SNR和PSNR之间的差异

我了解到，SNR是信号功率与噪声功率之比。在图像方面，原始图像如何受添加的噪波影响。在PSNR中，我们将图像中峰值的平方（对于8位图像，峰值为255）除以均方误差。SNR和PSNR用于测量重建后的图像质量。我了解到SNR或PSNR越高，重建效果越好。我不了解SNR和PSNR关于重建图像的结论有何不同。

• 图像的PSNR得出什么结论，而同一图像的SNR无法得出结论？
• PSNR的结论与SNR的结论有何不同？

让我们从数学定义开始。

离散信号功率被定义为

$$P_s = \sum_{-\infty}^{\infty}s^2[n] = \left|s[n]\right|^2.$$

我们可以将这个概念噪声一些信号来计算的顶部P w ^以同样的方式。那么信噪比（SNR）就是 P S N R = P $w$$P_w$

$$P_{SNR}=\frac{P_s}{P_w}$$

如果我们收到了一个噪声破坏信号则我们按以下方式计算SNR$x[n] = s[n]+w[n]$

$$P_{SNR}=\frac{P_s}{P_w} = \frac{P_s}{\left|x[n]-s[n]\right|^2}.$$

这里只是原始信号和损坏信号之间的平方误差。请注意，如果我们根据信号中点的数量来缩放功率的定义，那么这将是均方误差（MSE），但是由于我们正在处理功率之比，因此结果保持不变。$\left|x[n]-s[n]\right|^2$

现在让我们解释这个结果。这是信号功率与噪声功率之比。从某种意义上讲，功率是信号的平方规范。它显示了您与零之间的平均平方偏差。

您还应该注意，我们可以通过简单地将图像矢量的行和列相加两次，或者将整个图像扩展为单个像素矢量并应用一维定义，来将这一概念扩展到图像。您会看到，没有任何空间信息被编码为幂的定义。

现在让我们看一下峰值信噪比。这个定义是

$$P_{PSNR}=\frac{\text{max}(s^2[n])}{\text{MSE}}.$$

$P_{SNR}$$P_{PSNR} \ge P_{SNR}$ and that they will only be equal to each other if your original clean signal is constant everywhere, and with maximum amplitude. Notice that although the variance of a constant signal is null, its power is not; the level of such constant signal does make a difference in SNR but not in PSNR.

Now, why does this definition make sense? It makes sense because the case of SNR we're looking at how strong the signal is and to how strong the noise is. We assume that there are no special circumstances. In fact, this definition is adapted directly from the physical definition of electrical power. In case of PSNR, we're interested in signal peak because we can be interested in things like the bandwidth of the signal, or number of bits we need to represent it. This is much more content-specific than pure SNR and can find many reasonable applications, image compression being on of them. Here we're saying that what matters is how well high-intensity regions of the image come through the noise, and we're paying much less attention to how we're performing under low intensity.

Signal to Noise Ratio

It shows the relationship between the real image and estimated image. This ratio indicates how strong the noise corrupted the original image.

Peak Signal to Noise Ratio

在PSNR中，我们对信号峰值感兴趣。这比纯SNR更具内容特定性。在这里，我们说图像的高强度区域如何通过噪声，而对低强度区域的关注却少得多。

SNR适用于强度均匀分布的图像，而psnr适用于强度变化很大的图像。因此，根据情况，我们可以使用其中任何一种。