Essential Mathematics for Data Scientists
Assessment 2B: Image compression code workbook
After working through the image compression example in MATLAB we ask you to use
MATLAB to do two items that when combined present a reconstructed version of an image
using the SVD.
1. Write a MATLAB function called SVDcompress THAT will take two arguments: a
filename and the number of singular values with which to reconstruct the image in the
file. This time the function will reconstruct a colour image, rather than a greyscale
image. The function will be defined like this:
function outimage = SVDcompress(filename, Nretain)
While you can use your code for any image, for this task the filename will be one of
• prague-astronomical-clock-detail-871291743639AGq.jpg
• boat-in-cari
ean-14884763094mZ.jpg
2. Display images that are constructed using 5, 10, 50 and 100 singular values from the
original dataset.
You should be able to base your code for this task on that given in compress.m. The a
ay
outimage contains the information that is needed to generate the reconstructed image,
which will be done outside the function. It will have three indicies, the last one,
colour_ind, takes the value 1, 2 or 3 and caters for the three different base colours that
are combined to form the image. Each base colour will have an SVD computed for it. The
SVD is truncated by taking Nretain singular values and outimage is calculated by
multiplying the retained components of the SVD: outimage(:,:,colour_ind) =
Uret*Sret*Vret'. Here Uret, etc are the retained components of the original U, etc.
This exercise forms part of your coding workbook. You need to include your code,
(appropriately commented) and the output from the code (as in step 2 above).