Sparse regularization for reconstructing transient sources with time domain nearfield acoustical holography

Abstract

In this paper, the ℓ1-norm sparse regularization method is applied to the time domain reconstruction of transient acoustic fields such as impulse noise. This method properly reconstructs the back-propagated sound field where its amplitude should be null: for transient sources, this occurs mostly for positions and times that precede the arrival of the first wave front. Therefore, it significantly reduces causal errors typically found in time domain reconstruction when standard Tikhonov regularizations is applied. The reconstructions obtained from both Tikhonov and sparse regularization methods are compared using a transient baffled piston model, and show that the global root-mean-square (RMS) error is significantly reduced when using sparse regularization. The improvement provided depends on the level of sparsity of the reconstructed signal. For the studied cases, it can represent a reduction of the global RMS error by up to a factor of 3. The performance of Pareto frontier curve for predicting the optimal sparse regularization parameter is examined; it leads to accurate predictions especially for lower noise levels. Finally, sparse regularization is applied to experimental data over time and spatial domains in order to obtain an accurate reconstruction of the transient sound field produced by an impacted plate.