Using a wavelet transform, the wavelet compression methods are adequate for representing transients, such as percussion sounds in audio, or high-frequency components in two-dimensional images, for example an image of stars on a night sky. This means that the transient elements of a data signal can be represented by a smaller amount of information than would be the case if some other transform, such as the more widespread discrete cosine transform, had been used.
Wavelet compression is not good for all kinds of data: transient signal characteristics mean good wavelet compression - smooth, periodic signals are better compressed by other methods. Data statistically indistinguishable from random noise is not compressible by any means.
Examples for wavelet compression: