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IEEE TRANSACTIONS ON IMAGE PROCESSING
创建日期：2024-05-16 18:11:38
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TRANSACTIONS ON IMAGE PROCESSING

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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 18, NO. 10, OCTOBER 2009 2221

Nonlocal Means-Based Speckle Filtering for
Ultrasound Images
Pierrick Coupé, Pierre Hellier, Charles Kervrann, and Christian Barillot
Abstract—In image processing, restoration is expected to im-
prove the qualitative inspection of the image and the performance
of quantitative image analysis techniques. In this paper, an adap-
tation of the nonlocal (NL)-means filter is proposed for speckle
reduction in ultrasound (US) images. Originally developed for
additive white Gaussian noise, we propose to use a Bayesian
framework to derive a NL-means filter adapted to a relevant
ultrasound noise model. Quantitative results on synthetic data
show the performances of the proposed method compared to
well-established and state-of-the-art methods. Results on real
images demonstrate that the proposed method is able to preserve
accurately edges and structural details of the image.
I. INTRODUCTION
I N ultrasound imaging, denoising is challenging since thespeckle artifacts cannot be easily modeled and are known
to be tissue-dependent. In the imaging process, the energy of
the high frequency waves are partially reflected and transmitted
at the boundaries between tissues having different acoustic im-
pedances. The images are also log-compressed to make easier
visual inspection of anatomy with real-time imaging capability.
Nevertheless, the diagnosis quality is often low and reducing
speckle while preserving anatomic information is necessary to
delineate reliably and accurately the regions of interest. Clearly,
the signal-dependent nature of the speckle must be taken into ac-
count to design an efficient speckle reduction filter. Recently, it
has been demonstrated that image patches are relevant features
for denoising images in adverse situations [1]–[3]. The related
methodology can be adapted to derive a robust filter for US im-
ages. Accordingly, in this paper we introduce a novel restoration
scheme for ultrasound (US) images,strongly inspired from the
NonLocal (NL-) means approach [1] introduced by Buades et al.
[1] to denoise 2-D natural images corrupted by an additive white
Gaussian noise. In this paper, we propose an adaptation of the
NL-means method to a dedicated US noise model [4] using a
Bayesian motivation for the NL-means filter [3]. In what fol-
lows, invoking the central limit theorem, we will assume that
Manuscript received September 26, 2008; revised April 28, 2009. First pub-
lished May 27, 2009; current version published September 10, 2009. The as-
sociate editor coordinating the review of this manuscript and approving it for
publication was Dr. John Kerekes.
P. Coupé, P. Hellier, and C. Barillot are with the University of Rennes I-
CNRS UMR 6074, IRISA, Campus de Beaulieu, F-35042 Rennes, France, and
also with the INRIA, VisAGeS U746 Unit/Project, IRISA, Campus de Beaulieu,
F-35042 Rennes, France, and also with the INSERM, VisAGeS U746 Unit/
Project, IRISA, Campus de Beaulieu, F-35042 Rennes, France.
C. Kervrann is with the INRIA, VISTA Project, IRISA, Campus de Beaulieu,
F-35042 Rennes, France, and also with the INRA, UR341 Mathématiques et
Informatique Appliquées, Domaine de Vilvert 78352 Jouy en Josas, France.

Digital Object Identifier 10.1109/TIP.2009.2024064
the observed signal at a pixel is a Gaussian random variable with
mean zero and a variance determined by the scattering proper-
ties of the tissue at the current pixel.
The remainder of the paper is organized as follows. In
Section II, we give an overview of speckle filters and re-
lated methods. Section III described the proposed Bayesian
NL-means filter adapted to speckle noise. Quantitative results
on artificial images with various noise models are presented in
Section IV. Finally, qualitative result on real 2-D and 3-D US
images are proposed in Section V.
II. SPECKLE REDUCTION: RELATED WORK
The speckle in US images is often considered as undesirable
and several noise removal filters have been proposed. Unlike the
additive white Gaussian noise model adopted in most denoising
methods, US imaging requires specific filters due to the signal-
dependent nature of the speckle intensity. In this section, we
present a classification of standard adaptive filters and methods
for speckle reduction.
A. Adaptive Filters
The adaptive filters are widely used in US image restoration
because they are easy to implement and control. The commonly
used adaptive filters—the Lee’s filter [5], Frost’s filter [6], and
Kuan’s filter [7]—assume that speckle noise is essentially a
multiplicative noise. Many improvements of these classical fil-
ters have been proposed since. At the beginning of the 1990s,
Lopes et al. [8] suggested to improve the Lee’s and Frost’s
filters by classifying the pixels in order to apply specific pro-
cessing to the different classes. Based on this idea, the so-called
Adaptive Speckle Reduction filter (ASR) exploits local image
statistics to determine specific areas to be processed further. In
[9], the kernel of the adaptive filter is fitted to homogeneous re-
gions according to local image statistics. Analyzing local homo-
geneous regions was also investigated in [10], [11] to spatially
adapt the filter parameters. Note that the Median filter has been
also examined for speckle reduction in [4]. Very recently, a sto-
chastic approach to ultrasound despeckling (SBF) has been de-
veloped in [12] and [13]. This local averaging method removes
the local extrema assumed to be outliers in a robust statistical
estimation framework. Finally, the Rayleigh-Maximum-Likeli-
hood (R-ML) filter has been derived with similar methodolog-
ical tools in [14].
B. Partial Differential Equations (PDE) -Based Approaches
Adapted formulations of the Anisotropic Diffusion filter
(AD) [15] and the Total Variation minimization scheme (TV)
[16] have been developed for US imaging. In [17] and [18], the


Speckle Reducing Anisotropic Diffusion (SRAD) was intro-
duced and involves a noise-dependent instantaneous coefficient
of variation. In [19] the Nonlinear Coherent Diffusion (NCD)
filter is based on the assumption that the multiplicative speckle
in US signals is transformed into an additive Gaussian noise
in Log-compressed images. Recently, the Oriented SRAD
(OSRAD) filter has been proposed in [20]; this filter takes into
account the local directional variance of the image intensity,
i.e., the local image geometry. Finally, the TV minimization
scheme has been adapted to ultrasound imaging in [21] and
[22]. Unlike the previous adaptive speckle filters, all the consid-
ered PDE-based approaches are iterative and produce smooth
images while preserving edges. Nevertheless, meaningful
structural details are unfortunately removed during iterations.
C. Multiscale Methods
Several conventional wavelet thresholding methods [23]–[25]
have also been investigated for speckle reduction [26]–[28] with
the assumption that the logarithm compression of US images
transforms the speckle into an additive Gaussian noise. In order
to relax this restrictive assumption, Pizurica et al. [29] proposed
a wavelet-based Generalized Likelihood ratio formulation and
imposed no prior on noise and signal statistics. In [30]–[33],
the Bayesian framework was also explored to perform wavelet
thresholding adapted to the non-Gaussian statistics of the signal.
Note that other multiscale strategies have been also studied in
[34]–[36] to improve the performance of the AD filter; in [37],
the Kuan’s filter is applied to interscale layers of a Laplacian
pyramid.
D. Hybrid Approaches
The aforementioned approaches can be also combined in
order to take advantage of the different paradigms. In [38],
the image is preprocessed by an adaptive filter in order to
decompose the image into two components. A Donoho’s soft
thresholding method is then performed on each component.
Finally, the two processed components are combined to reduce
speckle. PDE-based approaches and a wavelet transform have
been also combined as proposed in [39].
III. METHOD
The previously mentioned approaches for speckle reduction
are based on the so-called locally adaptive recovery paradigm
[40]. Nevertheless, more recently, a new patch-based nonlocal
recovery paradigm has been proposed by Buades et al. [1]. This
new paradigm proposes to replace the local comparison of pixels
by the nonlocal comparison of patches. Unlike the aforemen-
tioned methods, the so-called NL-means filter does not make any
assumptions about the location of the most relevant pixels used
to denoise the current pixel. The weight assigned to a pixel in the
restoration of the current pixel does not depend on the distance
between them (neither in terms of spatial distance nor in terms
of intensity distance). The local model of the signal is revised
and the authors consider only information redundancy in the
image. Instead of comparing the intensity of the pixels, which
may be highly corrupted by noise, the NL-means filter analyzes
the patterns around the pixels. Basically, image patches are com-
pared for selecting the relevant features useful for noise reduc-
tion. This strategy leads to competitive results when compared
to most of the state-of-the-art methods [3], [41]–[46]. Neverthe-
less, the main drawback of this filter is its computational burden.
In order to overcome this problem, we have recently proposed
a fast and optimized implementation of the NL-means filter for
3-D magnetic resonance (MR) images [46].
In this section, we rather revise the traditional formulation of
the NL-means filter, suited to the additive white Gaussian noise
model, and adapt this filter to spatial speckle patterns. Accord-
ingly, a dedicated noise model used for US images is first con-
sidered. A Bayesian formulation of the NL-means filter [3] is
then used to derive a new speckle filter.
A. Nonlocal Means Filter
Let us consider a gray-scale noisy image
defined over a bounded domain , (which is usually
a rectangle of size ) and is the noisy observed
intensity at pixel . In the following, denotes the
image grid dimension ( or respectively for
2-D and 3-D images). We also use the notations given below.
Original pixelwise NL-means approach
square search volume centered at pixel
of size , ;
square local neighborhood of of size
, ;
vector
gathering the intensity values of ;
• true intensity value at pixel ;
restored value of pixel ;
weight used for restoring given
and based on the similarity of
patches and .
Blockwise NL-means approach
square block centered at of size
, ;
• unobserved vector of true values of block
;
vector gathering the intensity values of
block ;
restored block of pixel ;
weight used for restoring given
and based on the similarity of
blocks and .
Finally, the blocks are centered on pixels with
and represents the
distance between block centers.
1) Pixelwise Approach: In the original NL-means filter [1],
the restored intensity of pixel , is the weighted
average of all the pixel intensities in the image
(1)

Fig. 1. Pixelwise NL-means filter ( and ). The restored value at
pixel (in red) is the weighted average of all intensity values of pixels in
the search volume . The weights are based on the similarity of the intensity
neighborhoods (patches) and .
where is the weight assigned to value for
restoring the pixel . More precisely, the weight evaluates the
similarity between the intensities of the local neighborhoods
(patches) and centered on pixels and , such that
and (see Fig. 1).
The size of the local neighborhood and is .
The traditional definition of the NL-means filter considers that
the intensity of each pixel can be linked to pixel intensities of
the whole image. For practical and computational reasons, the
number of pixels taken into account in the weighted average is
restricted to a neighborhood, that is a “search volume” of
size , centered at the current pixel .

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MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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