Image Processing Reference
In-Depth Information
lows the overall signal shape to be taken into account without increasing the search
space drastically. For realistic-sized training sets, results show that the H-shaped
window gives better results than either the smaller area in the center or the overall H
window at full resolution.
An example is given for 1D apertures comparing two full-resolution apertures
and an H-shaped multiresolution aperture. Each operator was designed to denoise a
signal in which 10% of the points have been corrupted with Gaussian noise of vari-
ance 5. The test was carried out using 60 training signals, each of length 1024. The
first aperture is an H-shaped aperture
H
where all of the cells are retained at the fin-
est resolution. The second aperture is a “standard” aperture
ψ
S
. This occupies just the
central portion of the H-shaped aperture. The third aperture is the multiresolution ap-
erture
ψ
M
. It is produced by taking the H-shaped mask and mapping the groups of
cells furthest from the center into single large cells. It was arranged that the total
number of cells was the same for the second and third aperture.
Figure 7.18 shows the three apertures and gives the plots of MAE after filtering
compared to the number of training examples. It can be seen that for the amount of
training data used, the standard aperture performs much better than the H-shaped
aperture. This is because there are far fewer patterns to be optimized in the standard
aperture and so it has a much lower estimation error, i.e.,
ψ
S
,
n
].
Figure 7.18 also gives the MAE plot for the multiresolution aperture. The
multiresolution aperture combines estimates from a number of high-resolution pat-
terns, it therefore gives a better estimate of the ideal signal. It also spans a larger
area without increasing the size of the search space. It further gains an advantage
ε
[
ψ
H
,
n
]>
ε
[
ψ
Figure 7.18
Comparison of H-shaped, standard, and multiresolution apertures.
