# Denoising Directional Room Impulse Responses with Spatially Anisotropic Late Reverberation Tails
## 5 Results
### Simulated Reverberation Tail  
A fully incoherent reverberation tail is simulated once again using 625 zero-mean Gaussian noise signals, each associated to an incident direction on a corresponding Sloan-Womersley hyperinterpolation grid. To create highly anisotropic conditions, a broadband (frequency-independent) exponential decay envelope is applied to the synthesized signals using cardioid distributions for both the initial power \(P_{0}(\Omega)\) (over a 15-dB dynamic range) and the reverberation time \(T_{60}(\Omega)\) (from 4 s at the maximum of the power distribution to 2 s at its minimum), both centered on \(\Omega=(0^{\circ},0^{\circ})\). Finally, a \(-60\)-dB constant-power noise floor is synthesized over the 625-signal grid and added to the decaying signals. As before, this simulation is encoded to the 4 th-order truncated SHD and then decomposed onto a 25-point Fliege set of look directions by PWD. The spatial energy decay of the resulting PWD-domain signals is shown in Figure 3; the EDCs are calculated individually for each look direction and then projected onto the azimuthal plane by cubic Hermite spherical interpolation [30] in dB scale. The proposed denoising process is then applied in turn to each PWD look direction signal, as described above (Section 4). Note that only steps 5 and 6 of the complete procedure outlined in Section 4.3 are performed here, since, by construction, the simulation is known to be incoherent (furthermore, the SMA measurement is not simulated; the synthesized spatial signals are directly transformed to the SHD). Due to the large difference in dynamic range between the noisy simulated reverberation tail and the result of the denoising procedure (whose arbitrary dynamic range is fixed to match the quantization noise floor for a given bit depth), it is more appropriate to use a spatial energy decay deviation (EDD) [12] to compare the two. The EDD is determined by  
\[\mathrm{EDD}(\Omega_{d},t)=\mathrm{EDC}_{\mathrm{dB}}(\Omega_{d},t)-\overline{ \mathrm{EDC}}_{\mathrm{dB}}(t), \tag{16}\]  
where \(\overline{\mathrm{EDC}}_{\mathrm{dB}}(t)\) is the spatial mean over the dB-scale EDCs of the \(D\) look directions at each time step. Figure 4 shows the EDD (projected once more onto the azimuthal plane by cubic Hermite spherical interpolation) for the simulated late reverberation tail, before (Figure 3(a), corresponding to Figure 2(b)) and after applying the proposed denoising process (Figure 3(b)). Figure 3(a) clearly shows the isotropic noise floor reached around 3 s (in broadband terms), concurring with Figure 2(b). As expected due to the anisotropic conditions created upon synthesis (cardioid distributions for both \(P_{0}(\Omega)\) and \(T_{60}(\Omega)\)), the dynamic range of the denoised EDD (Figure 3(b)) increases as the reverberation tail decays. This provides the first clear evidence that the proposed procedure preserves and correctly extends the spatial features of anisotropic late reverberation. Figure 4: Energy decay deviations (EDD) of (**a**) the simulated noisy late reverberation tail and (**b**) the result of applying the proposed denoising process. EDDs are calculated over PWD look directions and projected onto the azimuthal plane by cubic Hermite spherical interpolation. Figure 3: Reverse-integrated energy decay of the simulated anisotropic late reverberation tail, (**a**) before and (**b**) after the addition of an isotropic nondecaying noise floor. The energy decay curves (EDC) calculated for each PWD look direction are projected onto the azimuthal plane by cubic Hermite spherical interpolation (in dB scale). To examine how well these features correspond to that of the originally simulated reverberation tail, Figure 5 compares the results of the PWD-domain EDR analysis (which parameterize the tail resynthesis in the denoising process) with the target cardioid distributions used in the simulation. Figure 5 thus reveals the impact of the inevitable spatial overlap due to the finite-order PWD on the spatial features of the anisotropic reverberation tail.