# Denoising Directional Room Impulse Responses with Spatially Anisotropic Late Reverberation Tails
## 6 Conclusions  
This paper has addressed the problem of removing the nondecaying noise floor from DRIRs measured with an SMA and presented spatially anisotropic yet incoherent late reverberation tails. Building on previous work done in the highly diffuse or spatially isotropic case, it has been shown that the noise floor can be replaced by a resynthesized prolongation of the late reverberation tail following a PWD of the HOA-encoded DRIR into a spatial domain carefully chosen to maximize independent coverage of the sphere. The spatial incoherence of the DRIR can be accurately analyzed in this domain, and its temporal evolution can be used to estimate the mixing time, a crucial step in verifying that the late reverberation tail has become maximally incoherent before reaching the noise floor and can therefore be synthesized as independent zero-mean Gaussian noise signals per look direction, subjected to the exponentially decaying envelope extracted from the DRIR by EDR analysis.  
The proposed method is shown to correctly reconstruct the spatial characteristics of anisotropic late reverberation within the limitations inherent to a finite-order PWD. Further research will attempt to overcome these limitations by optimizing the beamforming characteristics of the PWD with respect to the maximum independent coverage criteria--the front-to-back ratio, which seems to enable more accurate spatial analysis of reverberation properties; and the arrangement of the look directions on the sphere. Any beamforming optimization will additionally have to work within the constraint of having \(D=(L+1)^{2}\) look directions in order for the spatial domain signals to be transformed back into the SHD for posterior applications in HOA spatialization systems, e.g., recreating spatialized reverberation effects by multichannel convolution.  
Finally, the spatial EDR analysis results obtained from measured anisotropic DRIRs highlight the need for further developments in stochastic reverberation modeling. A theoretical basis for the analysis of anisotropic energy decay in enclosed spaces would provide the grounds for a true acoustical interpretation of such results. To this end, a preliminary exploration of the acoustic properties of anisotropic spaces could, for example, make use of the procedures presented in this paper to perform a comprehensive study of multiple source-receiver pairs in a single anisotropic space.  
Conceptualization, P.M. and M.N.; methodology, P.M. and M.N.; software, T.C. and P.M.; validation, M.N., T.C., and O.W.; formal analysis, P.M.; investigation, P.M.; resources, P.M., M.N., T.C., and O.W.; data curation, P.M. and T.C.; writing-original draft preparation, P.M.; writing-review and editing, M.N., T.C., and O.W.; visualization, P.M.; supervision, M.N. and O.W.; project administration, M.N. All authors have read and agreed to the published version of the manuscript.  
This work was funded in part by a doctoral research grant from the Ecole doctorale Informatique, Telecommunications, et Electronique (Paris) at Sorbonne Universite.  
The authors would like to thank [PERSON] (IRCAM) and [PERSON] for providing the DRIR database, measured as part of their IRCAM Artistic Research Residency Program project, as well as [PERSON] (PhD candidate, Aalto University) for his collaborative work on anisotropic reverberation and the EDD.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.