There are a number of lossless methods for progressively transmitting images already existing today. One of the more common methods is used in the GIF format, a graphic file format common on the Internet. While to the user this kind of progressive transmission may seem to be very similar to wavelet-based compression, it is actually a completely different method. An exploration into the heart of the Haar transform will reveal the differences. In 1847, a man by the name of Joseph Fourier discovered a new way to transform functions, by representing the functions as a composite of sine waves.
Fourier analysis is good for describing signals in a very concise manner.
Sine waves, used in Fourier analysis, have the characteristic of repeating periodically forever. It is this property of sine waves that allows Fourier analysis to represent long, regular signals very well. In 1909, a man by the name of Haar discovered an alternative. A 1-D signal can easily be transformed using the Haar system. Next, the image is also passed through a high-pass filter, computed using the differences.