An application of multi-scale directional dictionaries to RIR interpolation

The spatio-temporal sparsity of room impulse responses (RIRs) degrades in the late part due to the stronger wave interference compared with the early part. Meanwhile, such an interference decays in amplitude as time progresses due to absorption in the room, resulting in a decreasing dynamic range of the measurement. Together these aspects pose challenging conditions for compressive sensing applications, such as the interpolation of RIRs measured at sparse microphone positions. In the search of sparse transformation spaces, this paper examines the application of a multi-scale directional dictionary (known as shearlets) to interpolate RIR measurements. These redundant dictionaries consist of multiple curved elementary functions, which offer a decomposition of the acoustic wavefronts into various wavelengths, propagation directions, and times of arrival. Results reported in this paper demonstrate the potential these dictionaries have to interpolate RIRs in both convex and nonconvex rooms, motivating further examination under experimental conditions and in broader frequency ranges.QC 20210914