Source sparsity control of sound field reproduction using the elastic-net and the lasso minimizers

Sound field reproduction is aimed at the reconstruction of a sound pressure field in an extended area using dense loudspeaker arrays. In some circumstances, sound field reproduction is targeted at the reproduction of a sound field captured using microphone arrays. Although methods and algorithms already exist to convert microphone array recordings to loudspeaker array signals, one remaining research question is how to control the spatial sparsity in the resulting loudspeaker array signals and what would be the resulting practical advantages. Sparsity is an interesting feature for spatial audio since it can drastically reduce the number of concurrently active reproduction sources and, therefore, increase the spatial contrast of the solution at the expense of a difference between the target and reproduced sound fields. In this paper, the application of the elastic-net cost function to sound field reproduction is compared to the lasso cost function. It is shown that the elastic-net can induce solution sparsity and overcomes limitations of the lasso: The elastic-net solves the non-uniqueness of the lasso solution, induces source clustering in the sparse solution, and provides a smoother solution within the activated source clusters.