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Abstract
1. Introduction
2.Minimizing the L1-Norm
3.Uniqueness in L1-Norm Minimization
4.Stability of the Reconstruction
5.Simulation
6.Exact recovery of L1-norm
7.Error of Recovery L1-Norm
8.Conclusion
Reference
Abstract
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.
Introduction
The sampling in SI has been discussed in recent years. As discussed by A. Aldroubi in [1], a selection of the generator eliminates some problems which relate to the classical sampling. The model contains the signals which can be used to signal processing. For example, the band-limited signal is SI with Sinc[2], [3] and pulse modulation in signal processing. The signals can be described using multiple generators, multiband signal [4], [5], [6]. Therefore, we give a Si generated by the L function, which shift with the period T.