Abstract:

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.

Key words: Sub Nyquist sampling, Random demodulator (RD), Sparse bayesian learning (SBL), Dictionary optimization, Frequency estimation