Error using .* Integers can only be combined with integers of the same class, or scalar doubles.

clc
clear all
close all

lena = imread('eight.tif');
A = fftshift(fft2(lena));
S = imnoise(lena,'Gaussian',0,1);

% define spatial filters
h_gauss= fspecial('gaussian', 15, 1.0);
% results after spatial filtering
lena_h_gauss = imfilter(S, h_gauss, 'replicate');
% fourier transformed filters
H_gauss = fftshift(fft2(lena_h_gauss));

% filtering in frequency domain
%Lena_H_gauss = S .* H_gauss;
w=  (abs(H_gauss))
size(S)
size(w)
lena_H_gauss = S.* w;
lena_H_gauss = ifft2(ifftshift(lena_H_gauss));
% print results
subplot(3,3,1); imshow(lena); title('Original Image');
subplot(3,3,2); imshow(lena_h_gauss); title('Gauss-Filtered Image');
subplot(3,3,3); imshow(real(log(double(lena))), []);  title('FT (Original Image)');
subplot(3,3,4); imshow(real(log(double(H_gauss))), []); title('FT (Gauss Filter)');
subplot(3,3,5); imshow(lena_H_gauss);  title('Result FT Gauss');

Answer 1

[Image Analyst]

I think this is really what you were trying to do:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 15;

% Get noise-free original gray scale image.
grayImage = imread('eight.tif');
% Get the dimensions of the image.  
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);
% Create noisy image from it.
noisyImage = imnoise(im2double(grayImage), 'Gaussian', 0, 0.01);

% Define spatial filters as a 15x15 window.
gaussianSpatialFilter = fspecial('gaussian', 15, 1.0);
% Do a filter by blurring with a Gaussian kernel in the spatial domain:
spatialDomainFilteredImage = imfilter(noisyImage, gaussianSpatialFilter, 'replicate');
% Display results:
subplot(2, 4, 1); imshow(grayImage, []); title('Original Image', 'FontSize', fontSize); axis on;
subplot(2, 4, 2); imshow(noisyImage, []); title('Noisy Image', 'FontSize', fontSize); axis on;
subplot(2, 4, 3); imshow(gaussianSpatialFilter, []); title('Blur Kernel', 'FontSize', fontSize); axis on;
subplot(2, 4, 4); imshow(spatialDomainFilteredImage, []); title('Image filtered with Gaussian in the spatial domain', 'FontSize', fontSize); axis on;

% Define frequency domain filter the same size as the image.
gaussianFreqFilter = fspecial('gaussian', [rows, columns], 0.2*rows); % Keep the low frequencies.
% gaussianFreqFilter = ones(rows, columns); % Keep all frequencies.

% Fourier transform the noisy image.
freqDomainImage = fftshift(fft2(noisyImage));

% Now do filtering in the frequency domain
filteredFreqDomain = freqDomainImage .* gaussianFreqFilter;
% Now transform back to spatial domain:
spatialImage = real(ifft2(ifftshift(filteredFreqDomain)));

% Display results:
subplot(2, 4, 5); imshow(gaussianFreqFilter, []); title('Freq Domain Filter', 'FontSize', fontSize); axis on;
subplot(2, 4, 6); imshow(log(abs(freqDomainImage)), []); title('Original Freq Domain Image', 'FontSize', fontSize); axis on;
subplot(2, 4, 7); imshow(log(abs(filteredFreqDomain)), []);  title('Filtered Freq Domain Image', 'FontSize', fontSize); axis on;
subplot(2, 4, 8); imshow(spatialImage, []); title('Back in Spatial Domain', 'FontSize', fontSize); axis on;

% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')