JPEG 2000 uses wavelet, and a few other I can't remember their names, none of them has better image / pref than the best ones on the market or soon to be released image format based on X Codec. So in reality much like Wavelet in video, it hasn't worked out well at all in real world implementation.
There's a big thing that bugs me about that when it comes to the web: Software patents and licenses basically ruined wavelet-based image compression schemes on the web.
Wavelets would have been ideal. Basically, the lossy compression would work about the same as the cosine transform in JPEG, but by using the discrete wavelet transform, you basically get thumbnailing built in: Imagine transmitting a tiny little thumbnail of your image. Then, you transmit the information used to derive a version 4x that size (2x width, 2x height) from that. Then, you transmit the data used to derive the next 4x layer. Rinse, repeat -- that's exactly how image data is organized after a wavelet transform.
With some clever adaptions, this could have done away with so much cruft and complexity we have today (like image sets and @media queries for background images): Imagine just putting a 4K version of your background on the server and telling the browser how to render it (an <img> tag with a specified size, or background-size in css). The browser could then start loading the image until it realizes it has all the data for your resolution (say on your phone), and just terminate the transmission before the whole image is downloaded.