# Denoising Directional Room Impulse Responses with Spatially Anisotropic Late Reverberation Tails
## 5 Results
### Simulated Reverberation Tail
More specifically, it appears that spatial anisotropy in the reverberation time \(T_{60}\) is less well retained than in the initial spectrum \(P_{0}\); the analyzed \(T_{60}\) range is only 40.1% of its target range (49% for a 7 th-order analysis), while this goes up to 67.1% for \(P_{0}\) (78.7% for 7 th-order). However, the mean relative errors (17.2% for \(T_{60}\) and 15.9% for \(P_{0}\) at 4 th-order; 13.6% and 8.45%, respectively, at 7 th-order, averaged over the 25 analyzed look directions) are comparable, although the \(P_{0}\) analysis sees greater improvement with increased order. Furthermore, comparisons between the \(P_{0}\) in dB and the \(T_{60}\) in seconds are not necessarily straightforward. Indeed, any evaluation of the reconstruction of spatial variations in these parameters must take into account the secondary lobe behavior of the finite-order PWD's directivity, especially with respect to the cardioid configuration used in this simulation. The most important secondary lobe in \(w_{d}(\Omega)\) is the \"back\" lobe, centered 180\({}^{\circ}\) opposite the look direction \(\Omega_{d}\) (see Figure 1; the back lobe peaks at around \(-14\) dB). For a look direction pointing near the \"back\" of the cardioid distribution used for \(P_{0}\) and \(T_{60}\), i.e., \(\Omega_{d}=(\pm 180^{\circ},0^{\circ})\), where both \(P_{0}(\Omega)\) and \(T_{60}(\Omega)\) are at their respective minima, the signal contribution from the back lobe located near \(\Omega=(0^{\circ},0^{\circ})\), where \(P_{0}(\Omega)\) and \(T_{60}(\Omega)\) at their respective maxima will become increasingly important, and very quickly even more so than that from the main lobe (since the latter will be decaying faster and from a lower starting power). If such is the case, the use of a beamformer optimized to reduce contributions from the back lobes instead of the \"natural\" PWD weighting used so far (\(\alpha_{l}=1\)\(\forall\)\(l\in[0,L]\)) should help remedy this problem. The maximum front-to-back ratio (MFB) beamformer [31] is designed precisely through such an optimization, at the cost of an increased main lobe width. Figure 6 shows the analysis results obtained using a 4 th-order MFB beamformer, compared to the 4 th-order natural PWD and the synthesized cardioid distributions. The relative errors for \(P_{0}\) and \(T_{60}\) fall to 15.3% and 13.3%, respectively, and it is qualitatively clear that the distributions' shapes are more closely matched. Figure 5: Comparison of broadband energy decay relief (EDR) analysis results for (**a**) the initial spectrum \(P_{0}\) and (**b**) the reverberation time \(T_{60}\) (red dashed and blue dash-dot lines for 4 th-order and 7 th-order analyses, respectively), with respect to the cardioid distributions used to synthesize the simulation (black solid lines). Projection onto azimuthal plane by spherical interpolation; radii represent (**a**) dB and (**b**) seconds. Unfortunately, the MFB beamformer cannot be used directly as-is for denoising anisotropic DRIRs, as the increased overlap between adjacent main lobes heavily affects the independence of the beamformed signals and therefore the overall spatial incoherence (\(\Gamma_{\text{iso}}=0.469\) and \(\Gamma_{\text{aniso}}=0.442\)). However, the results of Figure 6 suggest that a specific beamformer optimization constrained with respect to both the maximum independent coverage criteria elaborated in Section 3 as well as the front-to-back ratio may be able to increase the spatial accuracy of the EDR analysis while maintaining high incoherence between signals. Simultaneous optimization of the \(D\) look directions' arrangement over the sphere may also be possible.