Regularized smoothed ℓ⁰ norm algorithm and its application to CS-based radar imaging

Sparse signal recovery is attractive in compressed sensing (CS). Based on the smoothed ℓ⁰ norm (SL0) algorithm, we have developed an error-tolerant regularized SL0 (ReSL0) algorithm, which has the same computational advantages as the SL0 algorithm while having better immunity against inaccuracy caused by noise or model mismatch. The performance of the ReSL0 is evaluated with simulated data. In addition, we have extended the ReSL0 to the matrix form (MReSL0), which is more suitable for dealing with matrix form signals and also has good resilience against inaccuracy. Finally we apply the ReSL0 and MReSL0 to joint CS-based radar imaging and phase error correction. Experimental results from both simulated and real data demonstrate that the proposed algorithms provide remarkable performance improvements in inaccurate scenarios (such as noisy data and mismatched settings) compared with the SL0 algorithm.