66 Image and Video Compression
Here, a = 2
k
dilation takes place for the discrete values; and d(k,l) is the
wavelet transform of f(t) at
k
k
. This is equivalent to sampling the
coordinates (a,b) at the intervals differing by a factor of two. Such sampling
is known as dyadic sampling, and d(k,l), a two-dimensional sequence, is
referred to as the discrete wavelet transform (DWT) of f(t).
4.6.1 Wavelet Transform—Multiresolution Analysis
An N-dimensional data sequence X
n
can be considered as an N-dimensional
vector in N-dimensional space V
n
. If we represent the same vector using the
N − 1 dimensional subspace we get an approximation of the signal X
n–1
(i.e.,
we are representing the signal with lower resolution). The error between the