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

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

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

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

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