Compressed Sensing with Prior Information: Optimal Strategies, Geometry, and Bounds
arXiv:1408.5250
Abstract
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 known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via L1-L1 and L1-L2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, L1-L1 minimization improves the performance of CS dramatically. In contrast, L1-L2 minimization has a performance very similar to classical CS and brings no significant benefits. All our findings are illustrated with experimental results.
submitted to IEEE Transactions on Information Theory
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- Classification and Reconstruction of High-Dimensional Signals from Low-Dimensional Features in the Presence of Side Information
- Recovery of Structured Signals with Prior Information via Maximizing Correlation
- Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtraction
- Binary Rate Distortion With Side Information: The Asymmetric Correlation Channel Case
- Performance Analysis of Joint-Sparse Recovery from Multiple Measurements and Prior Information via Convex Optimization