Question

As part of a digital image processing class, we have been assigned the Inverse Filter for image restoration. I’m using numpy. The variable names below try to follow the names in Digital Image Processing Gonzalez+Woods, 3e.

A zoom of the original image.
.

Gaussian kernel “zz.tif” same size as original image.

Zoom of the gaussian smoothed image with no noise added

f = imtools.load_image( sys.argv[1], mode="L", dtype="float" )
zz = imtools.load_image( "zz.tif", mode="L", dtype="float" )

F = np.fft.fft2( f )
F2 = np.fft.fftshift( F )

# normalize to [0,1]
H = zz/255.

# calculate the damaged image
G = H * F2

# Inverse Filter 
F_hat = G / H

# cheat? replace division by zero (NaN) with zeroes
a = np.nan_to_num(F_hat)
f_hat = np.fft.ifft2( np.fft.ifftshift(a) )

imtools.save_image( np.abs(f_hat), "out.tif" )

imtools is just my wrapper using PIL+numpy to load/store images. (Can post that src, too.)

Zoom of the inverse filtered image.

Am I calculating the Inverse Filter correctly? Am I using numpy correctly?

Is the ringing in the final image expected or am I doing something wrong?

Answer 1

Generally, yes you seem to be doing things correctly, as far as I know.

The ringing is due to an overly “sharp” high pass filter, but that’s what the method you’re using does.

However, you might consider using numpy.fft.rfft2 (“real fft”) and numpy.fft.irfft2 instead of numpy.fft.fft2 and numpy.fft.ifft2 because you’re dealing purely with real values. It should be slightly faster.