Removing Gaussian noise from an image (method comparison)

Can someone give me a steer on the best way to remove random speckle from a monochrome image?
I have a series of 16-bit monochrome images which show the pattern of light uniformity on a flat surface at different wavelengths. The images are stored in a 3-d array such that the first two dimensions (row, column) are the image pixel values and the third dimension (‘page’) is the wavelength value.
The images are ‘noisy’. That is, if you chose a page of the array and plotted its 2-d surface, it would not be smooth but show small peaks and troughs either side of a mean value at every pixel location. I want to smooth out these peaks and troughs.
The imgaussfilt function applies a Gaussian smoothing filter to images. There is also a method using the polyfitn function on file exchange. What is the difference in outcome between these approaches?
I tried comparing the two using the code below (my histogram comparison method is crude!). Visually, method 2 looks best but I don’t know whether it’s a fair test. Also, I can select the polyfitn polynomial order that works best only when I know the original noise-less signal. How should I select the order when the signal is unknown?
%Make up 3 dummy test images 64 x 80
rows = 64;
columns = 80;
y=1:rows;
x=1:columns;
x1=(2-exp(x./1000)).*50000;
y1= 1 – (y.*0.008-0.4).^2; % profile at wavelength 1
y2= 1 – (y.*0.009-0.4).^2; % profile at wavelength 2
y3= 1 – (y.*0.01-0.4).^2; % profile at wavelength 3
y1=y1′;y2=y2′;y3=y3′;
zSignal= cat (3, y1*x1, y2*x1, y3*x1);

% Add some noise to images
z= zSignal + 350.*rand(rows,columns,3); % randn more realistic?
z= round(z); %

% SMOOTHING METHOD 1 (Try blurring the image on page 1)
image1 = uint16(squeeze(z(:,:,1))); % create the dummy image
zBlur = double(imgaussfilt(image1,2));
figure;
histogram (zBlur-zSignal(:,:,1)); % check for absolute error #1

%SMOOTHING METHOD 2 (Create a model zPred for each page)
% (with thanks to ImageAnalyst)
zPred = zeros (64,80,3);
[X,Y] = meshgrid(1:columns, 1:rows);
x1d = reshape(X, numel(X), 1);
y1d = reshape(Y, numel(Y), 1);
zPred = zeros (64,80,3);
for page = 1:3
image = uint16(squeeze(z(:,:,page))); % create the dummy image
z1d = double(reshape(image, numel(image), 1));
polynomialOrder = 4;
p = polyfitn([x1d y1d], z1d, polynomialOrder);
zg = polyvaln(p, [x1d y1d]);
zPred(:,:,page) = reshape(zg, [rows columns]);
end
figure;
histogram (zPred(:,:,1)-zSignal(:,:,1)); % check for error #2
return;Can someone give me a steer on the best way to remove random speckle from a monochrome image?
I have a series of 16-bit monochrome images which show the pattern of light uniformity on a flat surface at different wavelengths. The images are stored in a 3-d array such that the first two dimensions (row, column) are the image pixel values and the third dimension (‘page’) is the wavelength value.
The images are ‘noisy’. That is, if you chose a page of the array and plotted its 2-d surface, it would not be smooth but show small peaks and troughs either side of a mean value at every pixel location. I want to smooth out these peaks and troughs.
The imgaussfilt function applies a Gaussian smoothing filter to images. There is also a method using the polyfitn function on file exchange. What is the difference in outcome between these approaches?
I tried comparing the two using the code below (my histogram comparison method is crude!). Visually, method 2 looks best but I don’t know whether it’s a fair test. Also, I can select the polyfitn polynomial order that works best only when I know the original noise-less signal. How should I select the order when the signal is unknown?
%Make up 3 dummy test images 64 x 80
rows = 64;
columns = 80;
y=1:rows;
x=1:columns;
x1=(2-exp(x./1000)).*50000;
y1= 1 – (y.*0.008-0.4).^2; % profile at wavelength 1
y2= 1 – (y.*0.009-0.4).^2; % profile at wavelength 2
y3= 1 – (y.*0.01-0.4).^2; % profile at wavelength 3
y1=y1′;y2=y2′;y3=y3′;
zSignal= cat (3, y1*x1, y2*x1, y3*x1);

% Add some noise to images
z= zSignal + 350.*rand(rows,columns,3); % randn more realistic?
z= round(z); %

%SMOOTHING METHOD 2 (Create a model zPred for each page)
% (with thanks to ImageAnalyst)
zPred = zeros (64,80,3);
[X,Y] = meshgrid(1:columns, 1:rows);
x1d = reshape(X, numel(X), 1);
y1d = reshape(Y, numel(Y), 1);
zPred = zeros (64,80,3);
for page = 1:3
image = uint16(squeeze(z(:,:,page))); % create the dummy image
z1d = double(reshape(image, numel(image), 1));
polynomialOrder = 4;
p = polyfitn([x1d y1d], z1d, polynomialOrder);
zg = polyvaln(p, [x1d y1d]);
zPred(:,:,page) = reshape(zg, [rows columns]);
end
figure;
histogram (zPred(:,:,1)-zSignal(:,:,1)); % check for error #2
return; Can someone give me a steer on the best way to remove random speckle from a monochrome image?
I have a series of 16-bit monochrome images which show the pattern of light uniformity on a flat surface at different wavelengths. The images are stored in a 3-d array such that the first two dimensions (row, column) are the image pixel values and the third dimension (‘page’) is the wavelength value.
The images are ‘noisy’. That is, if you chose a page of the array and plotted its 2-d surface, it would not be smooth but show small peaks and troughs either side of a mean value at every pixel location. I want to smooth out these peaks and troughs.
The imgaussfilt function applies a Gaussian smoothing filter to images. There is also a method using the polyfitn function on file exchange. What is the difference in outcome between these approaches?
I tried comparing the two using the code below (my histogram comparison method is crude!). Visually, method 2 looks best but I don’t know whether it’s a fair test. Also, I can select the polyfitn polynomial order that works best only when I know the original noise-less signal. How should I select the order when the signal is unknown?
%Make up 3 dummy test images 64 x 80
rows = 64;
columns = 80;
y=1:rows;
x=1:columns;
x1=(2-exp(x./1000)).*50000;
y1= 1 – (y.*0.008-0.4).^2; % profile at wavelength 1
y2= 1 – (y.*0.009-0.4).^2; % profile at wavelength 2
y3= 1 – (y.*0.01-0.4).^2; % profile at wavelength 3
y1=y1′;y2=y2′;y3=y3′;
zSignal= cat (3, y1*x1, y2*x1, y3*x1);

% Add some noise to images
z= zSignal + 350.*rand(rows,columns,3); % randn more realistic?
z= round(z); %

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