TFR Reconstruction From Incomplete m-D Signal via Adaptive Hadamard Product Parametrization

In micromotion signature analysis, the radar return signal with missing sampling may cause defocused time–frequency representation (TFR) and thus prevent micromotion characteristics acquisition. To address the issue, we present an adaptive time–frequency distribution reconstruction method based on $L_{1}$ regularization. First, the $L_{1}$ regularization is expressed as a combination of two $L_{2}$ regularizations based on Hadamard product parametrization. Then, the iterated Tikhonov regularization is applied to solve each $L_{2}$ regularization alternatively. Moreover, the regularization parameter is updated adaptively based on the matching pursuit principle at each iteration. Finally, the reconstructed TFR is updated based on least-square-error criterion to eliminate the attenuation of signal amplitude. Simulation and measurement data examples have demonstrated the effectiveness of the method.