computing convolution kernel from smoothed and original image

Question

I need to recover the sigma of a gaussian blur. I have both the original image and the smoothed image.

I tried a deconvolution type approach:

import numpy as np


nz = 141
nx = 681
h = 25

x = [i*h / 1000 for i in range(nx)]
z = [i*h / 1000 for i in range(nz)]

vp_true = np.fromfile("vp_true", np.float32).astype(np.float64).reshape(nz, nx, order='F')
vp_smooth = np.fromfile("vp_smooth", np.float32).astype(np.float64).reshape(nz, nx, order='F')

fft_vp_true = np.fft.fft2(vp_true)
fft_vp_smooth = np.fft.fft2(vp_smooth)

fft_g = np.fft.fftshift(fft_vp_smooth) / np.fft.fftshift(fft_vp_true)
g = np.real(np.fft.fftshift(np.fft.ifft2(np.fft.ifftshift(fft_g))))

fig = plt.figure()
ax = plt.gca()

im = ax.pcolorfast(x, z, g, cmap="jet")
ax.invert_yaxis()
ax.set_aspect('equal')

plt.tight_layout()
plt.savefig("test.pdf")
plt.show()

However, the kernel (g) obtained this way is not Gaussian at all Am I doing something wrong here ?