Image De-Noising Using Deep Neural Network

Advanced Computational Intelligence: An International Journal (ACII), Vol.1, No.2, October 2014
1
IMAGE DE-NOISING USING DEEP NEURAL
NETWORK
Jason Wayne
Department of Computer Engineering, University of Sydney, Sydney, Australia
ABSTRACT
Deep neural network as a part of deep learning algorithm is a state-of-the-art approach to find higher level
representations of input data which has been introduced to many practical and challenging learning
problems successfully. The primary goal of deep learning is to use large data to help solving a given task
on machine learning. We propose an methodology for image de-noising project defined by this model and
conduct training a large image database to get the experimental output. The result shows the robustness
and efficient our our algorithm.
KEYWORDS
Deep Neural Network, Image De-noising, Machine Learning, Large-scale Database
1. INTRODUCTION
Image de-noising issue could be defined as the problem of mapping from a noisy image to a
noise-free image. Various methods have been proposed for image de-noising. One approach is
linear or non-linear filtering methods which are a relatively simple approach based on smoothing,
such as Median filtering which replace each pixel with the median of the value of a set of
neighboring pixels[1], linear smoothing and wiener filtering. Another one is methods based on
wavelet or dictionary decompositions of the image. Wavelet decompositions is to transfer image
signals to an alternative domain where they can be more easily separated from the noise, such as
BLS-GSM[2]. The dictionary-based method is to de-noise by approximating the noisy patch
using a sparse linear combination of atoms, including KSVD[3] which is an iterative algorithm
that learns a dictionary on the noisy image at hand, NLSC[4] which is one of the best currently
available de-noising algorithms in terms of quality of the results, but requires long computation
times. The last one is methods based on global image statistics or other image properties, such as
self-similarities. Typical schemes include EPLL[5] and BM3D[6] which are often considered the
state-of-the-art in image de-noising.
While these models have been successfully in practice, they share a shallow linear structure.
Recent research suggests, however, that non-linear, deep models can achieve superior
performance in various real world problems. A few of deep models have also been applied to
image de-noising [7-11].
Deep learning is an emerging approach within the machine learning research community [12].
Deep learning algorithms have been proposed in recent years to move machine learning systems
towards the discovery of multiple levels of representation. Learning algorithms for deep

2
architectures are centered on the learning of useful representations of data, which are better suited
to the task at hand, and are organized in a hierarchy with multiple levels. There are several
motivations for deep architectures: Brain inspiration (several areas of the brain are organized as a
deep architecture); Cognitive arguments and engineering arguments (humans often organize ideas
and concepts in a modular way, and at multiple levels.); Sharing of statistical strength for multi-
task learning; Computational complexity [13]. In fact, it was found recently that the features
learned in deep architectures resemble those observed in the areas V1 and V2 of visual cortex
[14], and that they become more and more in variant to factors of variation in higher layers.
Learning a hierarchy of features increases the ease and practicality of developing representations
that are at once tailored to specific tasks, yet is able to borrow statistical strength from other
related tasks. Finally, learning the feature representation can lead to higher-level (more abstract,
more general) feature that are more robust to unanticipated sources of variance extant in real data.
In this paper, we present an algorithm for image restoration task that combines sparse coding and
deep networks pre-trained with de-noising auto-encoder (DAE) defined by this model, and show
that by training on large image databases we are able to outperform the current state-of-the-art
image de-noising methods. Our algorithms will first learn a large basis functions, and then
reconstruct any new input image using a weighted combination of a few of these basis functions.
The weights of these basis functions then give a slightly higher-level and more succinct
representation of the input; this representation can then be used in image restoration task.
2. OUR METHOD
The basic framework for our models is auto-encoder[12]. A basic auto-encoder is comprised of an
encoder function ()
⋅
h maps an original input d
R
x ∈ to some hidden layers and get the
representation of ( ) n
d
R
x
h ∈ , whereas a decoder ()
.
g maps this hidden representation back to the
reconstructed version of x , therefore ( )
( ) x
x
h
g ≈ . The parameters of the auto-encoders are settled
to minimize the reconstruction error, measured by the absolute loss defined as ( )
( )
( )
x
h
g
x
L , . Here,
we use squared error defined as:
( )
( )
( ) ( )
( )
( )2
, x
h
g
x
x
h
g
x
L −
= (1)
De-noising Auto-encoders [9] incorporate a slight modification to this setup and corrupt the
inputs before mapping them into the hidden representation. They are trained to reconstruct the
original input x from its corrupted version x
~ by minimizing:
( )
( )
( ) ( )
( )
( )2
, x
h
g
x
x
h
g
x
L −
= (2)
Typical choices of corruption include additive white Gaussian noise or binary masking noise. In
this work, we use the former one with standard deviation .This is a rational and non-bias choice
for natural images captured by a digital camera. The DAE architecture is shown in Figure 1.

