrical Interpretation and Performance Bounds
This work addresses signal reconstruction efficiency in compressed sensing for applications like imaging or communications, but it appears incremental as it builds on existing minimization methods.
The paper tackles the problem of compressed sensing with side information by integrating it via L1-L1 and L1-L2 minimization, showing that L1-L1 minimization significantly reduces the required measurements when side information is of good quality.
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.