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Image Restoration Techniques: Gaussian and Wiener Filtering in MATLAB

This document provides an in-depth examination of image restoration methods utilizing Gaussian and Wiener filters. It includes MATLAB implementations for generating Gaussian functions, simulating image damage through noise, and applying inverse and Wiener filtering for restoration. The techniques are demonstrated with specific Gaussian parameters and Signal-to-Noise Ratio (SNR) adjustments. Key results are shown for cases involving motion blur and defocus blur, illustrating the efficacy of these filtering approaches in improving image quality.

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Image Restoration Techniques: Gaussian and Wiener Filtering in MATLAB

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  1. ROZ2 – cvičení 2 Image restoration - výsledky

  2. Maska gaussiánu function h = gauss(N, sigma) PI = 4*atan(1); npul = (N-1)/2; [x,y] = meshgrid(-1*npul:npul); h = 1/(2*PI*sigma^2) * exp(-1*(x.^2 + y.^2)/(2*sigma^2)); h = h / sum(h(:)); gauss(11,5) gauss(21,7)

  3. Poškození obrázku function g = poskod(f, h, SNR) g1 = conv2(f, h); MinI = min(g1(:)); MaxI = max(g1(:)); var_f = var(f(:)); var_n = var_f / 10^(SNR / 10); g = g1 + var_n*randn(size(g1)); g(g<MinI) = MinI; g(g>MaxI) = MaxI;

  4. Výsledky gauss(11,3) gauss(21,7) BSNR 1/0 60 50

  5. Inverzní filtr SNR 200 150 function f = inverz(g, h) G = fft2(g); H = fft2(h, size(g,1), size(g,2)); F = G ./ H; f = ifft2(F); 120 130 140

  6. Wienerův filtr Gauss(11,3) SNR 60 function f = wiener(g, h, konst) G = fft2(g); H = fft2(h, size(g,1), size(g,2)); R = conj(H) ./ (abs(H).^2 + konst); F = R .* G; f = ifft2(F); konst 0,1 0,01 0,001 0,0001

  7. Rozmazání pohybem h = ones(1,10);

  8. Rozmazání pohybem m1 = log(abs(fft2(f).^2)); m2 = real(fft2(m1)); mi = min(m2(:)); m3 = m2 < 0.9*mi; m3 m1 fftshift+výřez

  9. Rozmazání defokusací h =kruh(20,10);

  10. Rozmazání defokusací m1 = log(abs(fft2(f).^2)); m2 = real(fft2(m1)); mi = min(m2(:)); m3 = m2 < 0.9*mi; fftshift(m3) fftshift(m1)

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