Noname manuscript No.
(will be inserted by the editor)

Sharpness-aware Low dose CT denoising using
conditional generative adversarial network
Xin Yi · Paul Babyn

arXiv:1708.06453v2 [] 19 Oct 2017

Received: date / Accepted: date

Abstract Low Dose Computed Tomography (LDCT) has offered tremendous
benefits in radiation restricted applications, but the quantum noise as resulted
by the insufficient number of photons could potentially harm the diagnostic
performance. Current image-based denoising methods tend to produce a blur
effect on the final reconstructed results especially in high noise levels. In this
paper, a deep learning based approach was proposed to mitigate this problem. An adversarially trained network and a sharpness detection network were
trained to guide the training process. Experiments on both simulated and real
dataset shows that the results of the proposed method have very small resolution loss and achieves better performance relative to the-state-of-art methods
both quantitatively and visually.
Keywords Low Dose CT · Denoising · Conditional Generative Adversarial
Networks · Deep Learning · Sharpness · Low Contrast

1 Introduction
The use of Computed Tomography (CT) has rapidly increased over the past
decade, with an estimated 80 million CT scans performed in 2015 in the United
States [9]. Although CT offers tremendous benefits, its use has lead to significant concern regarding radiation exposure. To address this issue, the as low as
reasonably achievable (ALARA) principle has been adopted to avoid excessive
radiation dose for the patient.
X. Yi
B255, Health Science Bldg, 107 Wiggins Rd, Saskatoon, SK S7N 5E5
E-mail: xiy525@mail.usask.ca
P. Babyn
Rm 1566.1, Royal University Hospital, 103 Hospital Drive Saskatoon SK S7N 0W8
E-mail: Paul.Babyn@saskatoonhealthregion.ca

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Diagnostic performance should not be compromised when lowering the
radiation dose. One of the most effective ways to reduce radiation dose is to
reduce tube current, which has been adopted in many imaging protocols. However, low dose CT (LDCT) inevitably introduces more noise than conventional
CT (convCT), which may potentially impede subsequent diagnosis or require
more advanced algorithms for reconstruction. Many works have been devoted
to CT denoising with promising results achieved by a variety of techniques,
including those in the image, and sinogram domains and with iterative reconstruction techniques. One recent technique of increasing interest is deep
learning (DL).
DL has been shown to exhibit superior performance on many image related tasks, including low level edge detection [7], image segmentation [70],
and high level vision problems including image recognition [27], and image
captioning [62], with these advances now being brought into the medical domain [13, 14, 34, 68]. In this paper, we explore the possibility of applying
generative adversarial neural net (GAN) [23] to the task of LDCT denoising.
In many image related reconstruction tasks, e.g. super resolution and inpainting, it is known that minimizing the per-pixel loss between the output
image and the ground truth alone generate either blurring or make the result
visually not appealing [29, 38, 73]. We have observed the same effect in the
traditional neural network based CT denoising works [13, 14, 34, 68]. The adversarial loss introduced by GAN can be treated as a driving force that can
push the generated image to reside in the manifold of convCTs, reducing the
blurring effect. Furthermore, an additional sharpness detection network was
also introduced to measure the sharpness of the denoised image, with focus
on low contrast regions. SAGAN (sharpness-aware generative adversarial network) will be used to denote this proposed denoising method in the remainder
of the paper.

2 Related Works
LDCT Denoising algorithms can be broadly categorized into three groups,
those conducted within the sinogram or image domains and iterative reconstruction methods (which iterate back and forth across the sinogram and image
domains).
The CT sinogram represents the attenuation line integrals from the radial
views and is the raw projection data in the CT scan. Since the sinogram is
also a 2-D signal, traditional image processing techniques have been applied
for noise reduction, such as bilateral filtering [42], structural adaptive filtering [5], etc. The filtered data can then be reconstructed to a CT image with
methods like filtered back projection (FBP). Although the statistical property
of the noise can be well characterized, these methods require the availability
of the raw data which is not always accessible. In addition, by application of
edge preservation smoothing operations (bilateral filtering), small edges would

Title Suppressed Due to Excessive Length

3

inevitably be filtered out and lead to loss of structure and spatial resolution
in the reconstructed CT image.
Note that the above method only performs a single back projection to reconstruct the original image. Another stream of works performs an additional
forward projection, mapping the reconstructed image to the sinogram domain
by modelling the acquisition process. Corrections can be made by iterating the
forward and backward process. This methodology is referred as model-based
iterative reconstruction (MBIR). Usually, MBIR methods model scanner geometry and physical properties of the imaging processing, e.g. the photon
counting statistics and the polychromatic nature of the source x-ray [6]. Some
works add prior object information to the model to regulate the reconstructed
image, such as total variation minimization [61, 75], Markov random fields
based roughness or a sparsity penalty [8]. Due to its iterative nature, MBIR
models tend to consume excessive computation time for the reconstruction.
There are works that are trying to accelerate the convergence behaviour of
the optimization process, for example, by variable splitting of the data fidelity term [50] or by combining Nesterov’s momentum with ordered subsets
method [35].
To employ the MBIR method, one also has to have access to the raw
sinogram data. Image-based deniosing methods do not have this limitation.
The input and output are both images. Many of the denoising methods for
LDCT are borrowed from natural image processing field, such as Non-Local
means [10] and BM3D [19]. The former computes the weighted average of similar patches in the image domain while the latter is computed in a transform
domain. Both methods assume the redundancy of image information. Inspired
by these two seminal works, many applications have emerged applying them
into LDCTs [15, 16, 24, 26, 41, 71, 72]. Another line of work focuses on compressive sensing, with the underlying assumption that every local path can be
represented as a sparse combination of a set of bases. In the very beginning,
the bases are from some generic analytic transforms, e.g. discrete gradient,
contourlet [49], curvelet [11]. Chen et al. built a prior image constrained compressed sensing (PICCS) algorithm for dynamic CT reconstruction under reduced views based on discrete gradient transform [40]. It has been found that
these transforms are very sensitive to both true structures and noise. Later
on, bases learned directly from the source images were used with promising
results. Algorithms like K-SVD [2] have made dictionary learning very efficient
and has inspired many applications in the medical domain [17, 18, 39, 40, 67].
Convolutional neural network (CNN) based methods have recently achieved
great success in image related tasks. Although its origins can be traced back
to the 1980s, the resurgence of CNN can be greatly attributed to increased
computational power and recently introduced techniques for efficient training
of deep networks, such as BatchNorm [30], Rectifier linear units [21] and residual connection [27]. Chen et al. [13] first used CNN to denoise CT images by
learning a patch-based neural net and later on refined it with a encoder and
decoder structure for end-to-end training [14]. Kang et al. [34] devised a 24
convolution layer net with by-pass connection and contracting path for de-

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noising but instead of mapping in the image domain, it performed end-to-end
training in the wavelet domain. Yang et al. [68] adopted perceptual loss into
the training, which measures the difference of the processed image and the
ground truth in a high level feature space projected by a pre-trained CNN.
Suzuki et al. [59] proposed to use a massive-training artificial neural network
(MTANN) for CT denoising. The network accepts local patches of the LDCT
and regressed to the center value of the corresponding patch of the convCT.
Generative adversarial network was first introduced in 2014 by Goodfellow et al. [23]. It is a generative model trying to generate real world images
by employing a min-max optimization framework where two networks (Generator G and Discriminator D) are trained against each other. G tries to
synthesize real appearing images from random noise whereas D is trying to
distinguish between the generated and real images. If the Generator G get
sufficiently well trained, the Discriminator D will eventually be unable to tell
if the generated image is fake or not.
The original setup of GAN does not contain any constraints to control
what modes of data it can generate. However, if auxiliary information were
provided during the generation, GAN can be driven to output images with
specific modes. GAN in this scenario is usually referred as conditional GAN
(cGAN) since the output is conditioned on additional information. Mirza et al.
supplied class label encoded as one hot vector to generate MINIST digits [45].
Other works have exploited the same class label information but with different
network architecture [47, 46]. Reed et al. fed GAN with text descriptions
and object locations [51, 52]. Isola et al. proposed to do a image to image
translation with GAN by directly supplying the GAN with images [31]. In
this framework, training images must be aligned image pairs. Later on, Zhu
et al. relaxed this restriction by introducing the cycle consistency loss so that
images can be translated between two sets of unpaired samples [74]. But as also
mentioned in their paper, the paired training remains the upper bound. Pathak
et al. generated missing image patches conditioned on the surrounding image
context [48]. Sangkloy et al. generated images constrained by the sketched
boundaries and sparse colour strokes [54]. Shrivastava et al. refined synthetic
images with GAN trying to narrowing the gap between the synthetic images
and real image [57]. Walker et al. adopted a cGAN by conditioning on the
predicted future pose information to synthesize future frames of a video [64].
Two works have also applied cGAN for CT denoising. In both their works,
together with ours, the denoised image is generated by conditioning on the
low dose counterparts. Wolterink et al. employed a vanilla cGAN where the
generator was a 7 layers all convolutional network and the discriminator is a
network to differentiate the real and denoised cardiac CT using cross entropy
loss as the objective function [66]. Yang et al. adopted Wasserstein distance
for the loss of the discriminator and incorporated perceptual loss to ensure
visual similarity [69]. Using Wasserstein distance was claimed to be beneficial
at stabilizing the training of GAN but not claimed to generate images of
better quality [3, 25]. Our work differs in many ways and we would like to
highlight some key points here. First, in our work, the generator used a U-

Title Suppressed Due to Excessive Length

5

Net style network with residual components and is deeper than the other
two works. The superiority of the proposed architecture in retaining small
details was shown in our simulated noise experiment. Second, our discriminator
differentiates patches rather than full images which makes the resulted network
have fewer parameters and applicable to arbitrary size image. Third, CT scans
of a series of dose levels and anatomic regions were evaluated in this for the
generality assessment. Noise and artifacts differs throughout the body. Our
work showed that a singe network could potentially denoise all anatomies.
Finally, a sharpness loss was introduced to ensure the final sharpness of the
image and the faithful reconstruction of low contrast regions.
Sharpness Detection The sharpness detection network should be sensitive to low contrast regions. Traditional methods based on local image energy
have intrinsic limitations which is the sensitivity to both the blur kernel and
the image content. Recent works have proposed more sophisticated measures
by exploiting the statistic differences of specific properties of blur and sharp region, e.g. gradient [56], local binary pattern [70], power spectrum slope [56, 63],
Discrete Cosine Transform (DCT) coefficient [22]. Shi et al. used sparse coding to decompose local path and quantize the local sharpness with the number
of reconstructed atoms [32]. There is research that tries to directly estimate
the blur kernel but the estimated maps tend to be very coarse and the optimization process is very time consuming [76, 12]. There are other works that
can produce a sharpness map, such as in depth map estimation [77], or blur
segmentation [60], but the depth map is not necessarily corresponding to the
amount of sharpness and they tend to highlight blurred edges or insensitive
to the change of small amount of blur. In this work, we adopted the method
of [70] given its sensitivity to sharp low contrast regions. Detailed description
can be found in section 3.2.3 and 4.3.2.
The rest of the paper is organized as follows. The proposed method is
described in section 3. Experiments and results are presented in section 4 and 5.
Discussion of the potential of the proposed method is in 6 with conclusion
drawn in section 7.

3 Methods
3.1 Objective
As shown in Figure 1, SAGAN consists of three networks, the generator G,
discriminator D and the sharpness detection network S. G learns a mapping
G : x → ŷ, where x is the LDCT the generator is conditioned upon. ŷ is the
denoised CT that is expected to be as possible close as to the convCT (y)
and we call it virtual convCT here. D’s objective is to differenciate the virtual
image pair (x, ŷ) from the real one (x, y). Note that the input to D is not just
the virtual (ŷ) and real convCT (y), but also LDCT (x). x is concatenated to
both y and ŷ and is served as additional information for D to rely on so that
D can penalize the mismatch. In simpler term, G tries to synthesize a virtual

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Xin Yi, Paul Babyn

Virtual
or Real
Pair?
Virtual Pair

Real Pair

(x, ŷ)

(x, y)

Ladv (G, D)

D

Same
Sharpness?

LDCT

x

G

Virtual convCT

convCT

ŷ

y

Virtual convCT

Lsharp (G)

S

ŷ

Same Content?
Virtual convCT

convCT

ŷ

y

LL (G)
1

Fig. 1: Overview of SAGAN. G is the generator that is responsible for the
denoising. D is the discriminator employed to discriminate the virtual and
real image pairs. S is a sharpness detection network and used to compare
between the sharpness of the generated and real image. The system accepts
the LDCT x and convCT y as the input and outputs virtual convCT (noise
removed) ŷ.

convCT that can fool D whereas D tries to not get fooled. The training of G
against D forms the adversarial part of the objective, which can be expressed
as
Ladv (G, D) = Ex,y∼pdata (x,y) [(D(x, y) − 1)2 ] + Ex∼pdata (x) [D(x, ŷ)2 ],
G is trying to minimize the above objective whereas D is trying to maximize
it. We adopt the least square loss instead of cross entropy loss in the above
formulation because the least square loss tend to generate better images [43].
This loss is usually accompanied by traditional pixel-wise loss to encourage
data fidelity for G, which can be expressed as
LL1 (G) = Ex,y∼pdata (x,y) [||y − ŷ||L1 ],
Moreover, we proposed a sharpness detection network S to explicitly evaluate the denoised image’s sharpness. The generator now not only has to fool
the discriminator by generating a image with similar content to the real convCT in a L1 sense, but also has to generate a similar sharpness map as close
as to the real convCT. With S denoting the mapping from the input to the
sharpness map, the sharpness loss can be expressed as:
Lsharp (G) = Ex,y∼pdata (x,y) [||S(ŷ) − S(y)||L2 ],

Title Suppressed Due to Excessive Length

7
×K

n128s2

n256s2

n128s1

n128s2

n64s2
n1s1

+

n64s1

1 × 256 × 256

256 × 128 × 128

64 × 256 × 256

128 × 256 × 256
1 × 256 × 256

128 × 128 × 128

256 × 64 × 64

1 × 256 × 256‘

256 × 64 × 64

···

LDCT

Virtual convCT

Convolution
LeakyRelu

Relu

Batch Normalization

Tanh

Deconvolution

Fig. 2: Proposed generator of the SAGAN. The residual block in the center of
the network is repeated K times and K was chosen as 9 for the experiment.

Combining these three losses together, the final objective of SAGAN is
LSAGAN = arg min max(Ladv (G, D) + λ1 LL1 (G) + λ2 Lsharp (G)),
G

D

where λ1 and λ2 are the weighting terms to balance the losses. Note that in
the traditional GAN formulation, the generator is also conditioned on random
noise z to produce stochastic outputs. But in practice, people have found
that the adding of noise in the conditional setup like ours tends to be not
effective [31, 44]. Therefore, in the implementation we have discarded z so
that the network only produces deterministic output.

3.2 Network Architecture
3.2.1 Generator
There are several different variants of generator architecture that have been
adopted in the literature for image-to-image translation tasks; the EncoderDecoder structure [28], the U-Net structure [53, 31], the Residual net structure [33] and one for removing of rain drops (denoted as Derain) [73]. The
Encoder-Decoder structure has a bottleneck layer that requires all the information pass through it. The information consolidated by the encoder only
encrypts the global structure of the input while discarding the textured details. U-Net is similar to this architecture with a slight difference in that it adds
long skip connections from encoder to decoder so that fine-grained details can
be recovered [53]. The residual components, first introduced by He et al. [27]
is claimed to be better for the training of very deep networks. The reason is
that the short skip connection of the residual component can directly guide

