Compressed Sampling in Union of Shift-Invariant Subspace Based on Sparse Bayesian Learning

For the signals in a special union of shift-invariant subspaces (USI) when the active kernel functions are unknown, a concrete compressed sampling scheme is proposed. We regard the process of signal reconstruction as a lin-ear regression model and acquire the optional weights by sparse bayesian learning, then the signal can be reconstructed accurately from the support of weight vector set. For a continuous-time sparse signal in shift-invariant spaces which is generated by M kernels with period T, however, there are only K out of the M kernels are active and we do not know which K are chosen, we can sample the signal at 2K/T rate by the sampling scheme,which is the minimal sampling rate with exploiting sparsity K. Simulation results are presented to show that our compressed sampling scheme can reduce the sampling rate effectively.