Sparse reconstruction of overpressure field for aerial explosive shock wave based on weighted total variation combined group sparse regularization

An ill-posed analysis matrix exhibits pathological sparsity owing to the limited number of shockwave test nodes. In this paper, we propose a weighted total variation combined group sparse regularization method to reconstruct an invertible wave overpressure field. In order to better preserve image edge information, a weighted total variation method is utilized to process the image gradients by setting learnable parameters associated with the structure of the data space. Subsequently, a group sparse representation method, which is based on low-rank constraints using block-matching, is employed to achieve similarity among the non-local sub-blocks of the shock wave data to preserve the subtle details of the image. Lastly, the propose model is optimized through the alternating direction of the multipliers with alternating iterations. We also conduct simulations and field experiments to demonstrate the proposed method, where the reconstruction error of the entire area is reduced to approximately 13.5 % compared with existing methods.