SVD image reconstruction in Python

Question

I am trying to do a Singular Value Decomposition of this image:

taking the first 10 values. I have this code:

from PIL import Image
import numpy as np

img = Image.open('bee.jpg')
img = np.mean(img, 2)
U,s,V = np.linalg.svd(img)
recon_img = U @ s[1:10] @ V

but when I run it it throws me this error:

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 9 is different from 819)

So I think I do something wrong when I do the reconstruction. I am not sure of the dimensions of the matrix np.linalg.svd(img) creates. How can I solve?

Sorry for the english

Answer 1

The issue is the dimension of s, if you print the U, s and V dimensions, I get:

print(np.shape(U))
print(np.shape(s))
print(np.shape(V))

(819, 819)
(819,)
(1024, 1024)

So U and V are square matrix, s is an array. You have to create a matrix with the same dimensions of you image (819 x 1024) with s on the main diagonal with this:

n = 10
S = np.zeros(np.shape(img))
for i in range(0, n):
    S[i,i] = s[i]
print(np.shape(S))

output:

(819, 1024)

Then you can proceed with your elaboration. For a comparison, check this code:

from PIL import Image
import numpy as np
import matplotlib.pyplot as plt

img = Image.open('bee.jpg')
img = np.mean(img, 2)

U,s,V = np.linalg.svd(img)

n = 10
S = np.zeros(np.shape(img))
for i in range(0, n):
    S[i,i] = s[i]

recon_img = U @ S @ V

fig, ax = plt.subplots(1, 2)

ax[0].imshow(img)
ax[0].axis('off')
ax[0].set_title('Original')

ax[1].imshow(recon_img)
ax[1].axis('off')
ax[1].set_title(f'Reconstructed n = {n}')

plt.show()

which give me this: