发表机构
organization= Independent researcher , city= Lille , country= France
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对单通道分离的时频掩蔽，分析其几何上限，通过 MUSDB18 实验发现非圆高斯混合先验下的后验均值比逐帧上限低 11.44 dB，且障碍源于准则而非先验。
AI 中文摘要
大多数单通道分离器通过对每个时频 bin 中的混合信号施加实增益来估计源信号。该格式的最优解（作为界限的神谕掩蔽无法达到）是源信号在混合信号张成直线上的正交投影，其残差由两者之间的夹角决定。定位估计器可简化为堆叠频谱上实线性算子的块结构，形成四个嵌套类的链，其中三个较大的类对应三个先验假设：零均值、圆度和无频间耦合。该链保持固定时是四个正交投影的级联；逐帧重新拟合时，它会坍缩到第一项，将整个残差归因于每个 bin 中缺失的一个实参数，即相位。当相位后验关于混合信号方向对称时，最小均方估计会回到该直线，增益为神谕增益的后验均值，超额误差为其方差。在 MUSDB18 数据集上，非圆高斯混合先验下的后验均值虽仍处于该类中，但比逐帧上限低 11.44 dB，且四倍多的分量和 7.5 倍的数据量也无法缩小该差距；一个闭式门控在分贝尺度上将约 70% 的差距归因于预测方差。最宽的固定类比同一上限低 6.70 dB。处于该类中与最小化平方误差是相互冲突的需求：障碍在于准则而非先验。
英文摘要
Most single-channel separators estimate a source by applying a real gain to the mixture in each time-frequency bin. The optimum of that format, which the oracle masks used as bounds do not attain, is the orthogonal projection of the source onto the line spanned by the mixture, its residual set by the angle between them. Locating an estimator reduces to the block structure of a real-linear operator on stacked spectra, giving a chain of four nested classes whose three larger terms match three assumptions on the prior: zero means, circularity and absence of inter-frequency coupling. Held fixed the chain is a cascade of four orthogonal projections; refitted per frame it collapses onto its first term, attributing the whole residual to one missing real parameter per bin, the phase. When the phase posterior is symmetric about the mixture direction, the minimum mean-square estimate falls back onto the line, with gain the posterior mean of the oracle gain and excess error its variance. On MUSDB18 a posterior mean under a non-circular Gaussian-mixture prior leaves the class yet stays 11.44 dB under the per-frame ceiling, which four times as many components and 7.5x the data do not close; a closed-form gate attributes some 70% of it, in decibels, to the predicted variance. The widest fixed class stays 6.70 dB under the same ceiling. Leaving the class and minimising squared error are conflicting requests: the barrier lies in the criterion rather than in the prior.
CommentsSubmitted to Digital Signal Processing (Elsevier), manuscript DSP-S-26-06261. 33 pages, 6 figures. Companion paper: What Selects, What Reconstructs (submitted to IEEE/ACM TASLP)
