ABSTRACT
The requirement that no information be lost in the compression process puts a limit on the amount of compression we can obtain. The lowest number of bits per sample is the entropy of the source. This is a quantity over which we generally have no control. In many applications this requirement of no loss is excessive. For example, there is high frequency information in an image which cannot be perceived by the human visual system. It makes no sense to preserve this information for images that are destined for human consumption.

In short, there are numerous applications in which the preservation of all information present in the source output is not necessary. For these applications we relax the requirement that the
Finally, the quantizer labels are encoded.
Transform coding generally involves linear transforms. Consider the situation where the data is
Blocked into vectors of length M. The transform coefficients can be obtained by multiplying the data
With a transform matrix of dimension M.

D. Subband/Wavelet Coding

Transform coding at low rates tends to give the reconstructed image a blocky appearance. The blocky appearance is clearly apparent. This has led to the increasing popularity of subband and wavelet-based schemes. The implementation for both subband and wavelet-based schemes is similar. The input is filtered through a bank of filters, called the analysis filterbank. The filters cover the entire frequency range of the signal. As the bandwidth of each filter is only a fraction of the bandwidth of the original signal, the Nyquist criterion dictates that the number of samples required at the output of the filter be less than the number of samples per second required at the input of the filter. The output of the filters is subsampled or decimated and encoded. The decimated output values are quantized, and the quantization labels are encoded. At the decoder, after the received samples are decoded they are upsampled by the insertion of zeros between the received samples and filtered using a bank of reconstruction filters. The major components of the design of subband coding schemes are the selection of the filters and the encoding