Digital Signal Processing Reference
In-Depth Information
In capturing a view of multilayered reality in an image, we are also picking up
noise at different levels. Therefore, in trying to specify what is noise in an image, we
may find it effective to look for noise in a range of resolution levels. Such a strategy
has proven quite successful in practice.
Noise, of course, is pivotal for the effective operation, or even selection, of anal-
ysis methods. Image deblurring, or deconvolution or restoration, would be trivially
solved were it not for the difficulties posed by noise. Image compression would also
be easy were it not for the presence of what is, by definition, noncompressible, that
is, noise.
In all these areas, efficiency and effectiveness (or quality of the result) are im-
portant. Various application fields come immediately to mind: astronomy, remote
sensing, medicine, industrial vision, and so on.
All told, there are many and varied applications for the methods described in
this topic. On the basis of the description of many applications, we aim to arm the
reader for tackling other, similar applications. Clearly this objective holds, too, for
tackling new and challenging applications.
1.4 NOVEL APPLICATIONS OF THE WAVELET
AND CURVELET TRANSFORMS
To provide an overview of the potential of the methods to be discussed in later
chapters, the remainder of the present chapter is an appetizer.
1.4.1 Edge Detection from Earth Observation Images
Our first application (Figs. 1.2 and 1.3) in this section relates to Earth observation.
The European Remote Sensing Synthetic Aperture Radar (SAR) image of the Gulf
of Oman contains several spiral features. The Sea-viewing Wide Field-of-view Sen-
sor (SeaWiFS) image is coincident with this SAR image.
There is some nice correspondence between the two images. The spirals are vis-
ible in the SAR image as a result of biological matter on the surface, which forms
into slicks when there are circulatory patterns set up due to eddies. The slicks show
up against the normal sea surface background due to reduction in backscatter from
the surface. The biological content of the slicks causes the sea surface to become
less rough, hence providing less surface area to reflect back emitted radar from the
SAR sensor. The benefit of SAR is its all-weather capability; that is, even when
SeaWiFS is cloud covered, SAR will still give signals from the sea surface. Returns
from the sea surface, however, are affected by wind speed over the surface, and this
explains the large black patches. The patches result from a drop in the wind at these
locations, leading to reduced roughness of the surface.
Motivation for us was to know how successful SeaWiFS feature (spiral) detection
routines would be in highlighting the spirals in this type of image, bearing in mind
the other features and artifacts. Multiresolution transforms could be employed in
this context, as a form of reducing the background signal to highlight the spirals.
Figure 1.2 shows an original SAR image, followed by a superimposition of
resolution-scale information on the original image. The right-hand image is given
