It is well-known that the performance of the Gaussian Mixture Model (GMM) based Acoustic-to-Articulatory Inversion (AAI) improves by either incorporating smoothness constraint directly in the inversion criterion or smoothing (low-pass filtering) estimated articulator trajectories in a post-processing step, where smoothing is performed independently of the inversion. As the low-pass filtering is independent of inversion, the smoothed articulator trajectory samples no longer remain optimal as per the inversion criterion. In this work, we propose a sparse smoothing technique which constrains the smoothed articulator trajectory to be different from the estimated trajectory only at a sparse subset of samples while simultaneously achieving the required degree of smoothness. Inversion experiments on the articulatory database show that the sparse smoothing achieves an AAI performance similar to that using low-pass filtering but in sparse smoothing ～15% (on average) of the samples in the smoothed articulator trajectory remain identical to those in the estimated articulator trajectory thereby preserve their AAI optimality as opposed to 0% in low-pass filtering.
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