# How to Estimated the Noise Standard Deviation (STD - $\sigma$) as a Function of Brightness from an Image?

Hi I don't know where to start from.

I'm trying to implement a plot of noise with MATLAB.

I have found a plot of noise standard deviation sigma vs. brightness from a images in the blog post - Profiling Sensor and Photon Noise.

But I think I need to some reference to implement profiling as above.

I also encountered the following reference - Noise Estimation from a Single Image.

How to make a plot of noise standard deviation sigma vs. brightness from a images?

I didn't read the article you referred to but I can try giving you some idea.

Run along the image for each pixel consider its 9 x 9 neighborhood.
For each pixel's neighbor hood calculate the STD and the Mean.

Use the Mean as the brightness value.
Plot the STD as a function of the mean value.

Some ideas for improvement:

• Set the neighborhood size in an adaptive manner to only include data from the same brightness level.
• For patches with the same value, aggregate the STD and average it.
• Sir, I have one more query about the noise curve. I think your way is real measure method. But I also need to estimation noise curve not measure noise curve. Typically, the paper have presented with both curves. Estimated curve on measure curve – gmotree Apr 30 '15 at 3:58
• I don't understand the observation you make. What I described can be a pretty good estimate of the curve. – Royi Apr 30 '15 at 10:28
• I think that are not estimate because that are using the real image with noise. Also that equation used with the real image. Then let me ask you thing what do you think the difference between black line curve and dots and r,g,b line curve? – gmotree May 1 '15 at 3:48
• Sir, I have read MLE maximum likelihood estimation to use denoise. But I can't quite a catch the concetp to use denoise. If you know why we use MLE, would you please let me know? – gmotree May 18 '15 at 5:19
• Sorry, but I didn't understand your question. The MLE is a method for creating an estimator. Do you want to estimate the noise STD or the the Denoised Image? You can use the estimated noise std as a parameter in a denoising algorithms. – Royi May 19 '15 at 5:58