【Dual

DPRNN使用的loss函数是 SI-SNR

SI-SNR 是scale-invariant source-to-noise ratio的缩写，中文翻译为尺度不变的信噪比，意思是不受信号变化影响的信噪比

公式

公式如下：
{ s t a r g e t = ⟨ s ^ , s ⟩ s ∣ ∣ s ∣ ∣ 2 e n o i s e = s ^ − s t a r g e t S I S N R = 10 l o g 10 ∣ ∣ s t a r g e t ∣ ∣ 2 ∣ ∣ e n o i s e ∣ ∣ 2 \begin{cases} s_{target} = \cfrac {\lang{\hat s,s}\rangle s} {||s||^2} \\ e_{noise} = \hat s - s_{target} \\ SISNR = 10 log_{10} \cfrac {||s_{target}||^2} {||e_{noise}||^2} \end{cases} ⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧​starget​=∣∣s∣∣2⟨s^,s⟩s​enoise​=s^−starget​SISNR=10log10​∣∣enoise​∣∣2∣∣starget​∣∣2​​

其中 s ^ \hat s s^是评估信号， s s s是纯净信号；
⟨ s ^ , s ⟩ \lang{\hat s,s}\rangle ⟨s^,s⟩是元素乘积再求和运算
∣ ∣ s ∣ ∣ 2 ||s||^2 ∣∣s∣∣2是L2norm(2范数)，它相当于 ⟨ s , s ⟩ \lang{s,s}\rangle ⟨s,s⟩

2范数公式如下 ∣ ∣ x ∣ ∣ 2 = ∑ 0 n x i 2 ||x||_2= \sqrt{ \displaystyle\sum_0^nx_i^2} ∣∣x∣∣2​=0∑n​xi2​ ​，简单地理解它为二维空间所有点到圆心的距离

SNR是纯净信号与噪音的声强的比，而SISNR是通过正则化消减信号变化导致的影响。

在DPRNN源码中，信号s同样做了“特殊处理”，先是将s减去平均值，然后再套用公式计算。

源码如下

def sisnr(x, s, eps=1e-8):"""calculate training lossinput:x: separated signal, N x S tensors: reference signal, N x S tensorReturn:sisnr: N tensor"""def l2norm(mat, keepdim=False):return torch.norm(mat, dim=-1, keepdim=keepdim)if x.shape != s.shape:raise RuntimeError("Dimention mismatch when calculate si-snr, {} vs {}".format(x.shape, s.shape))x_zm = x - torch.mean(x, dim=-1, keepdim=True)s_zm = s - torch.mean(s, dim=-1, keepdim=True)t = torch.sum(x_zm * s_zm, dim=-1,keepdim=True) * s_zm / (l2norm(s_zm, keepdim=True)**2 + eps)return 20 * torch.log10(eps + l2norm(t) / (l2norm(x_zm - t) + eps))

【Dual

DPRNN使用的loss函数是 SI-SNR

SI-SNR 是scale-invariant source-to-noise ratio的缩写，中文翻译为尺度不变的信噪比，意思是不受信号变化影响的信噪比

公式

公式如下：
{ s t a r g e t = ⟨ s ^ , s ⟩ s ∣ ∣ s ∣ ∣ 2 e n o i s e = s ^ − s t a r g e t S I S N R = 10 l o g 10 ∣ ∣ s t a r g e t ∣ ∣ 2 ∣ ∣ e n o i s e ∣ ∣ 2 \begin{cases} s_{target} = \cfrac {\lang{\hat s,s}\rangle s} {||s||^2} \\ e_{noise} = \hat s - s_{target} \\ SISNR = 10 log_{10} \cfrac {||s_{target}||^2} {||e_{noise}||^2} \end{cases} ⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧​starget​=∣∣s∣∣2⟨s^,s⟩s​enoise​=s^−starget​SISNR=10log10​∣∣enoise​∣∣2∣∣starget​∣∣2​​

其中 s ^ \hat s s^是评估信号， s s s是纯净信号；
⟨ s ^ , s ⟩ \lang{\hat s,s}\rangle ⟨s^,s⟩是元素乘积再求和运算
∣ ∣ s ∣ ∣ 2 ||s||^2 ∣∣s∣∣2是L2norm(2范数)，它相当于 ⟨ s , s ⟩ \lang{s,s}\rangle ⟨s,s⟩

2范数公式如下 ∣ ∣ x ∣ ∣ 2 = ∑ 0 n x i 2 ||x||_2= \sqrt{ \displaystyle\sum_0^nx_i^2} ∣∣x∣∣2​=0∑n​xi2​ ​，简单地理解它为二维空间所有点到圆心的距离

SNR是纯净信号与噪音的声强的比，而SISNR是通过正则化消减信号变化导致的影响。

在DPRNN源码中，信号s同样做了“特殊处理”，先是将s减去平均值，然后再套用公式计算。

源码如下

def sisnr(x, s, eps=1e-8):"""calculate training lossinput:x: separated signal, N x S tensors: reference signal, N x S tensorReturn:sisnr: N tensor"""def l2norm(mat, keepdim=False):return torch.norm(mat, dim=-1, keepdim=keepdim)if x.shape != s.shape:raise RuntimeError("Dimention mismatch when calculate si-snr, {} vs {}".format(x.shape, s.shape))x_zm = x - torch.mean(x, dim=-1, keepdim=True)s_zm = s - torch.mean(s, dim=-1, keepdim=True)t = torch.sum(x_zm * s_zm, dim=-1,keepdim=True) * s_zm / (l2norm(s_zm, keepdim=True)**2 + eps)return 20 * torch.log10(eps + l2norm(t) / (l2norm(x_zm - t) + eps))