3
Figure 1. The DAE Architecture
The auto-encoder then maps it to y and attempts to reconstruct x via decoder, resulting in the
reconstructed z . Reconstruction error is measured by loss ( )
z
x
LH , . We could then use the trained
model to get the representation of the original images.
3. FEATURE LEARNING
We performed all our experiments on grey-scale images, but there is no difficulty in generalizing
to colored images. Image de-noising aim to map a noisy image to a cleaner version. However, the
complexity of a mapping from images to images is large, so in practice we chop the image into
possibly overlapping patches and learn a mapping from a noisy patch. to a clean patch. To de-
noise a given image, all image patches are de-noised separately by that map. The de-noised image
patches are then combined into a de-noised image.
To evaluate the model we use a set of 60, 000 images from the CIFAR-bw data set. Our system
performs the following steps to feature extraction and image restoration: a. Extract random
patches from training images. b. Apply a pre-processing stage to the patches. c. Learn a feature-
mapping using stacked DAE learning algorithm. d. Train a image restoration algorithm. We will
now describe the components of this pipe line and its parameters in more detail.
3.1. Feature Learning
We have tested our approach on a benchmark image sets, namely: CIFAR-bw: a gray-scale
version of the CIFAR-100[17].The CIFAR-100 is labeled subsets of the 80 million tiny images
dataset. They were collected by Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The Sample
images are shown in Figure 2.
Figure 2. Sample Images
Next, we get corrupted images. Assuming x
~ is the observed noisy image and x is the original
noise-free image, we could then formulate the image corruption process as:
( )
x
q
x =
~ (3)

4
Where n
n
R
R
q →
: is an arbitrary stochastic corrupting process that corrupts the input x . For
most of our experiments, we use AWG noise with 25
=
σ . However, we also show results for
other noise levels.
Finally, as mentioned above, the system begins by extracting random sub-patches from input
images. Each patch has dimension n
n
N ×
= . Each n
n× patch can be represented as a vector in
N
R of pixel intensity values. We then construct a dataset of m randomly sampled patches,
( ) ( ) ( )
{ }
m
x
x
x
X ,
,
, 2
1
L
= where ( ) N
i
R
x ∈ . Given this dataset, we could apply the pre-processing and
unsupervised deep learning steps.
3.1.1. Image Pre-processing
Data pre-processing plays a important role in many deep learning algorithms. In practice, many
methods work best after the data has been normalized. In this work, we assume that every patch is
normalized by simple re-scaling, subtracting the mean and dividing by the standard deviation of
its elements. For visual data, this corresponds to local brightness and contrast normalization.
3.1.2. Feature Extraction and Selection
The basic building block of our framework is a one-layer DAE. The DAE tries to learn an
essential function ( ) x
x
h b
w ≈
~
, , which minimizes the squared reconstruction loss:
( ) ( )
( ) ( ) KL
W
x
x
h
m
b
W
J
m
i
i
b
w β
λ
+
+
−
= ∑
∑
=1
2
1
,
2
~
1
, (4)
Where
( ) ( ) ( )
( )
∑
=
=
−
−
−
+
=
=
m
i
b
w
j
j
j
j x
h
m
KL
KL
1
1
,
~
1
,
1
1
log
1
log
|| ϑ
ϑ
ρ
ρ
ϑ
ρ
ρ
ϑ
ρ (5)
The first term in the definition of ( )
b
W
J , is an average sum-of-squares error term. The second
term is a regularization term (also called a weight decay term) that tends to decrease the
magnitude of the weights, and helps prevent over fitting. The third term is a sparsity penalty term
then enforce the average activation of hidden is a small value close to zero. λ and β controls the
weights of the penalty term. We choose to minimize the squared error since it is monotonically
related to the PSNR, which is the most commonly, used measure of image quality. Thus
minimizing the squared error will maximize PSNR values. One-layer DAE is a computational
unit that takes as input x
~ , and outputs
( ) ( )
b
wx
f
x
h +
=
~ (6)
Where R
R
f →
: is activation function. In this work, we will choose ()
⋅
f to be Sigmiod function:
( )
( )
z
z
f
−
+
=
exp
1
1
. We evaluate different hidden layers, and find that it is not always beneficial to
add hidden layers. A possible explanation is that SDAE with more hidden layers become more
difficult to learn. Indeed, each hidden layer adds non-linearities to the model. It is therefore
possible that the error landscape is complex and that stochastic gradient descent gets stuck in a
poor local optimum from which it is difficult to escape. In the meantime, we try different patch
sizes and find that higher noise level generally requires larger patch size.

