Math 3360 Mathematical Imaging Lecture 4 Singular Value

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

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

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

Example of SVD decompsition of an image Example 2. 1: SVD decomposition of an image

Example of SVD decompsition of an image Example 2. 1: SVD decomposition of an image The image looks like:

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!!

Example of SVD decompsition of an image Example 2. 1: SVD decomposition of an image The corresponding first five eigenvectors are:

Example of SVD decompsition of an image Example 2. 1: SVD decomposition of an image The corresponding first five eigenvectors are:

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

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 e) k=5 c) k=3 Original d) k=4

Example of SVD decompsition of an image Example 2. 1: SVD decomposition of an image Error in the reconstruction: