07-05-2011, 11:05 AM
Abstract
This paper proposes a two-phase scheme for removing salt-and-pepper impulse noise. In the first
phase, an adaptive median filter is used to identify pixels which are likely to be contaminated by noise
(noise candidates). In the second phase, the image is restored using a specialized regularization method
that applies only to those selected noise candidates. In terms of edge preservation and noise suppression,
our restored images show a significant improvement compared to those restored by using just nonlinear
filters or regularization methods only. Our scheme can remove salt-and-pepper-noise with noise level as
high as 90%.
Index Terms
Impulse noise, adaptive median filter, edge-preserving regularization.
I. INTRODUCTION
Impulse noise is caused by malfunctioning pixels in camera sensors, faulty memory locations in
hardware, or transmission in a noisy channel. See [5] for instance. Two common types of impulse noise
are the salt-and-pepper noise and the random-valued noise. For images corrupted by salt-and-pepper
noise (respectively random-valued noise), the noisy pixels can take only the maximum and the minimum
values (respectively any random value) in the dynamic range. There are many works on the restoration
of images corrupted by impulse noise. See, for instance, the nonlinear digital filters reviewed in [1]. The
median filter was once the most popular nonlinear filter for removing impulse noise, because of its good
denoising power [5] and computational efficiency [16]. However, when the noise level is over 50%, some
details and edges of the original image are smeared by the filter [20].
Different remedies of the median filter have been proposed, e.g. the adaptive median filter [17], the
multi-state median filter [11], or the median filter based on homogeneity information [12], [21]. These
so-called “decision-based” or “switching” filters first identify possible noisy pixels and then replace them
by using the median filter or its variants, while leaving all other pixels unchanged. These filters are good
at detecting noise even at a high noise level. Their main drawback is that the noisy pixels are replaced
by some median value in their vicinity without taking into account local features such as the possible
presence of edges. Hence details and edges are not recovered satisfactorily, especially when the noise
level is high.
For images corrupted by Gaussian noise, least-squares methods based on edge-preserving regularization
functionals [4], [9], [10], [22] have been used successfully to preserve the edges and the details in the
images. These methods fail in the presence of impulse noise because the noise is heavy tailed. Moreover
the restoration will alter basically all pixels in the image, including those that are not corrupted by
the impulse noise. Recently, non-smooth data-fidelity terms (e.g. `1) have been used along with edgepreserving
regularization to deal with impulse noise [19].
In this paper, we propose a powerful two-stage scheme which combines the variational method proposed
in [19] with the adaptive median filter [17]. More precisely, the noise candidates are first identified by the
adaptive median filter, and then these noise candidates are selectively restored using an objective function
with an `1 data-fidelity term and an edge-preserving regularization term. Since the edges are preserved
for the noise candidates, and no changes are made to the other pixels, the performance of our combined
approach is much better than that of either one of the methods. Salt-and-pepper noise with noise ratio
as high as 90% can be cleaned quite efficiently.
The outline of the paper is as follows. The adaptive median filter and the edge-preserving method
are reviewed in Section II. Our denoising scheme is presented in Section III. Experimental results and
conclusions are presented in Sections IV and V, respectively
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