Digital Signal Processing Reference
In-Depth Information
Figure 4.5. Comparison between the starlet transform, the MMT, and Med-WT. From top to
bottom, the figure shows a signal that contains a Gaussian (
σ
= 10) centered at position
512, a “glitch” at position 480, and additive Gaussian noise; the fourth scale of the starlet
transform; the fourth scale of the MMT; and the fourth scale of the Med-WT transform,
respectively.
In this algorithm, the linear filtering involved in the wavelet transform is not ap-
plied to the strong features contained in the image. Indeed, significant pixel values
are detected at step 3 and are replaced by the median in step 5. Regions containing
no bright object are treated as if the wavelet transform were used. The threshold pa-
rameter
used in step 3 must be large enough to be sure that noise is not filtered by
the median (
τ
τ
=
5 seems high enough, in practice). Because this transform merges
the wavelet transform and the MMT, we call it the Med-WT transform. Med-WT
is computationally slower than the MMT, but this algorithm shares the advantages
of the MMT, without suffering its drawbacks. The reconstruction is the same as for
the MMT. The same approach can be used to combine the PMT and the wavelet
transform (Starck 2002).
4.5 GUIDED NUMERICAL EXPERIMENTS
4.5.1 Starlet, Multiscale Median Transform, and Median-Wavelet
Transform in IDL
The goal of this code is to show the difference between the starlet transform, the
MMT, and the Med-WT transform. We create a signal that contains a Gaussian (of
standard deviation = 10) centered at position 512, a “glitch” at sample 480, and addi-
tive white Gaussian noise. Figure 4.5 (top) shows this signal. The Gaussian feature is
