Digital Signal Processing Reference
In-Depth Information
Figure 5.11. DCTG1 flowchart. The figure illustrates the decomposition of the original
image into subbands, followed by the spatial partitioning of each subband. The
ridgelet transform is then applied to each block.
5.4.1.3 Sparse Representation by First-Generation Curvelets
The CurveletG1 elements can form either a frame or a tight frame for
L
2
(
2
)
(Candes and Donoho 2002), depending on the 2-D WT used and the DRT
implementation (rectopolar or FSS Radon transform). The frame elements are
anisotropic by construction and become successively more anisotropic at progres-
sively higher scales. These curvelets also exhibit directional sensitivity and dis-
play oscillatory components across the “ridge.” A central motivation leading to
the curvelet construction was the problem of nonadaptively representing piecewise
smooth (e.g.,
C
2
) images
f
, which have discontinuity along a
C
2
curve. Such a model
is the so-called cartoon model of (nontextured) images. With the CurveletG1 tight
R
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Figure 5.12. A few first-generation curvelets.
