a la physique de l'information - Lisa - Université d'Angers

noises Z i in (3) are chosen Gaussian. Other measures of similarity (like
the peak-signal-to-noise ratio), images and PDF for Z i have been tested.
Results were quantitatively and qualitatively similar to the ones
presented below. In Fig. 1, the similarity between the restored and
original image, assessed by the normalised cross-covariance of (5),
surpasses the classical Perona-Malik process for all values tested for M.
This demonstrates the possibility of improving the performance of the
Perona-Malik process by injecting a nonzero amount of the M noises Z i
in (4). Moreover, in Fig. 1, one can also notice that the convergence
speed of the diffusion process is increased with the presence of the M
noises Z i. This acceleration of the convergence is another benefit
shown in Fig. 1, which is also perceptible within the images themselves
(Fig. 2). The addition of noise leads to a better contrast and a better
preservation of the structure, which are characterised by small gradient
(e.g. the buildings in the background are more visible and the texture of
the grass is preserved by comparison with the classical Perona-Malik
process). In Fig. 3, the number of iterations n of the diffusion processes
of (3) and (4) is fixed. The normalised cross-covariance of (5)
culminates at a maximum for an optimal nonzero noise level of the
M noises injected in (4). This clearly demonstrates the possibility of a
constructive role of noise in the diffusion process of (3) and (4) for an
image restoration task.
Fig. 3 Normalised cross-covariance of (5) against RMS amplitude sZ of
noise purposely injected in (4)
– – – our modified version of Perona-Malik process of (3) and (4) for various
number M of independent noises Zi ——— classical Perona-Malik process of (2)
Number of iterations n fixed for all lines to n ¼ 75
# IEE 2006 27 January 2006
Electronics Letters online no: 20060180
doi: 10.1049/el:20060180
A. Histace and D. Rousseau (Laboratoire d’Ingénierie des Systèmes
Automatisées (LISA CNRS FRE 2656), 62 avenue Notre Dame du Lac,
49000 Angers, France)
E-mail: aymeric.histace@univ-angers.fr
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