Recovery of Compressed Sampling in Shift-Invariant Spaces Base on L1 Norm

摘要

Compressed sampling in shift-invariant spaces (SI) is an effective method for sampling of sparse signals. But, reconstruction of compressed sampling may be unstable. In the paper, the possibility of stable reconstruction under a sufficient sparsity is proven. Further, we consider the situation where the minimal L1 norm is used to recover sparse signals from the noisy data. The result shows that they are stable. Finally, we show that the minimal L1 norm through the simulation, and explain the applicability of our algorithm to sampling systems.