Inverse Acoustic Problems under Spatial Uncertainties

Many spatial audio applications, including active noise control, virtual reality, and the generation of individual sound zones, rely on an understanding of acoustic propagation. In room acoustics, which is the focus of this thesis,the sound field generated by a point source is typically modelled as a linear time-invariant system, described by its room impulse response (RIR). The RIR captures the room’s contribution to the source signal at a given receiverposition. To estimate the RIR, an inverse problem is typically solved using both measurements of the sound field and assumptions about the corresponding spatial parameters, such as microphone and source positions, roomgeometry, and temperature. While errors in sound field measurements have been extensively studied, less attention has been given to errors in these spatial assumptions. Typically, the inverse problems are addressed by introducingpriors directly on the amplitudes of the RIR or on the boundary conditions of the room. However, when spatial errors are introduced, the problem is further complicated by the uncertainties in the RIR’s delay structure or inthe positions of the reflectors, respectively. This thesis revisits three inverse acoustic problems for estimating the RIR and develops estimators that are robust to these spatial uncertainties. While the first two papers introducesrobustness to somewhat traditional problem settings, the last contribution illustrates that robustness to this class of errors also allows for incorporating new types of information when solving acoustic inverse problems. Thefirst problem considers the interpolation of an RIR, where estimates of RIRs at nearby microphone positions are available, but errors exist in the assumed microphone positions. The second problem addresses the estimationof a sequence of RIRs from a slowly moving source, where two adjacent RIRs differ only in the source position, given the source and receiver signals. Finally, the third problem considers estimating an RIR from the sourceand receiver signals, assuming that a rough approximation of the room geometry is available. Common for these three methods is the construction of optimal transport distances to introduce robustness for the correspondingerror models. While the optimal transport distance is defined directly on the RIRs in the two latter papers, the first paper instead considers the convex relaxation of an equivalent source model by the means of multi-marginaloptimal transport.