# Denoising Directional Room Impulse Responses with Spatially Anisotropic Late Reverberation Tails
## 5 Results
### Application to a Measured DRIR
#### 5.2.2 EDR Analysis and Tail Resynthesis  
Next, the EDR analysis is performed for each look direction individually, as described above. Figure 8 presents the results of this analysis for the initial spectrum (\(P_{0}(f,\Omega_{d})\), Figure 8a) and reverberation time (\(T_{60}(f,\Omega_{d})\), Figure 8b), once more projected onto the azimuthal plane by cubic Hermite spherical interpolation. Since real room reverberation has a strong frequency dependence, these results are shown averaged over four octave bands in the SMA's optimal frequency range (the spatial aliasing limit of the mh acoustics Eigenmike(r) is \(f_{a}\simeq 5200\) Hz with a radius of 4.2 cm, and the directivity of the 4 th-order PWD is essentially omnidirectional under 325 Hz).  
Figure 8 suggests that the anisotropy of this particular DRIR stems from its initial spectrum \(P_{0}(f,\Omega_{d})\). However, it must be noted that any acoustical interpretation of such anisotropic analysis results will necessitate developments in stochastic reverberation modeling beyond the scope of this discussion. In the anisotropic case, contrary to classical diffuse reverberation theory, the quantities \(P_{0}(f)\) and \(T_{60}(f)\) cannot be considered independent either of each other or of the source and receiver positions in the room. As such, it is currently unclear which acoustical factors affect the anisotropy  
Figure 7: Spatial incoherence analysis for the DRIR measured in the neo-Gothic chapel at the Dominics of Haute-Alsace cultural centre and former convert. Mathematical expectations are estimated by averaging over short-term Fourier transform frames for a total window length of 40 ms. The mixing time \(t_{\text{mix}}\) is estimated algorithmically by identifying the maximum incoherence reached after the period of initial instability due to the arrival of coherent early reflections. Note the gradual increase in incoherence throughout the reverberation tail due to the increasing influence of the background noise floor.  
of these parameters, although the simulation results from Section 5.1 above show that their analysis through a PWD is affected by the lobe overlap of the beamformed signals.  
With such reservations considered, it will be nonetheless interesting to note that while the dynamic range in \(P_{0}\) increases with frequency, from \(9.57\) dB in the \([325,650]\) Hz band to \(15.1\) dB in the \([2600,5200]\) Hz band, the percent difference in \(T_{60}\) (with respect to its maximum value) decreases from \(11.3\%\) in the \([325,650]\) Hz band to only \(3.38\%\) in the \([2600,5200]\) Hz band.  
The spatial structure of this DRIR is shown in Figure 9, before (Figure 9a) and after (Figure 9b) application of the proposed denoising process, through the projection of the EDD onto the azimuthal plane by cubic Hermite spherical interpolation. Figure 9a reveals a slight amount of anisotropy in the nondecaying noise floor, showing that localized noise sources can be detected and removed by this method, as mentioned in Section 4.2. Figure 9b in turn confirms that the proposed procedure preserves the spatial distribution of the anisotropic reverberation tail as it is prolonged and resynthesized to replace the noise floor.  
Figure 8: (**a**) Initial spectrum (\(P_{0}\)) and (**b**) reverberation time (\(T_{60}\)) PWD-domain EDR analysis results for the directional room impulse responses (DRIR) measured in the neo-Gothic chapel at the Dominicans of Haute-Alsace cultural center, averaged over four frequency bands (and once again projected onto the azimuthal plane by cubic Hermite spherical interpolation). Radii represent (**a**) dB and (**b**) seconds.  
Figure 9: EDDs for (**a**) the noisy DRIR measured in the neo-Gothic chapel at the Dominicans of Haute-Alsace cultural centre and (**b**) the result obtained after application of the proposed denoising process. EDDs once again projected onto the azimuthal plane by cubic Hermite spherical interpolation.