# Big-Delay Estimation for Speech Separation in Assisted Living Environments
## 6 Discussion and Future Work  
This paper introduced a reformulation of the AdRess demixing technique, an extension of the classical DUET algorithm. AdRess was developed for the pan-pot mixing model to address target speaker recovery in anechoic, competing speaker scenarios characterized by relative attenuations and delays. A stereo mixture provides spatial cues that help identify a signal propagating from a specific direction. Using this information, we proposed the use of a remote microphone to isolate the speaker of interest and directed the separated audio to a smart HA, enhancing speech accessibility for individuals with hearing impairments. The main contribution of this paper lies in extending two source demixing algorithms--DUET and AdRess--by incorporating a large relative delay estimation technique called the Elevatogram, which was introduced in [5], with the derived TF masks. The masks developed used both spectral and spatial information and can function in anechoic scenarios. The two proposed techniques, Elevato-DUET and Elevato-AdRess, outperformed the benchmark techniques in scenarios where the speech source suffers large relative delays. In the experiments, the speech utterances were mixed in anechoic model with different attenuation and relative delays. Care was taken to ensure distinct spatial signatures--relative attenuations and delays--for each source, minimizing proximity effects that could hinder separation performance. In both proposed TF-masks, the spectral cue depends on the spatial cue. The step concerning accurate delay subtraction helped us to localize the spectral energy of the target source on the frequency--azimuth plane. It is essential to estimate the relative delay accurately for the proposed techniques to function. Inaccurate spatial cues will localize the spectral energies at erroneous positions on the gain axis in Figure 3a. In Elevato-DUET, it is important to maintain the quality of the TF mask. Unlike Elevato-AdRess, which focuses solely on localizing the IID cues of the target speaker, Elevato-DUET requires estimating the attenuation-delay pairs for all constituent sources. The TF mask, in Equation (37), is then computed by iterating over these pairs to derive the best mask to isolate the target source. As demonstrated in [9], the failure to find a good mask results in lower separation quality. In short, these results underline the importance of accurate relative delay estimation, when the separation between sensors is large in AL  
Figure 8: The intelligibilty of the demixed speech recovered by DUET, Elevato-DUET and Elevato-AdRess is quantified. The IBM is used as the benchmark technique. Sources experience a relative delay of 120 samples and the sampling rate of \(F_{s}=16\) kHz. The results for the NarrowBand (NB) MOS are given on the LHS. The NB MOS-Listening Quality Objective (LQO) results are given in the center. The WideBand (WB) MOS-LQO scores of the separated utterances are given on the RHS. Elevato-AdRess improves speech intelligibility in comparison with Elevato-DUET and the IBM. It achieves higher MOS and LQQ scores in both the NB and WB evaluations. environments, and provide additional evidence that the Elevatogram [5] provides accurate large relative delay estimates. In summary, in terms of speech separation quality, as measured by BSS_Eval metrics (SDR, SAR, and SIR) and PEASS scores (OPS, TPS, IPS, and APS), as well as intelligibility quality assessed by PESQ, Elevato-AdRess demonstrated superior performance compared to Elevato-DUET. The Elevato-AdRess technique focuses on isolating the components of the frequency-azimuth matrix, where the IID spectral cues of the target speaker are localized under the constraint that discrete frequencies must be non-overlapping. TF-bins where the spectral energies overlap on the frequency-azimuth plane, in Figure 3c, are excluded during the extraction process, leading to a loss of information that significantly introduces distortion that affects the SDR and SNR scores of recovered speech utterances.