In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3A/V4 — Paris, France, 3-4 September, 2009 
Bandpass Filtering Before the computation of the ridgelets can 
be done, the original image has to be separated out into a se 
ries of disjoint scales. This is done by a Laplacian pyramid 
which implies a high redundancy in the order of multiply 
ing the original data volume by the factor 16 (Donoho and 
Duncan, 2000). The interesting thing for images with edges 
is, that most of these coefficients can be set to zero with 
out loosing any structures. So, data volume reduction gets 
possible although the initial increase. 
If one compares the original SAR image (Fig. 2(a)) to the coef 
ficients’ magnitudes (Fig. 2(b)) it is recognizable that the main 
axes of the city center (a cross slightly rotated clockwise to the 
vertical and the horizontal direction respectively) correspond in 
their direction with accumulations of brighter points, i.e. with 
higher coefficients, in the illustration of the curvelet representa 
tion. Now, the idea is to manipulate these coefficients to accent 
certain structures by preserving the related coefficients or to sup 
press certain structures by removing the related coefficients be 
fore the inverse curvelet transform is done to get the enhanced 
image in the spatial domain. 
4 IMAGE ENHANCEMENT 
The first application presented here is image enhancement by 
simple noise suppression and structure extraction respectively. 
4.1 Image denoising 
Noise is commonly associated with insignificant curvelet coeffi 
cients, therefore a thresholding can set minor coefficients to zero. 
One problem is that the number of coefficients preserved also 
corresponds to the complexity of the scene, i.e. if the number of 
coefficients preserved is defined as constant in advance the com 
plexity of all scenes is seen as equal. By contrast if a magnitude 
threshold is chosen to exclude minor coefficients, the complexity 
of the scenes may vary. But in this case the mean magnitude of 
the coefficients, which is con-elated with the contrast in the origi 
nal image, is misleadingly seen as constant. So, only structures of 
a certain contrast would be extracted. Fig. 3(a) shows an exam 
ple where a magnitude threshold of 0.1 was applied, i.e. all lower 
coefficients were set to zero. It is obvious that the main structures 
are enhanced, but also many artifacts are produced, that constrain 
the interpretation. Hence, the determination of a suitable thresh 
old is a difficult task. 
4.2 Structure enhancement 
Another possibility is to access the structures via their belong 
ing scale. The finest structures are gray value differences in a 
N4-neighborhood. As this scale probably only contains noise, all 
coefficients of this scale are set to zero. The coarsest scale influ 
ences the brightness of the image and should be kept unchanged. 
The scales in-between gather the remaining structures according 
to their length. So, it is possible to choose only those structures 
of a certain length to be kept and to suppress all other structures 
by setting the corresponding coefficients to zero. For example in 
Fig. 3(b) only the structures of a length from 3 to 300 m are pre 
served to extract structures that presumably belong to buildings. 
One can perceive that the main structures of the original image 
(Fig. 2(a)) are strengthened and all clutter is removed. At first 
glance the Touzi edge extractor (Fig. 3(c)) and the curvelet ap 
proach provide similar results. The lines extracted by the Touzi 
operator (Touzi et al., 1988) are smoother and closed, but also 
many lines inside the building blocks are displayed. The impor 
tant difference between the two approaches is that the curvelet 
(a) Reconstructed ’’denoised” image 
(b) Structure reconstruction by curvelets 
(c) Touzi edge extractor (r=4) 
Figure 3: Denoising and structure extraction of Fig. 2(a) 
approach only enhances the existing structures while the Touzi 
extractor traces discontinuities in-between dark and bright struc 
tures. Hence, a single linear bright feature on a dark background 
is strengthened by the curvelet approach, but it is split into two 
edges by the Touzi extractor.