Digital Signal Processing Reference
In-Depth Information
Table 8.2.
Experimental Setup for 2-D Separation and Inpainting Examples
Image
Dictionaries
Task
Algorithm Parameters
Boy +
Texture
256×256
Curvelets (cartoon)
(coarsest scale 2)
Global DCT (texture)
(low frequencies removed)
Decomposition
(Algorithm 31)
N
iter
= 50,
γ
= 0
.
1
(TV on cartoon part),
λ
min
= 0,
exponentially
decreasing threshold
Barbara
512×512
Curvelets (cartoon)
(coarsest scale 2)
Decomposition
(Algorithm 31)
N
iter
= 300,
γ
= 2
(TV on cartoon part),
λ
min
= 0,
exponentially
decreasing threshold
Local DCT (texture)
(sine-bell window, width= 32,
low frequencies removed)
Inpainting
(Algorithm 31,
Section 8.7.2)
N
iter
= 300,
γ
= 0(no
TV),
λ
min
= 0, linearly
decreasing threshold
Lines +
Gaussians
256×256
Curvelets (lines)
(coarsest scale 3)
Inpainting
(Algorithm 30,
Section 8.7.2)
N
iter
= 50,
γ
= 0
(no TV),
λ
min
= 0,
linearly
decreasing threshold
UWT (Gaussians)
(Symmlet 6, coarsest scale 2)
Inpainting
(Algorithm 33,
Section 8.7.3)
no noise,
δ
= 1E-6,
λ
= 3
Lena
512×512
Curvelets
(coarsest scale 2)
Inpainting
(Algorithm 30,
Section 8.7.2)
N
iter
= 300,
γ
= 0
(no TV),
λ
min
= 0,
exponentially
decreasing threshold
Inpainting
(Algorithm 33,
Section 8.7.3)
no noise,
δ
= 1E-6,
λ
= 10
images) and then decompose or inpaint them using MCA Algorithms 30 and 31.
Only signals and images with two morphological components, and hence two dictio-
naries, can be processed with this GUI; see Fadili et al. (2010) for details.
8.8.2 Reproducible Experiments
Data description, dictionaries, and algorithm parameters used in the experiments of
this section are summarized in Table 8.1 and Table 8.2.
8.8.2.1 One-Dimensional Examples
TwinSine + Diracs
The synthetic signal of Fig. 8.17(a) (dashed line) consists of three randomly located
spikes and the TwinSine signal: two cosines with frequencies separated by less than
the Rayleigh distance. The TwinSine appears in the work of Chen et al. (1999). We
