MATLAB Image Denoising: Scale 32x32 Filters to 128x128

Denoising 128x128 Images via Filter Scaling

This technical guide demonstrates how to apply a frequency-domain filter (like a Wiener filter template) originally designed for a 32x32 image onto a 128x128 noisy image using interpolation techniques in MATLAB.

By rescaling the filter, we can apply pre-defined noise reduction characteristics to higher-resolution data, provided we account for coordinate shifting and domain transformations correctly.

Run the Image Processing Simulator

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Step-by-Step Methodology

Step 1: Load or create the noisy image (128x128). We generate a base signal (checkerboard) and add Gaussian noise.

Step 2: Load the Wiener filter coefficients designed for a 32x32 image.

Step 3: Rescale the Wiener filter from 32x32 to 128x128 using bilinear interpolation.

Step 4: Convert the noisy image to the frequency domain using 2D Fast Fourier Transform (FFT2).

Step 5: Convert the scaled filter to the frequency domain. We use ifftshift to ensure the filter origin aligns with the FFT origin.

Step 6: Apply the filter in the frequency domain via element-wise multiplication.

Step 7: Convert the result back to the spatial domain using inverse FFT (IFFT2) and retain the real part.

Step 8: Display the comparative results (Noisy vs. Denoised).

MATLAB Implementation

MATLAB Script

% Step 1: Create a 128x128 test image and add noise
original_image = im2double(checkerboard(16, 4, 4)); 
noisy_image = imnoise(original_image, 'gaussian', 0, 0.01); 

% Step 2: Create filter coefficients (32x32)
filter_32x32 = fspecial('gaussian', [32 32], 2); 

% Step 3: Rescale filter to 128x128 using bilinear interpolation
filter_128x128 = imresize(filter_32x32, [128 128], 'bilinear');

% Step 4: Frequency domain conversion of image
noisy_image_fft = fft2(noisy_image);

% Step 5: Frequency domain conversion of filter
% Centering the filter to prevent image shifting
filter_128x128_fft = fft2(ifftshift(filter_128x128));

% Step 6: Apply the filter (Frequency Domain multiplication)
result_fft = noisy_image_fft .* filter_128x128_fft;

% Step 7: Inverse FFT back to Spatial Domain
denoised_image = real(ifft2(result_fft));

% Step 8: Display results
figure;
subplot(1, 3, 1); imshow(noisy_image, []); title('Noisy Image');
subplot(1, 3, 2); imshow(denoised_image, []); title('Denoised Image');
subplot(1, 3, 3); imshow(filter_128x128, []); title('Wiener Filter Template');

Analysis & Accuracy

To ensure 100% accuracy in the implementation:

Phase Alignment: Using ifftshift before FFT is critical. Without it, the spatial filter is treated as if its peak is at the top-left corner, causing the denoised image to wrap around the edges.
Data Types: Images are converted to double to prevent clipping during FFT calculations.
Domain Logic: The real() function is used after IFFT to remove negligible imaginary components resulting from floating-point errors.

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