Basis function selection for compressed sensing and sparse representations of pulsed radar echoes

Abstract

Compressed sensing theory supposes that a sparse signal can be sampled at a rate much lower than the Nyquist–Shannon rate and reconstructed with high probability. Such lower sampling rate commonly requires finding a set of the optimal basis functions to sparsely represent the signal first. This paper provides a simple and effective working process to select the basis functions for a family of pulsed radar echoes. The selection process is performed in two steps. First,the waveform matching based on the the known array excitation is carried out to select a mother function from a wavelet dictionary. Second, the spectrum matching principle is used to produce a small set of basis functions from the selected mother function. The proposed method is numerically validated by a pulsed radar system equipped with two different dipole arrays. The results demonstrate that the new method is quite effective. With the selected basis functions, all echoes can be under-sampled at a rate lower than of the conventional Nyquist–Shannon rate and reconstructed with the root mean-squared error of less than .

Keywords:

• compressed sensing
• sparse representation
• wavelet transform
• under-sampling

Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2011X008) and by the National Natural Science Foundation of China (Grant No.61071031 and No.61204041) in part.