Singular Value Decomposition

5/20/99

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Table of Contents

Singular Value Decomposition

What is the Singular Value Decomposition?

To Find An Eigenvalue

Determining the Eigenvectors

Set up the Augmented Matrix

Corresponding Eigenvectors

Corresponding Eigenvectors

I=imread('sanfran.tif');imshow(I);J=im2double(I);figureimshow(J)[U,S,V]=svd(J);for k = 1:10:70 K=U(:,1:k)*S(1:k,1:k)*V(:,1:k)'; imshow(K) pause end

The following image has dimensions 337 x 500. It will require the sum of all 500 singular values to obtain the exact image.Our approximation will require far fewer terms and our image will be “good enough.”

The following image has dimensions 222 x 324. To get an exact representation of the original image, we would need to sum up 324 singular value terms of the SVD.

First 10 Terms First 20 Terms

60 Terms 90 Terms

100 Terms vs. Original Image

What is happening with the image?

We have reduced the storage of the original image by nearly 70%!!!

If you’d like to know more…our paper is on the web!http://online.redwoods.cc.ca.us/instruct /darnold/laproj/index.htm

Special thanks to our math “guru” Dave ArnoldWe would also like to thank Warren StaleyDon HickethierJohn Andersonand evenPeter Gent!

Author: Sci-Math