Reconstruction is completely equivalent to compression, but much faster. You can get progressive renderings, with a handful of coefficients. Wavelet compression has yet to make a major impact on the transmission of images. But researchers have no doubt that its time will come, probably very soon. International committees that develop standards for Internet traffic have decided to include wavelet compression in the new JPEG-2000 standard, which will soon be finalized.
Research is also under way on extending the concept to moving images.
One part of MPEG 4, a standard for moving images, will use wavelets for the first time. Image compressed with the FWP wavelet packet coder of Francois Meyer. 1 Wavelet packets are relative of the wavelets that can be tailored to each image. In this case, the wavelet packet basis contains many functions similar to sine or cosine functions that are very well localized in frequency. These wavelet packets obviously match the texture on the scarf, the woman's legs, and the checker pattern on the tablecloth.