out.txt

2013 IEEE Conference on Computer Vision and Pattern Recognition

Texture Enhanced Image Denoising via Gradient Histogram Preservation

1

Wangmeng Zuo1,2 Lei Zhang2 Chunwei Song1 David Zhang2
Harbin Institute of Technology, 2 The Hong Kong Polytechnic University
{cswmzuo, wolvesandme}@gmail.com, {cslzhang, csdzhang}@comp.polyu.edu.hk

Abstract

tionary, the sparsity prior has proved to be effective in image denoising via l0 -norm or l1 -norm minimization [8, 9].
Another popular prior is the nonlocal self-similarity (NSS)
prior [2, 16]; that is, in natural images there are often many
similar patches (i.e., nonlocal neighbors) to a given patch,
which may be spatially far from it. The joint use of sparsity
prior and NSS prior has led to state-of-the-art image denoising results [7, 21]. However, the many denoising algorithms
based on the above priors can still fail to preserve the image fine scale texture structures, which have certain overlap
with noise in the frequency domain. The over-smoothing of
those detailed texture structures makes the denoised image
look less natural, degrading much the visual quality (please
refer to Fig. 1 for example).

Image denoising is a classical yet fundamental problem
in low level vision, as well as an ideal test bed to evaluate various statistical image modeling methods. One of
the most challenging problems in image denoising is how
to preserve the fine scale texture structures while removing noise. Various natural image priors, such as gradient based prior, nonlocal self-similarity prior, and sparsity
prior, have been extensively exploited for noise removal.
The denoising algorithms based on these priors, however,
tend to smooth the detailed image textures, degrading the
image visual quality. To address this problem, in this paper we propose a texture enhanced image denoising (TEID)
method by enforcing the gradient distribution of the denoised image to be close to the estimated gradient distribution of the original image. A novel gradient histogram
preservation (GHP) algorithm is developed to enhance the
texture structures while removing noise. Our experimental
results demonstrate that the proposed GHP based TEID can
well preserve the texture features of the denoised images,
making them look more natural.

With the rapid development of digital imaging technology, the resolution of imaging sensor is getting higher and
higher. On one hand, more fine texture features of the object and scene will be captured; on the other hand, the captured high resolution image is more prone to noise because
the smaller size of each pixel makes the exposure less sufficient. However, suppressing noise while preserving textures
is difficult to achieve simultaneously, and this has been one
of the most challenging problems in natural image denoising. Unlike large scale edges, the fine scale textures have
much higher randomness in local structure and they are hard
to characterize by using a local model. Considering the fact
that texture regions in an image are homogeneous and are
usually composed of similar patterns, statistical descriptors
such as histogram are more effective to represent them. Actually, in literature of texture representation and classification [13, 27, 28], global histogram of some local features is
dominantly used as the final feature descriptor for matching. Meanwhile, image gradients convey most of semantic
information in an image and are crucial to the human perception of image visual quality. All these motivate us to
use the histogram of image gradient to design new image
denoising models.

1. Introduction
The goal of image denoising is to estimate the latent
clean image x from its noisy observation y. One commonly
used observation model is y = x + v , where v is additive
white Gaussian noise. Image denoising is a classical yet still
active topic in image processing and low level vision, while
it is an ideal test bed to evaluate various statistical image
modeling methods. In general, we hope that the denoised
image should look like a natural image, and therefore the
statistical modeling of natural image priors is crucial to the
success of image denoising.
Based on the fact that natural image gradients exhibit
heavy-tailed distributions, gradient-based priors are widely
used in image denoising [10, 17, 18]. The well-known total variation minimization methods actually assume Laplacian distribution of image gradients [25]. By observing that
natural images can be sparsely coded over a redundant dic1063-6919/13 $26.00 © 2013 IEEE
DOI 10.1109/CVPR.2013.159

With the above consideration, in this paper we propose a
novel method for texture enhanced image denoising (TEID)
via gradient histogram preservation (GHP). From the given
noisy image y, we will estimate the gradient histogram of
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(a)

(b)
0

10

−1

10

−2

10

−3

10

Reference
SAPCA−BM3D
GHP

−4

10

−5

10

0

10

1

10

2

10

Gradient Magnitude

(c)

(d)

Figure 1. Denoised images and their gradient histograms. (a)
A cropped image with hair textures; (b) denoised image by the
SAPCA-BM3D method [16]; (c) denoised image by the proposed
texture enhanced image denoising via gradient histogram preservation (GHP); (d) the gradient histograms of the denoised images.
We can see that the proposed GHP method leads to better texture
preservation and visual perception, and the gradient histogram of
the denoised image by GHP is also closer to the reference gradient
histogram estimated from the noisy image.

original image x. Take this estimated histogram, denoted by
hr , as a reference, we search for an estimate of x with GHP,
i.e., the gradient histogram of the denoised image should
be close to hr . As shown in Fig. 1, the proposed TEID
method can well enhance the image texture regions, which
are often over-smoothed by other denoising methods. The
major contributions of this paper are as follows:
(1) A novel image denoising framework, i.e., TEID, is
proposed, which preserves the gradient distribution of
the original image. The existing image priors can be
easily incorporated into the proposed framework to improve the quality of denoised image.
(2) A histogram specification operator is developed to ensure the gradient histogram of denoised image being
close to the reference histogram, resulting in a simple
yet effective GHP based TEID algorithm.
(3) A simple but theoretically solid algorithm is presented
to estimate the gradient histogram from the given noisy
image, making TEID practical to implement.

2. Related work
Generally, image denoising methods can be grouped in
two categories: model-based methods and learning-based

methods. Most denoising methods reconstruct the clean image by exploiting some image and noise prior models, and
they belong to the first category. Learning-based methods
attempt to learn a mapping function from the noisy image
to the clean image [26], and have been receiving considerable research interests [3]. Numerous image denoising
algorithms have been proposed, and here we only review
those model-based denoising methods related to our work
from a viewpoint of natural image priors.
Studies on natural image priors aim to find suitable models to describe the characteristics or statistics (e.g., distribution) of images in some transformed domain. One representative class of image priors is the gradient priors based on
the observation that natural images generally have a heavytailed distribution of gradients. The use of gradient prior
can be traced back to 1990s, when Rudin et al. [25] proposed a total variation (TV) model for image denoising,
where the gradients are actually modeled by Laplacian distribution. Another well-known prior model, the mixture of
Gaussians (GMM), can also be used to approximate the
distribution of gradient magnitude [10, 19]. In addition,
the hyper-Laplacian model can more accurately model the
heavy-tailed distribution of gradients, and has been widely
applied to various image restoration tasks [4, 5, 15, 17, 18].
The image gradient prior is basically a kind of sparsity
prior, i.e., the gradient distribution is sparse. More generally, the sparsity prior has been well applied to filter responses, wavelet/curvelet transform coefficients, or the coding coefficients over a redundant dictionary. In [23, 29],
Gaussian scale mixtures are used to characterize the margin
and joint distributions of wavelet transform coefficients. In
[24, 31], the Student t-distributions are used for both learning basis filters and modeling filter responses. By assuming
that an image patch can be represented as a sparse linear
combination of the atoms in an over-complete dictionary, a
number of dictionary learning (DL) methods (e.g., K-SVD
[9], task driven DL [20], and ASDS [8]) have been proposed
and applied to image denoising and other restoration tasks.
Based on the fact that a similar patch to the given patch
may not be spatially close to it, another line of research is to
model the similarity between image patches, i.e., the image
nonlocal self-similarity (NSS) priors. The seminal work of
nonlocal means denoising in [2] has motivated a wide range
of studies on NSS, and has led to a flurry of NSS based
state-of-the-art denoising methods, e.g., BM3D [16], LSSC
[21], and EPLL [32], etc.
Different image priors characterize different and complementary aspects of natural image statistics, and thus it
is possible to combine multiple priors to improve the denoising performance. For example, Dong et al. [7] unified
both image local sparsity and nonlocal similarity priors via
clustering-based sparse representation. Recently, Jancsary
et al. [14] proposed a method called regression tree fields

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(RTF) to integrate different priors.
However, many existing image denoising algorithms, including those sparsity and NSS priors based ones, tend to
wipe out the image detailed textures while removing noise.
As we discussed in the Introduction section, considering
the randomness and homogeneousness of image texture regions, we propose to use the histogram of gradient to describe the image texture and design new image denoising
algorithm with gradient histogram preservation. In [4, 5],
Cho et al. used hyper-Laplacian to model gradient, and proposed a content-aware prior for image deblurring by setting
different shape parameters of gradient distribution in different image regions. By matching the gradient distribution
prior, Cho et al. found that the deblurred images can have
more detailed textures as well as better visual quality. However, in [4, 5] the estimation of desired gradient distribution
is rather heuristic, and the gradient histogram matching algorithm is very complex.

method will be discussed in Section 4). In order to make the
gradient histogram of denoised image xˆ nearly the same as
the reference histogram hr , we propose the following GHP
based image denoising model:
xˆ = arg minx,F

1
2σ2

y − x 2 + λR(x) + μ F(∇x) − ∇x
s.t. hF = hr

2

,

(2)
where F denotes an odd function which is monotonically
non-descending in (0, +∞), hF denotes the histogram of the
transformed gradient image |F (∇x)|, and ∇ denotes the gradient operator. By introducing the transform F, we can use
the alternating method for image denoising. Given F, we
can fix ∇x0 = F(∇x), and use the conventional denoising
methods to update x. Given x, we can update F simply
by the histogram operator introduced in Section 3.2. Thus,
with the introduction of F, we can easily incorporate gradient histogram prior with any existing image priors R(x).
The sparsity and NSS priors have shown promising performance in denoising, and thus we integrate them into the
proposed GHP model. Specifically, we adopt the sparse
nonlocal regularization term proposed in the centralized
sparse representation (CSR) model [7], resulting in the following denoising model:

3. Denoising with gradient histogram preservation (GHP)
In this section, we first present the image denoising
model by gradient histogram preservation with sparse nonlocal regularization, and then present an effective histogram
specification algorithm to solve the proposed model for texture enhanced image denoising.

y − x 2 + λ i αi − βi
+μ F(∇x) − ∇x 2
s.t. x = D ◦ α, hF = hr
1
2σ2

xˆ = arg minx,F

3.1. The denoising model

1

, (3)

where λ is the regularization parameter, D is the dictionary
and α is the coding coefficients of x over D.
Let’s explain more about the model in Eq. (3). Let xi =
Ri x be a patch extracted at position i, i = 1, 2, . . . , N, where
Ri is the patch extraction operator and N is the number of
pixels in the image. Each xi is coded over the dictionary D,
and the coding coefficients is αi . Let α be the concatenation
of all αi , and then x can be reconstructed by

Given a clean image x, the noisy observation y of x is
usually modeled as
y = x + v,
(1)
where v is the additive white Gaussian noise (AWGN)
with zero mean and standard deviation σ. The goal of
image denoising is to estimate the desired image x from
y. One popular approach to image denoising is the variational method, in which the denoised image is obtained by
xˆ = arg minx 2σ1 2 y − x 2 + μ · R(x) , where R(x) denotes
some regularization term and μ is a positive constant. The
specific form of R(x) depends on the used image priors.
One common problem of image denoising methods is
that the image fine scale details such as texture structures
will be over-smoothed. An over-smoothed image will have
much weaker gradients than the original image. Intuitively,
a good estimation of x without smoothing too much the textures should have a similar gradient distribution to that of
x. With this motivation, we propose a gradient histogram
preservation (GHP) model for texture enhanced image denoising (TEID).
Our intuitive idea is to integrate the gradient histogram
prior with the other image priors to further improve the denoising performance. Suppose that we have an estimation
of the gradient histogram of x, denoted by hr (the estimation

N

x= D◦α

i=1

RTi Ri

−1

N
i=1

RTi Dαi .

(4)

The physical meaning of Eq. (4) is that we use xˆ i = Dαi
to reconstruct each patch xi , and then put all reconstructed
patches together as the denoised image xˆ (the overlapped
pixels between neighboring patches are averaged).
In Eq. (3), βi is the nonlocal means of αi in the sparse
coding domain. With the current estimate xˆ , we use the
blocking matching method as in [7] to find the non-local
q
q
neighbors of xˆ i , denoted by xˆ i . Denote by αi the coding
q
coefficients of xˆ i . Then βi is computed as the weighted avq
erage of αi ,
q q
βi =
wi αi ,
(5)
q

q

where the weight wi is defined as
wqi =

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1
W

exp − 1h xˆ i − xˆ qi

2

,

(6)

where h is a parameter to control the decay rate and W is
q
a normalization factor to guarantee q wi = 1. Clearly, the
regularization term i αi − βi 1 enforce the coding coefficients αi to approach to its nonlocal means βi so that noise
can be removed, while the l1 -norm comes from the fact that
αi − βi 1 follows Laplacian distribution [7].
From the GHP model with sparse nonlocal regularization
in Eq. (3), one can see that if the histogram regularization
parameter μ is high, the function F (∇x) will be close to ∇x.
Since the histogram hF of |F (∇x)| is required to be the same
as hr , the histogram of ∇x will be similar to hr , leading to
the desired gradient histogram preserved image denoising.
Next, we will see that there is an efficient iterative histogram
specification algorithm to solve the model in Eq. (3).

3.2. Iterative histogram specification algorithm
Eq. (3) is minimized iteratively. As in [7], the local PCA
bases are used as the dictionary D. Based on the current
estimation of image x, we cluster its patches into K clusters,
and for each cluster, a PCA dictionary is learned. Then for
each given patch, we first check which cluster it belongs,
and then use the PCA dictionary of this cluster as the D.
We propose an alternating minimization method to solve
the problem in Eq. (3). Given the transform function F, we
introduce a variable g = F(∇x), and update x (i.e., α) by
solving the following sub-problem:
minx

1
2σ2

y−x

2

+ λ i αi − βi
s.t. x = D ◦ α

1

+ μ g − ∇x

2

monotonic non-parametric mapping function F so that the
histogram of |F (∇x)| is the same as hr .
Finally, we summarize our proposed iterative histogram
specification based GHP algorithm in Algorithm 1. It
should be noted that, for any gradient based image denoising model, we can easily incorporate the proposed GHP in it
by simply modifying the gradient term and adding an extra
histogram specification operation.
In [1], Attouch et al. showed that: for a nonconvex
function L(x, y) = f (x) + Q(x, y) + g(y), if L satisfies the
Kurdyka-Lojasiewicz inequality, proximal alternating minimization would converge to a critical point of L. Note that
our model has a similar form to the one discussed in [1], and
we also adopted an alternating minimization method. Thus
the conclusions in [1] ensure the convergence of the proposed GHP algorithm, and we empirically found that our
algorithm converges well.
Algorithm 1: Iterative Histogram Specification for GHP
1. Initialize k = 0, x(k) = y
2. Iterate on k = 0, 1, ..., J
3. Update g:
g = F(∇x)
4. Update x:
1
(y − x(k) )
2σ2
x(k+1/2) = x(k) + δ
T
+μ∇ (g − ∇x(k) )
5. Update the coding coefficients of each patch:
α(k+1/2)
= DT Ri x(k+1/2)
i
6. Update the nonlocal mean of coding vector αi :
βi = q wqi αqi
7. Update α:
1 T
D (Ri y − Dα(k+1/2)
)
i
+ βi
= S λ/d d
α(k+1)
i
+α(k+1/2)
−
β
i
i
8. Update x
x(k+1) = D ◦ α(k+1)
9. Update F via histogram specification by Eq. (11)
10. k ←− k + 1
11. x = x(k) + δ μ∇T (g − ∇x(k) )

. (7)

To get the solution to the above sub-problem, we first use a
gradient descent method to update x:
x(k+1/2) = x(k) + δ

1
(y
2σ2

− x(k) ) + μ∇T g − ∇x(k) ,

(8)

where δ is a pre-specified constant. Then, the coding coefficients αi are updated by
= DT Ri x(k+1/2) .
α(k+1/2)
i

(9)

By using Eq. (5) to obtain βi , we further update αi by
⎛ 1 T
⎞
⎜⎜⎜ d D Ri y − Dα(k+1/2)
⎟⎟⎟
(k+1)
i
(10)
= S λ/d ⎝⎜
αi
⎠⎟ + βi ,
(k+1/2)
− βi
+αi
where S λ/d is the soft-thresholding operator, and d is a constant to guarantee the convexity of the surrogate function
[6]. Finally, we use Eq. (4) to update the whole image and
let it be x(k+1) .
Once the estimate of image x is given, we can update F
by solving the following sub-problem:
minF F(∇x) − ∇x

2

s.t. hF = hr .

(11)

To solve this sub-problem, we let d0 = |∇x|, and use the
standard histogram specification operator [12] to obtain the

4. Reference gradient histogram estimation
To apply the model in Eq. (3), we need to know the reference histogram hr , which is supposed to be the gradient
histogram of original image x. In this section, we propose
a one dimensional deconvolution model to estimate the histogram hr . Assuming that all pixels in the gradient image
∇x are independent and identically distributed (i.i.d.), we
can view them as the samples of a scalar variable, denoted
by x. Then the normalized histogram of ∇x can be regarded
as a discrete approximation of the probability density function (PDF) of x. For the additive white Gaussian noise
(AWGN) v, we can readily model its elements as the samples of an i.i.d. variable, denoted by v. Since v ∼ N 0, σ2
and let g = ∇v, one can obtain that g is also i.i.d. Gaussian

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its performance in comparison with state-of-the-art denoising algorithms. Finally, we make some discussion of its potential improvements. The Matlab source code of our algorithm can be downloaded at http://www4.comp.polyu.
edu.hk/˜cslzhang/code.htm.

with PDF [22]
pg =

g2
1
√ exp − 2 .
4σ
2 πσ

(12)

Since y = x + v, we have ∇y = ∇x + ∇v. It is ready to
model ∇y as an i.i.d. variable, denoted by y, and we have
y = x + g. Let p x be the PDF of x, and py be the PDF of y.
Since x and g are independent, the joint PDF p (x, g) is,
p(x, g) = p x × pg .

5.1. Parameter setting
Our algorithm involves a few parameters to set, including the regularization parameters λ and μ in Eq. (7) to balance the effect of gradient preservation, constant δ in Eq.
(8) and d in Eq. (10) to ensure convexity. For the parameter
λ, we use the same strategy as in [8] to adaptively update
it according to the maximum a posterior (MAP) principle.
Based on our experimental experience, we set the parameter
μ to 5, and δ to 0.23 for noise level less than 30 while 0.26
for other noise levels. Based on the analysis in [6], to guarantee the convexity of surrogate function, d should be larger
than the spectral norm of dictionary D. Since in our algorithm D is an orthonormal PCA matrix, any d greater than
1 will be fine, and we set it to 3 by experience. Note that
these parameters are fixed to all images in our experiments.

(13)

Then the PDF py is
p x (x = a) × pg (g = (t − a)) da.

py (y = t) =

(14)

a

If we use the normalized histogram h x and hy to approximate p x and py , we can rewrite Eq. (14) in the discrete
domain as:
hy = h x ⊗ hg ,
(15)
where ⊗ denotes the convolution operator. Note that hg can
be obtained by discretizing pg , and hy can be computed directly from the noisy observation y.
Obviously, the estimation of h x can be generally modeled as a deconvolution problem:
hr = arg minhx

hy − h x ⊗ hg

2

+ c · R (h x ) ,

5.2. Denoising results
To verify the performance of our proposed GHP based
TEID method, we apply it to ten natural images with various texture structures. The scenes of these images can be
found in Fig. 3. Some state-of-the-art denoising methods are used for comparison, including shape-adaptive PCA
based BM3D (SAPCA-BM3D) [16], the learned simultaneously sparse coding (LSSC) [21] and the CSR [7] methods.
The codes of all the competing methods are provided by the
authors and we used the recommended parameters by the
authors. Considering the fact when noise is too strong, all
methods cannot recover the fine scale texture structures in
the image, and in practice the noise is often moderate or below, we set the AWGN noise level σ ∈ {20, 25, 30, 35, 40}
in the experiments.
The quantitative experimental results by the competing methods are shown Table 1. Apart from PSNR, we
also list the results by using the perceptual quality metric
SSIM [30]. From this table, we can see that the proposed
GHP method has similar PSNR/SSIM measures to SAPCABM3D, LSSC and CSR. Nonetheless, the goal of our GHP
method is to preserve and enhance the image texture structures, and let’s compare the visual quality of the denoised
images by these methods. Fig. 4 shows an example. In this
image, there are different texture regions, such as the sky,
tree, water and building. We can see that SAPCA-BM3D,
LSSC and CSR smooth much the textures in tree, water and
building areas, while SAPCA-BM3D introduces some artifacts in the smooth sky area. Though they have good PSNR
and even SSIM indices, the denoised images by them look
somewhat unnatural. In contrast, the proposed GHP method

(16)

where c is a constant and R(h x ) is some regularization term
based on the prior information of natural image’s gradient
histogram. Considering that h x , i.e., the discrete version
of p x , can be well modeled as hyper-Laplacian distribution
[4, 5, 17], in this paper we use a simple parametric method
to estimate p x and then discretize it into h x .
The hyper-Laplacian modeling of p x is:
p x = k exp (−κ|x|γ ) ,

(17)

where k is the normalization factor. The estimation of p x is
converted into the estimation of parameters κ and γ. Considering the fact that for natural images, κ and γ will have
a relatively narrow range, we preset a range of each of the
two parameters, and then search for the pair (κ, γ) which
2
makes hy − h x ⊗ hg the smallest. Specifically, we let
κ ∈ [0.001, 3] and γ ∈ [0.02, 1.5]. In addition, in our
experiments the Nelder-Mead method is used to make the
searching more efficient. Fig. 2 shows an example of reference gradient histogram estimation. It can be seen that our
method can obtain a good estimation of h x .

5. Experimental results
We first give the parameter setting in our GHP based
TEID algorithm, and then conduct experiments to validate

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3000

4

3000
Real
Simulated

Real
2000

2000

Simulated

2

x 10

Real
Restored

1.5
1

1000

1000
0.5

0

0

100
200
Gradient magnitude

300

0

0

100
200
Gradient magnitude

(a)

300

0

0

50

(b)

100
150
200
Gradient magnitude

250

300

(c)

Figure 2. An example of reference gradient histogram estimation. (a) Real and simulated AWGN gradient histograms (noise level σ = 30);
(b) real and simulated gradient histograms of noisy image; and (c) real and estimated gradient histograms of the clean image.
Table 1. PSNR (dB) and SSIM results by different methods.
σ
1
2
3
4
5
6
7
8
9
10
Avg

SAPCA-BM3D[16]
20
25
30
35
40
30.83 29.66 28.75 28.02 27.41
0.876 0.849 0.825 0.803 0.784
28.07 26.99 26.18 25.54 25.02
0.817 0.773 0.734 0.699 0.668
28.39 27.43 26.66 26.01 25.46
0.755 0.721 0.692 0.667 0.647
26.86 25.68 24.79 24.08 23.50
0.803 0.758 0.715 0.677 0.641
30.88 29.96 29.21 28.58 28.06
0.812 0.780 0.754 0.730 0.709
28.59 27.32 26.35 25.59 24.97
0.888 0.856 0.824 0.794 0.765
30.17 29.14 28.35 27.71 27.18
0.839 0.803 0.771 0.744 0.721
31.58 30.48 29.64 28.94 28.37
0.900 0.879 0.861 0.843 0.828
27.58 26.37 25.44 24.73 24.15
0.821 0.778 0.740 0.707 0.677
31.23 30.28 29.53 28.92 28.42
0.823 0.791 0.763 0.740 0.721
29.42 28.33 27.49 26.81 26.25
0.833 0.799 0.768 0.740 0.716

LSSC[21]
20
25
30
35
40
30.69 29.56 28.62 27.91 27.32
0.872 0.846 0.820 0.800 0.781
27.98 26.94 26.14 25.51 24.98
0.815 0.773 0.734 0.700 0.670
28.46 27.52 26.66 26.03 25.47
0.762 0.728 0.696 0.670 0.647
26.75 25.61 24.76 24.06 23.48
0.803 0.758 0.717 0.678 0.643
30.75 29.81 29.04 28.41 27.90
0.809 0.776 0.744 0.718 0.696
28.47 27.26 26.33 25.59 24.98
0.883 0.850 0.825 0.795 0.769
30.18 29.18 28.40 27.81 27.32
0.840 0.807 0.775 0.751 0.729
31.38 30.33 29.54 28.86 28.32
0.894 0.872 0.858 0.840 0.826
27.58 26.40 25.48 24.77 24.19
0.822 0.782 0.748 0.716 0.687
31.04 30.08 29.36 28.75 28.24
0.818 0.787 0.755 0.732 0.712
29.33 28.27 27.43 26.77 26.22
0.832 0.798 0.767 0.740 0.716

preserves much better these fine texture areas, making the
denoised image look more natural and visually pleasant.
Due to the limit of space, here we cannot put more visual
results. More examples can be found in the supplementary
file attached to this paper.

