Periodic Non-Uniform Sampling and Reconstruction Based on Minimum L₁ Normal

A method to realize the sampling and reconstruction of the sparse signals is proposed in this paper based on minimum L1 normal. According to the feature of periodic non-uniform sampling that it needs multiple channels,the sampling and reconstruction of signals are transformed into matrix and vector operations by using theory of union of subspaces. Necessary condition of reconstruction is analyzed. Finally, taking multi-band sinusoidal signals as an example, we prove that the method can achieve the sampling and reconstruction of sparse signals.