利用字典优化方法实现sub Nyquist采样数据的频率估计

在稀疏重构理论中，重构信号需要预先设定稀疏表示字典，针对预设字典与真实字典之间的失配对信号稀疏表示造成的不利影响，提出一种基于字典优化和稀疏贝叶斯学习(Sparse Bayesian Learning, SBL)的频率估计算法。该算法首先构造基于sub Nyquist采样数据的信号稀疏表达式，然后利用SBL算法估计信号频率，同时根据估计结果优化字典，最后反复迭代上述步骤直至计算出的频率值和对应的幅度值趋于稳定。仿真结果校验了方法的有效性。

Frequency Estimation of Sub Nyquist Sampling Data Based Dictionary Optimization Approach

In the sparse reconstruction theory, signal reconstruction depends on the preset of an appropriate sparse representation dictionary, the mismatch between the preset and the actual dictionaries will cause adverse effects on sparse signal representation. In this paper, a parameter estimation algorithm is proposed based on dictionary optimization and sparse Bayesian learning (SBL). At first, the sparse representation of signal based on sub Nyquist sampling data is constructed. Then SBL algorithm is used to estimate frequency, and the dictionary is optimized according to the estimated value. Lastly, the iteration of the above steps will not terminate until the frequencies and the corresponding amplitudes trend toward to be stabilized. Numerical examples are carried out to demonstrate the effectiveness of the proposed method.