The expansion of the image into a set of basis functions is accomplished using a discrete-time filter bank. A perfect reconstruction filter bank reproduces the image exactly. The QMF filter bank provides nearly perfect reconstruction. The idea is to represent a signal using a set of orthonormal basis functions, 
such that,
The two channel filter bank is illustrated in Figure 2. It implements the orthonormal signal expansion when even shifts of the analysis and synthesis filters are related to the basis functions by,
The output of the analysis section, 
, where i = 0, 1, is given by,
Finally, the signal is reconstructed by synthesis filters, 
, using
Figure 2: Two channel filter bank, analysis filters 
and synthesis filters reconstruct 
.
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