the rate of noise presented in images I suppose that an image is affected by a multiplicative noise (or additive noise and etc.). I want to quantify and measure the rate of noise (for exemple 1%, 2%, ...,25%) present in an image. I used the snr and psnr but they give me the values measured in dB ​​(decibel). Also, how can I implement this in MATLAB?

Can I use the mse or the average between the noisy image and the original image mean?

After the answer of Mr. Tolga Birdal, I put the following code in matlab:

I=rgb2gray(imread('lena.png'));
J=imnoise(I,'speckle', 0.1); % 0.1 is the variance of the noise 
Sigma1 = estimate_noise(I) 


Its give to me : 


  Sigma1 = 6.9360


Sigma2= estimate_noise(J)


and   


  Sigma2= 10.1409


this mean that the level of noise present in the image J equals to 10.14 % ?
You could check out my MATLAB function, which estimates the variance of the noise. It is also mentioned in a Mathworks blog post, in comparison with other methods.

Regarding $\sigma$, you mention in the question, simple answer is yes, longer answer is no. It refers to the variance of the noise normalized with image dimensions as follows:

$$\sigma = \frac{\sigma_0\sqrt{0.5\pi}}{6(W-2)(H-2)}$$

$-2$ is due to the convolution kernel, applied previously. However, this is not a final quantity, giving you the absolute noise level. Nevertheless, for the variance, you could use it as a percentage, just like you mentioned.