1. Singular Value Decompsition The Chinese University of Hong Kong
Math 3360: Mathematical Imaging
Lecture 4:
Singular Value Decompsition
Prof. Ronald Lok Ming Lui Department of Mathematics,
The Chinese University of Hong Kong

2. Recap: Main idea For details, please refer to Supplementary note 2!
Stacking operator
For details, please refer to Supplementary note 2!

3. SVD For details, please refer to Supplementary note 2! SVD
An image can be decomposed as:
For details, please refer to Supplementary note 2!
Eigen-image

4. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image

5. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
The image looks like:

6. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
Consider the eigenvalues of:
Eigenvalues are:
We take first 5 eigenvalues!!

7. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
The corresponding first five eigenvectors are:

8. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
The corresponding first five eigenvectors are:

9. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
Compute the five eigenimages:
i=1
i=2
i=3
i=4
i=5

10. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
Compute the five eigen decomposition
a) k=1
b) k=2
c) k=3
d) k=4
e) k=5
Original

11. Example of SVD decompsition of an image
Example 2.1: SVD decomposition of an image
Error in the reconstruction: