JPEG and Wavelets

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I'm teaching a course on Multimedia Data Transmission and I had to give a couple of lectures on image encoding. So I had to attempt to build some understanding on how several standards work and their underlying math. As you are probably aware, JPEG standard allows you to encode continuous-tone images (photographs) with a typical reduction of 1:20 on the storage needs over other non-lossy methods. JPEG is based on the use of the Discrete Cosine Transform (DCT) that [basically] translates image spatial information to the frequency domain, where the weaker higher-frequency components can be removed without that being too noticeable.
JPEG 2000, on the other hand, is another image encoding standard based on the wavelet transform instead of DCT. Wavelets are families of functions that allow multirate analysis of signals. And here you will find the best tutorial on the subject I have found on the web. The end result is that wavelet-based image compression provides a smoother image than DCT-based ones for the same data rate. However, if compression is not extreme it is not so easy to tell when each one if used. So bottom-line is that most products for the moment do not use or support JPEG 2000 (which is not patent-free).

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