Impulse Noise Filtering Using Robust Pixel-Wise S-Estimate of Variance
EURASIP Journal on Advances in Signal Processing
Hindawi Publishing Corporation
Impulse Noise Filtering Using Robust Pixel-Wise S-Estimate of Variance
Vladimir Crnojevic´ 0
Nemanja I. Petrovic´ 0
Ling Shao
0 Communications and Signal Processing Group, Department of Electrical Engineering, University of Novi Sad , 21000 Novi Sad , Serbia
A novel method for impulse noise suppression in images, based on the pixel-wise S-estimator, is introduced. The S-estimator is an alternative for the well-known robust estimate of variance MAD, which does not require a location estimate and hence is more appropriate for asymmetric distributions, frequently encountered in transient regions of the image. The proposed computationally efficient modification of a robust S-estimator of variance is successfully utilized in iterative scheme for impulse noise filtering. Another novelty is that the proposed iterative algorithm has automatic stopping criteria, also based on the pixel-wise S-estimator. Performances of the proposed filter are independent of the image content or noise concentration. The proposed filter outperforms all state-of-the-art filters included in a large comparison, both objectively (in terms of PSNR and MSSIM) and subjectively.
1. Introduction
Corruption by the impulse noise is a frequent problem which
appears in digital images. It occurs as a consequence of
transmission errors, timing problems in analog-to-digital
conversion, or damaged pixel elements in image sensors [
1
].
Regardless of its origin, the impulse noise has two important
aspects: only certain parts of the image pixels are corrupted
by the noise and the intensities of contaminated pixels are
significantly different from the other noise-free pixels in their
neighborhoods. These properties can easily make any kind of
subsequent processing, such as segmentation, edge detection,
or object recognition, difficult or even impossible. Therefore,
the suppression of the impulse noise is usually a required
preprocessing step.
The major issue in impulse noise suppression is to
satisfy two opposing requests. The corrupted pixels should
be filtered whereas the image details have to be preserved.
This task is exceptionally difficult because even the smallest
amount of noise impulses which are not detected and filtered
causes significant deterioration of image quality due to
the nature of impulse noise. There have been proposed a
large number of filtering techniques for removal of impulse
noise. The classical approach is based on using median
or its modifications [
2
]. These space-invariant methods
are applied uniformly throughout the whole image, that
is, apart from the noisy pixels, they unnecessarily change
the noise-free pixels and impair image details. Most of the
modern impulse noise filters utilize the solution based on
switching scheme [
3
]. The noisy pixels are detected first and
filtered whereas the noise-free pixels are left intact. Thus, this
approach is space variant, and it is proven to be effective in
preserving image details.
The impulse noise detection is usually performed by
comparison of some robust statistics calculated in a local
neighborhood to the corresponding fixed or adaptively
calculated thresholds. A plethora of the algorithms has
been developed which uses this approach, for example,
switching median (SM) filter [
3
], three-state median (TSM)
filter [
4
], multistate median (MSM) [
5
], adaptive center
weighted median (ACWM) filter [
6
], state-dependent
rankorder mean (SDROM) filter [
7
], progressive switching
median (PSM) filter [
8
], conditional signal-adaptive median
(CSAM) filter [
9
], pixel-wise MAD (PWMAD) filter [
10
],
threshold boolean filter (TBF) [
11
], and so forth. The
detectors of the previous filters are constructed heuristically,
but it is also possible to use previous knowledge and machine
learning techniques in order to find an optimal decision
rule. Genetic programming is utilized in GP [
12–14
] filters,
and neural networks are employed in improved adaptive
impulsive noise suppression (IAINS) filter [
15
].
The other popular approach relies on fuzzy logic.
Impulse noise detection in fuzzy-based techniques models
ambiguities between noisy impulses and image structures in
order to preserve image details [
16–18
]. Further
enhancement of the fuzzy techniques is achieved by combining them
with neural networks into neurofuzzy systems [
19
].
Robust statistics play a central role in impulse detection,
being capable of producing correct estimates in the presence
of unreliable data. The most frequently used statistics are
the median and its variants such as center-weighted median.
Nevertheless, robust statistics based on absolute differences
are proven to be successful. The trilateral filter [
20
] was the
first one which employed rank-ordered absolute difference
(ROAD) statistics. Effective modifications are given by the
rank-ordered logarithmic difference (ROLD) detector [ (...truncated)