5
3.2. Image Restoration
We use standard testing images that have been used to evaluate other de-noising algorithms as the
testing set. To de-noise images, we decompose a given noisy image into overlapping patches. We
then normalize the patches (see Section 3.1.1), de-noise each patch separately and perform the
inverse normalization on the de-noised patches. The de-noised image is obtained by placing the
de-noised patches at the locations of their noisy counterparts, then averaging on the overlapping
regions.
After de-noising an image, we would like to know: How good is the de-noising result. A possible
solution to this problem would be to rely on human evaluation of the image quality. However,
this solution is too inconvenient for many applications. Hence, one is interested in automatic
image quality assessment and in particular in objective image quality metrics that correlate with
subjective image quality.
There are many image quality metrics, include peak signal-to-noise ration (PSNR [18]), structural
similarity index (SSIM [19]), information-content weighted PSNR (IW-PSNR [20]), the
information fidelity criterion (IFC[21]), DIIVINE[22], LBIQ[23], BIQI[24], etc. We employ
PSNR which is the most commonly used metric[25] to quantify de-noising results. The PSNR is
computed by( 2
e
σ is the mean squared error):








= 2
10
255
log
20
e
PSNR
σ
(7)
4. EXPERIMENTS
In this section, we demonstrate the results achieved by applying the above methods on several test
images. Before we present de-noising result, we first show visualizations of the learned feature
representations. The bases learned by SDAE are shown in Figure 4 for 8 pixel receptive fields.
We have compared our method to two well-known and widely-available de-noising algorithms:
KSVD [3] (a dictionary-based method) and BM3D [6] (a block matching procedure). Table 1
compares our method against KSVD and BM3D on the test set of 4 standard test images. The
result from left to right is KSVD, BM3D and our method.
Figure 3. Randomly Selected Bases

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σ Lena Barbara Boats House
10 35.5 35.9 35.8 34.4 34.9 34.1 33.6 33.9 33.8 35.9 36.7 35.9
25 31.3 32.2 32.2 29.6 30.9 29.7 29.2 30.0 29.9 32.1 32.9 32.5
50 27.4 28.9 29.2 25.2 27.2 25.3 25.9 26.8 26.9 27.4 29.7 29.6
75 24.8 27.1 27.6 22.5 25.1 23.4 23.6 25.1 25.8 24.5 27.4 27.8
The experimental results show that BM3D perform better than other methods on average.
Analyzing the outcomes of those experiments, we conclude than BM3D based on
knowledge about the image to be de-noised perform well on images with regular structure
(e.g., image “Barbara”), where as our methods based on knowledge about all images
perform well on images with complex structures(e.g., image “Lena”)or high noise levels.
5. CONCLUSION AND FUTURE RESEARCH
In this paper, we have described an algorithm for image de-noising task defined by the deep
learning framework. We have compared the results achieved by our approach against other
algorithms, and show that by training on large image databases we are able to outperform the
current state-of-the-art image de-noising methods.
In our future work, we would like to explore the possibility of adapting the proposed approach to
various other applications such as de-noising and in painting of text and audio and also find out
some math-related methods[26] to optimize the proposed algorithm. It is also meaningful to
investigate into the effects of different hyper parameter settings on the learned features.

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ACKNOWLEDGEMENTS
The authors would like to thank my adviser for her endless help and care.
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