通过对数变换将乘性噪声变为加性噪声

Question

In this paper , logarithmic transformation is offered to convert multiplicative noise in an image to additive noise before applying other filters.

logR(x,y) = log[O(x,y)×M(x,y)] = log{O(x,y)} + log{M(x,y)} = L(x,y) + S(x,y)

where F(x,y), L(x,y) and S(x,y) are the logarithms of R(x,y), O(x,y), and M(x,y), respectively.

However, I am confused about whether they just meant applying log transformation to the speckled image like below:

img_log = (np.log(img+1)/(np.log(1+np.max(img))))*255

Thanks in advance.

Answer 1

log(img+1) is not the same as log(img) . Follow the equation you got. If a pixel is 0, then log(img) will be -infinity for that pixel. This is OK:

0 * noise = 0 ==> -infinity + log(noise) = -infinity

If you add 1, you break the concept.

Also, no, you don't need to scale the result of the logarithm. log(img) should be a floating-point image, don't try to do complex arithmetic with integers. After filtering and back-transformation through exp(.) , you should have an image that is in the 0-255 range again, and can be converted to uint8, displayed, and/or saved like a regular image.