This course introduces the theory of wavelets and shows how wavelets are becoming increasingly useful for a wide variety of statistical problems because of their attractive properties. This course is mainly concerned with wavelets which form orthonormal bases for function spaces.
Sparse representation is very useful in image compression.
If the transform of your function is sparse this means that there are fewer image coefficients to compress. For example the FBI is using wavelets to compress fingerprint records . A sparse representation in noise is easier to estimate. We will make this more precise in the course. . Simplicity Ease of explanation.