Compressive high-range-resolution radar imaging using dynamic dictionaries

Compressive sensing theory suggests that accurate reconstruction of a signal can be achieved using its highly undersampled measurements, provided that the signal is sparse in an a priori known dictionary. For the range imaging problem in wideband radar, this dictionary is typically taken to be a DFT basis. However, since practical target scatterers do not lie exactly in the frequency lattice of the discrete Fourier transform (DFT) basis, there is always mismatch between the assumed DFT basis and the actual dictionary for sparsity. To address this, the authors consider the radar echo sparsifying dictionary as refinable and develop a compressive imaging approach using dynamic dictionaries. The approach treats the frequency gridding points as adjustable parameters of the sparsifying Fourier dictionary and achieves dynamical dictionary refinement via iterative optimisation of these parameters. To achieve joint image formation and dictionary refinement, the approach utilises the variational expectation-maximisation algorithm to iteratively perform a two-step process, that is, estimating sparse backscattering coefficients given a dictionary and then updating the dictionary to better fit the data sparsity model. The experimental results based on both synthetic and anechoic chamber data demonstrate that the approach improves the precision in range estimation and suppresses spurious spikes in the constructed profiles.