One of the classes I am taking is Numerical Linear Algebra and Optimization.  One thing we are working on is doing image compression (using a computer) and writing our own code.  So we take an image and 'read' the information in it into a computer file, and then we look at ways of making the file much smaller, without distorting the image too badly!  This is similar to the process that happens if you have a digital camera that takes many megapixel images and then you store them as much smaller files....
On the picture below, you can see the original image and each of the adjusted images.  The smaller the 'rank', the smaller the file, although the image can end up distorted.  The trick is to have a small file AND a decent image.