基于稀疏贝叶斯学习的联合平移不变子空间压缩采样

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

针对一类特殊的有效核函数(active kernel)未知的联合平移不变子空间(Union of Shift-Invariant Subspaces,USI)信号,构建了一种压缩采样模型,将信号的重构过程看作一个线性回归问题,利用稀疏贝叶斯学习(sparsebayesian learning,SBL)算法求得该回归模型中的权值参数的最优估计,根据权值参数向量集的支撑集实现信号的稀疏重构。理论分析表明,对于由M个核函数(kernel)以T为周期平移生成的平移不变空间(Shift-InvariantSpaces,SI),若M个核函数中至多有K(1≤K≤M/2)个且未知哪K个有效时,本文构建的压缩采样模型最低采样率能够达到2K/T,这也是利用稀疏度K所能达到的理论上的最低采样率。仿真结果表明,构建的压缩采样模型能够有效降低这类信号的采样率。

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.