A Computational Introduction to Digital Image Processing, 2nd Edition

Image Restoration 213

FIGURE 8.17: An attempt at inverse filtering

2. “Constrained division”: choose a threshold value d, and if |F (i, j)| < d, the original

value is returned instead of a division: Thus:

X(i, j) =











Y (i, j)

F (i, j)

if | F (i, j)| ≥ d,

Y (i, j) if |F (i, j)| < d.

The first method can be implemented by multiplying a Butterworth low pass filter to the

matrix

c1

above:

MATLAB/Octave

>> blf = fftshift(fft2(blur));

>> D = 40

>> bworth2 = 1./(1+(sqrt(2)-1)

*

((x.^2+y.^2)/D^2).^10);

>> blfb = blf./bworth.

*

bworth2;

>> ba = abs(ifft2(blfb));

>> imshow(mat2gray(ba))

or

Python

In : blf = fftshift(fft2(blur))

In : D = 40

In : bworth2 = 1/(1+(sqrt(2)-1)

*

((x

**