- In data compression, we start with a matrix A that contains perfect data, and we try to find a (lower-rank) approximation to the data that seeks to capture the principal elements of the data.
- we sacrifice only the less important parts that donâ€™t degrade data quality too much, in order to gain compression.

- In noise filtering, we start with a matrix A that contains imperfect data, and we try to find a (lower-rank) approximation to the data that seeks to capture the principal elements of the data.
- we give up only the less important parts that are typically noise.

- So both these tasks are related, and rely on the SVD to find a suitable lower-ranked approximation to a matrix