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Performs low-rank approximation of a given image. We compare two schemes, the higher order singular value decomposition (HOSVD), and the higher orthogonal iteration of tensors (HOOI).

$ python hooi_sample.py filename ratio

The 1st argument is input file. The 2nd argument determines how many ranks will be used for approximation. Consider a Image with the size of (w,h). Then the width will be truncated to be int(w*ratio) and the height to be int(h*ratio).

When the value of ratio is not specified, then 0.2 will be used.

$ python hooi_sample.py uma.jpg  
Ratio = 0.2
Performing HOSVD
0.966415890942
Saved as uma_hosvd.jpg
Performing HOOI
1.29997357769
0.977742274282
0.957462600028
0.953166704329
0.95163785607
0.950901319943
0.950467674764
0.950171911725
0.949946487327
0.949759967973
Saved as uma_hooi.jpg

The numbers denotes the residual. Suppose X is the original tensor and XP is the approximated tensor. Then residula r is defined by r = |X - XP|/|X|, where |X| denotes the Frobenius norm of X. The HOOI shows better performance than the HOSVD.

Input image (Original)

Approximated image (HOSVD, ratio = 0.2, r = 0.966415890942)

Approximated image (HOOI, ratio = 0.2, r = 0.949759967973)