How to convert multiplicative noise into additive white guassian noise ?

How to convert multiplicative noise into additive white guassian noise ? using the log transformation. plz give matlab code of it.

Answer 1

[Parag]

Hi, to convert multiplicative noise into additive white Gaussian noise (AWGN) using log transformation, you can follow these steps:

1. Apply log transformation: Convert the multiplicative noise model Y=X⋅N into an additive model by taking the natural logarithm:

log(Y)=log(X)+log(N)

Since log(N) can be approximated as Gaussian for small variations, it becomes an additive noise model.

2. Apply inverse transformation: To retrieve the original data, use the exponential function.

You can refer the following MATLAB code for the same.

% Generate a clean image (Example: grayscale image with values in [0,1]) 
X = im2double(imread('cameraman.tif')); % Read and normalize image 

% Define multiplicative noise parameters 
sigma = 0.2; % Noise standard deviation 
N = exp(sigma * randn(size(X))); % Multiplicative noise (log-normal distribution) 

% Apply multiplicative noise 
Y = X .* N;  

% Convert to additive noise model using log transformation 
log_Y = log(Y + eps);  % eps avoids log(0) 
log_X = log(X + eps); 
AWGN = log_Y - log_X;  % Extract additive Gaussian noise 

% Display results 
figure; 
subplot(1,3,1); imshow(X, []); title('Original Image'); 
subplot(1,3,2); imshow(Y, []); title('Image with Multiplicative Noise'); 
subplot(1,3,3); imshow(AWGN, []); title('Extracted Additive Noise'); 

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% If needed, reconstruct the image 
reconstructed_X = exp(log_Y - AWGN); 
figure; imshow(reconstructed_X, []); title('Reconstructed Image');