jpeg jpeg2000
JPEG uses DCT for compression whereas JPEG2000 relies on Wavelet/Subband Coding. Techincally, JPEG2000 has reversible compression with precision arithmetic, something not achievable with JPEG. JPEG2000 uses bit plane coding for more efficiency.
The novel aspect of JPEG2000 is that you encode once and decode multiple times on whatever device, resolution, you want. It is highly scalable. It will decode only the part of the picture that you want to see unlike JPEG. Also, there are many security related features supported by JPEG2000.