Reconstruction of articulatory measurements with smoothed low-rank matrix completion

Articulatory measurements have been used in a variety of speech science and technology applications. These measurements can be obtained with a number of technologies, such as electromagnetic articulography and X-ray microbeam, typically involving pellets attached to individual articulators. Due to limitations in the recording technologies, articulatory measurements often contain missing data when individual pellets are mis-tracked, leading to relatively high rates of loss in this expensive and time-consuming data source. We present an approach to reconstructing such data, using low-rank matrix factorization techniques combined with temporal smoothness regularization, and apply it to reconstructing the missing entries in the Wisconsin X-ray microbeam database. Our algorithm alternates between two simple steps, each having a closed form as the solution of a linear system. The algorithm gives realistic reconstructions even when a majority of the frames contain missing data, improving over previous approaches to this problem in terms of both root mean squared error and phonetic recognition performance when using the reconstructions.