Trucated SVD of an image

In [67]:

    

from scipy import ndimage
import numpy as np

import matplotlib.pyplot as plt
import seaborn as sns

%matplotlib inline


    

In [68]:

    

cameraman = ndimage.imread('cameraman.bmp')


    

In [77]:

    

plt.figure(figsize=(4, 4))

plt.title('original image: k = {}'.format(min(cameraman.shape)))
plt.imshow(cameraman, cmap='Greys_r')

plt.grid()
plt.show()


    

In [73]:

    

U, S, V = np.linalg.svd(cameraman)

# print the image with increasing numbers of singular values
fig, ax = plt.subplots(2, 4, figsize=(16, 8))

for n, k in enumerate([1, 2, 4, 8, 16, 32, 64, 128]):
    S_trunc = S.copy()
    S_trunc[k:] = 0

    cameraman_trunc = U.dot(np.diag(S_trunc).dot(V))
    axis = ax[n/4, n%4]
    
    axis.set_title('k = {}'.format(k))
    axis.imshow(cameraman_trunc, cmap='Greys_r')
    axis.grid()
    
plt.show()


    

In [76]:

    

plt.figure(figsize=(12, 8))

plt.title('singular value decay')
plt.semilogy(S)

plt.show()


    

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