*Participants*
August Masquelier, Rachel Brough, Scott Hoge, Ricardo Sonsini

*Title*
Implementing and Analyzing SVD Image Compression

*Abstract*
Commonly, image processing is categorized into two distinct categories
based on the "quality" of the end result. Lossless refers to images that
when processed, have a result exactly the same in terms of quality to the
original. On the other hand, lossy image processing refers to methods that
output a result that is of different quality to the original, usually
lower. When it comes to image compression, the ultimate goal is to decrease
the size of the file which requires some loss in quality. Many different
methods exist for image compression, but this document will specifically
take a look at singular value decomposition (SVD) and how it can be used to
compress images.

In general, images are simply matrices of color information about each
pixel that makes up the image. Each entry in the matrix might store the RGB
value of a specific pixel with each color being stored in a single byte
causing large images to require large amounts of storage. For example, a
1920x1080 image would have a rank of 1080 and require approximately 6.3Mb
of storage. As a result, computer scientists have developed methods,
utilizing linear algebra and the idea of a matrix, to compress these images
so that they take up less storage space. Both lossy and lossless methods,
as discussed above, can be achieved using a process called SVD or singular
value decomposition. The difference between the lossy and lossless SVD
image compression is determined by the number of terms, or rank, that the
matrix color representation is reduced to utilizing the SVD process. In
short, representing a large color range requires precise values,
specifically 8-bits or 1-byte, for each color value RGB from 0-255. If we
reduce the number of values that we are able to represent, we can
significantly reduce the size of the file at the cost of some quality,
which in the eyes of a computer scientist is a worthwhile trade.

*Outline*
- Abstract
- Applications of SVD
- Explanation of SVD
- Relative Information Retention
- Singular Values After Image Processing with SVD
- Choosing an Optimal Rank Value
- Image Samples
- Conclusion