Add white-noise on image based on SNR

Question

I would like to add white noise to an original image with different SNR levels, but not sure how to do.

The original image is (256, 128) I am using acoustics package to add noise.

original = cv2.imread(path)
white = acoustics.generator.white(256*128).reshape(256, 128)
out = original + white*255

cv2.imwrite(path, out)

My questions:

1. Does log10(mean(original)/ std(original + white*255)) count as SNR?(according to wiki)

2. If so, can I just modify *255 this number to modify SNR?

3. If not, how can I calculate the SNR value?

Answer 1

The key fact is that (this is maths, not code)

SNR = mean(s) / std(n)

Multiplying the noise by some constant A results in a new SNR -- SNR_new

mean(s) / std(A*n) 
= mean(s) / (A * std(n)) 
= (1 / A) * (mean(s) / std(n)) 
= SNR / A
= SNR_new

So working backwards, I think this is the correct approach in python is:

def add_noise(signal, snr):
    ''' 
    signal: np.ndarray
    snr: float

    returns -> np.ndarray
    '''

    # Generate the noise as you did
    noise = acoustics.generator.white(signal.size).reshape(*signal.shape)
    # For the record I think np.random.random does exactly the same thing

    # work out the current SNR
    current_snr = np.mean(signal) / np.std(noise)

    # scale the noise by the snr ratios (smaller noise <=> larger snr)
    noise *= (current_snr / snr)

    # return the new signal with noise
    return signal + noise