Árbók VFÍ/TFÍ - 01.06.2002, Blaðsíða 243
The details of each subband are about 2_2s wide.
f(A0, A/, A]/,...)
• Smooth Partioning: Define a collection of smooth windows localized
around dyadic squares,
e = [kjT,{k, + l)/2'] x [k2/r,(k2 + 0/2'].
The subimages A/are multiplied by a collection of smooth windows, which are localized
around dyadic squares.
A sf^(wQAsf) Vg
producing an image which is localized near Q. Doing this for all Q at certain scales, with
s fixed and íq and k2 varying, produces a smooth dissection of the subimages into ’squares'.
Renormalization: Each 'square' is renormalized to a unit scale
gQ={TeT'(weAJ),QseQSB
where the operator Tq is defined as
(V)(x„x2) = 2'/(2'x, -JTx, -k2 )
• Ridgelet analysis: Each ’square' is analysed in the ridgelet system, i.e.,
={gQ^a,„,e) (8)
Digital implementation of the curvelet transformation
In this section, a brief description of digital implementation of the curvelet transforma-
tion for 256 x 256 images is described. For more information refer to [7] Figure 3 shows
the digital curvelet transform
for a 256 x 256 digital image.
There are three steps involved
in the digital curvelet trans-
form; they are subband filter-
ing, tiling and ciigital ridgelet
transformation. The first step
of the digital curvelet trans-
form of a 256 x 256 image f is
to decompose it into sub-
bands. The frequency domain
is partitioned into three sub-
bands indexed by s = 1,2,3..
The curvelet subbands are best
described in relationship with
the wavelet subbands, i.e.,
Curvelet subband s <->
for s = 1, and
Curvelet subband s++ Wavelet subbands /e {2,S',2,v + I}. (10)
Wavelet subbands /g \2s - 2,2s + l},
(9)
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