Modifying NL-means to a universal filter
Zhonggui Sun
a,b
, Songcan Chen
a,
n
a
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
b
Department of Mathematics Science, Liaocheng University, Liaocheng 252000, PR China
article info
Article history:
Received 8 March 2012
Received in revised form
9 July 2012
Accepted 10 July 2012
Available online 10 August 2012
Keywords:
Image denoising
Mixed noise
Non-local means (NLM)
Universal NLM (UNLM)
abstract
Despite a state-of-the-art filter for removing Gaussian noise, non-local means filter (NLM), like its local
counterpart (the mean filter), is no longer so effective in removing salt–pepper noise which is common
in real world as well. By contrast, adaptive median filter (AMF) is concise and can remove this type of
noise effectively. Inspired by the AMF filtering strategies, in this paper, we modify NLM to a novel non-
local universal filter (UNLM) which can remove not only either of Gaussian noise and salt–pepper noise
but also their mixture. Experiments on artificial and benchmark images validate its feasibility and
effectiveness.
& 2012 Elsevier B.V. All rights reserved.
1. Introduction
Denoising is an important step in image processing and
remains an active research field [1]. Among various noises,
Gaussian noise and salt–pepper noise maybe are the most com-
mon types and have been studied mostly [2,3]. A common goal of
denoising methods is to reduce noise artifacts and retain good
details (such as edges) of given images at the same time, even
though this is seemingly contradictory [4]. To achieve the goal,
numerous methods have been developed separately. However, up
to date, not much work has been developed to remove Gaussian
noise and salt–pepper noise universally, because they degrade
images in totally different ways.
The existence of high degree redundancy (or self-similarity) is
prevalent in natural images and early applied in texture synth-
esis [5]. As a result, various denoising operators or filters based on
this characteristic have ,respectively, been developed [6]. And
likewise, inspired by the characteristic, an effective non-local
means filter (NLM) is recently proposed by Buades et al. [7,8].
Unlike its precursors typically operating on a local neighborhood
(window), NLM operates within a whole (non-local) image by
using a dissimilarity measure between patches [9]. Such a novel
viewpoint of NLM is so intuitive and powerful in removing
Gaussian noise that it has motivated many successive researches
and is at the core of most of the state-of-the-art image denoising
algorithms as reviewed in [10,11]. Unfortunately, NLM is not so
effective in removing salt–pepper noise. By contrast, adaptive
median filter (AMF) [12] can remove salt–pepper noise effec-
tively. Therefore, to alleviate the problem of NLM, in this paper,
we attempt to develop a novel filter which combines advantages
of NLM and AMF effectively. Consequently, a modified model of
NLM is proposed; compared with the original NLM, it has two
distinct characteristics: (1) it can remove not only Gaussian noise
but also salt–pepper noiserespectively; (2) more importantly, it
can remove the mixed noise of these two types too. Hence, in
such a sense, it is universal. And following the naming method in
[13], we call it as universal non-local means filter (UNLM, for
short). Furthermore, for such a modification for NLM, we are not
aware of similar work, though it is seemingly simple as seen later.
The experiments on often used images validate the feasibility and
effectiveness of the proposed filter.
The rest of this paper is structured as follows. In Section 2,we
briefly review the related works including NLM and AMF. In
Section 3, we propose the novel non-local universal filter (UNLM).
In Sections 4 and 5, we provide experiments to demonstrate the
advantages of our filter and a brief conclusion, respectively.
2. Related works
2.1. A brief introduction to non-local means filter (NLM)
Consider the following image denoising model for additive
Gaussian noise:
Y ¼ IþN ð1Þ
where Y is the noisy (observed) image, I is the original one we
want to recover, NA
l
2
(
O
) is the noise, and
O
¼½1, , m½1, , n
Contents lists available at SciVerse ScienceDirect
journal ho mepage: www.elsevier.com/locate/optcom
Optics Communications
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.optcom.2012.07.045
n
Corresponding author. Tel.: þ86 25 84892956.
E-mail address: s.chen@nuaa.edu.cn (S. Chen).
Optics Communications 285 (2012) 4918–4926