CSR[7]
20
25
30
30.59 29.46 28.58
0.869 0.843 0.820
27.91 26.87 26.08
0.807 0.764 0.727
28.11 27.16 26.39
0.736 0.702 0.675
26.65 25.52 24.64
0.782 0.737 0.697
30.64 29.68 28.91
0.802 0.770 0.742
28.49 27.24 26.30
0.882 0.851 0.820
30.13 29.14 28.38
0.833 0.799 0.770
31.41 30.35 29.52
0.897 0.877 0.860
27.34 26.18 25.31
0.804 0.764 0.729
30.98 30.03 29.30
0.813 0.781 0.755
29.23 28.16 27.34
0.823 0.789 0.760

35
40
27.76 27.19
0.793 0.776
25.37 24.87
0.681 0.651
25.64 25.10
0.640 0.621
23.84 23.26
0.640 0.604
28.27 27.76
0.710 0.690
25.49 24.90
0.788 0.761
27.71 27.22
0.738 0.717
28.79 28.24
0.841 0.827
24.47 23.92
0.683 0.655
28.76 28.28
0.728 0.710
26.61 26.07
0.724 0.701

GHP
20
25
30
35
40
30.49 29.35 28.40 27.31 26.49
0.864 0.837 0.811 0.792 0.775
27.80 26.68 25.81 24.85 24.16
0.810 0.768 0.731 0.689 0.656
28.09 27.14 26.36 25.46 24.88
0.756 0.721 0.691 0.656 0.635
26.59 25.43 24.51 23.62 22.91
0.796 0.752 0.715 0.673 0.637
30.56 29.54 28.63 27.66 26.75
0.805 0.773 0.742 0.714 0.688
28.35 27.11 26.11 25.16 24.46
0.874 0.844 0.816 0.798 0.776
30.07 28.98 28.13 27.11 26.37
0.840 0.806 0.776 0.746 0.722
31.19 30.04 29.09 27.87 27.05
0.889 0.865 0.844 0.832 0.820
27.26 26.09 25.18 24.18 23.53
0.809 0.769 0.737 0.700 0.671
30.85 29.73 28.78 27.73 26.83
0.814 0.780 0.749 0.723 0.699
29.13 28.01 27.10 26.10 25.34
0.826 0.792 0.761 0.732 0.708

results in all regions.

5.3. Discussions
It is worth noting that, to further enhance the noise removal and texture preservation performance of our method,
region-based GHP could be implemented. Since natural images often consist of different regions with different textures, the gradient distributions in these regions will also
vary. Therefore, with the help of image segmentation methods such as mean-shift [11], we can partition the noisy image into several homogeneous regions, and apply the GHP
method to each region. Fig. 5 shows an example. One can
see that without segmentation, the proposed GHP method
may generate some false textures in the less textured area
(e.g., cloud) due to the influence of other texture areas (e.g.,
trees). With roughly segment the image into 2 regions, as
shown in Fig. 5(c), GHP leads to very satisfying denoising

Figure 3. Ten test images. From left to right and top to bottom,
they are labeled as 1 to 10.

6. Conclusion
In this paper, we presented a novel gradient histogram
preserving (GHP) model for texture-enhanced image denoising (TEID). The GHP model can preserve the gradient distribution by pushing the gradient histogram of the
denoised image toward the reference histogram, and thus
is promising in enhancing the texture structure while re-

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moving random noise. To implement the GHP model, we
proposed an efficient iterative histogram specification algorithm. Meanwhile, we presented a simple but theoretically
solid algorithm to estimate the reference gradient histogram
from the noisy image. Experimental results verify the effectiveness of GHP based TEID. The proposed GHP has
similar PSNR/SSIM measures to state-of-the-art denoising
methods such as SAPCA-BM3D, LSSC and CSR; however,
it leads to more natural and visually pleasant denoising results by preserving better the image texture areas. In the
future, we will extend GHP to image deblurring, superresolution and other image reconstruction tasks.

Acknowledgements
This work is supported by NSFC under Grant No.
61271093, the Hong Kong Scholar Program, and the program of ministry of education for new century excellent talents.

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 4. Methods comparison. (a) Noisy image with AWGN of standard deviation 30; (b) SAPCA-BM3D [16] restoration result; (c)
LSSC [21] restoration result; (d) CSR [7] restoration result; (e) GHP restoration result; (f) ground truth.

(a)

(b)

(c)

(d)

(e)

Figure 5. Results comparison with and without segmentation. (a) Top: noisy image with AWGN of standard deviation 30; bottom: a
two-region segmentation of it; (b) SAPCA-BM3D [16] restoration results; (c) GHP restoration results without segmentation; (d) GHP
restoration results with segmentation; (e) ground truth.

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