Speaker
Description
Elementary wave models are at the core of microphone array processing and estimation problems in acoustics. Wave models are often formulated in the frequency domain, and the problems solved one frequency at a time. On the other hand, time-domain formulations are often more suitable, as they preserve the signals' spatio-temporal structure (e.g., temporal sparsity of wavefronts), and can utilize information common to all frequencies (e.g., source location). However, their computation is far more demanding. In this study we propose a computational framework to perform plane wave and point source expansions in time domain, which (a) overcomes memory limitations by a matrix-free implementation of the forward and adjoint operators, and (b) is differentiable with respect to wave coefficients, wave directions and source positions. We present results for direction of arrival estimation and source localization, yet our approach can be used in any acoustic application requiring elementary wave expansions. Our implementation supports execution on both CPU and GPU, and it is easily integrated with standard iterative solvers (to solve e.g., least-squares, ridge regression, and lasso problems) as well as in machine learning pipelines.