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Xin Yi, Paul Babyn

the gradient flow from deep layer to the shallow layer [20]. Later, we start to
see many works incorporating the residual block into the network architecture [54, 73, 74, 33] when the network gets deep. The Detain architecture and
its variants [69] share a common property which is that they maintained the
spatial size of the feature maps during the processing. An adverse effect of this
is that the number of feature maps need to remain small to avoid consuming
too much memory.
Applications like style transfer do not require preservation of local textures
and details of the content image (textures come from the style image) [33].
Therefore its rare to see long skip connections used in their network structure.
However, for CT noise removal, the recovery of the underlying detail is of
vital importance since the subtle structure could be a lesion that can develop
into cancer. Therefore, in this work we adopted the unet256 structure [31]
with long skip connections. The kernel stride is 1 for the first stage feature
extraction with no downsampling. We also incorporate several layers of the
residual connection in the bottle neck layers for stabilizing the training of the
network. Note that the feature of the bottleneck layers’ spatial dimension is
not reduced to 1 × 1 as in the Encoder-Decoder structure to reduce the model
size (similar to SegNet [4]) and we do not observe any significant performance
drop by doing this. The architecture can be seen in Figure 2. An experiment
to compare the different generator architecture can be found in section 5.1.
3.2.2 Discriminator
The objective of the discriminator is to tell the difference between the virtual
image pair (x, ŷ) and the real image pair (x, y). Here, we adopt the PatchGAN
structure from pix2pix framework [31], where instead of classifying the whole
image as real or virtual, it will focus on overlapped image patches. By using
G alone with L1 or L2 loss, the architecture would degrade to a traditional
CNN-based denoising methods.
3.2.3 Sharpness detection network
Bluring of the edges are a major problem faced by many image denoising methods. For traditional denoising methods using non-linear filtering, the edges will
be inevitably blurred no matter by averaging out neighbouring pixels or selfsimilar patches. It is even worse in high noise settings whereas noise can also
produce some edge-like structures. Neural network based methods could also
suffer the same problem if optimizing the pixel-wise differences between the
generated image and the ground truth, because the result that averages out all
possible solutions end up giving the best quantitive measure. The adversarial
loss used introduced by the discriminator of GAN is able to output a much
sharper and recognizable image from the candidates. However, the adversarial
loss does not guarantee the images to be sharply reconstructed, especially for
low contrast regions.

Title Suppressed Due to Excessive Length

9

We believe that auxiliary guided information should be provided to the
generator so that it can recover the underlying sharpness of the low contrast
regions from the contaminated noisy image, as similar to the frontal face predication [29] where the position of facial landmarks are supplied to the network.
Since the direct markup of low contrast sharp regions is not practical for
medical images, an independent sharpness detection network S was trained in
this work. During the training of SAGAN, the virtual convCT generated from
G is sent to S and the output sharpness map is compared with the map of
the ground truth image. We compute the mean square error between the two
sharpness maps and this error was back-propagated through the generator to
update its weights.

4 Experiment Setup
The proposed SAGAN was applied to both simulated low dose and real low
dose CT images to evaluate its effectiveness. In both settings, peak signal to
noise ratio (PSNR) and structured similarity index (SSIM) [65] were adopted
as the quantitive metrics for the evaluation (using abdomen window image).
The former metric is commonly used to measure the pair-wise difference of two
signals whereas the SSIM is claimed to better conform to the human visual
perception. For the real dataset, the mean standard deviation of 42 smooth
rectangular homogeneous regions (size of 21 × 21, 172.27 mm2 ) were computed
as direct measures of the noise level.
To further evaluate the general applicability of the proposed method, we
selected two patient’s LDCTs from the Kaggle Data Science Bowl 2017 [1] and
applied our trained model to it. Visual results and noise levels are provided
for evaluation in this case. 20 Rectangular homogeneous regions of size 21 × 21
were selected for the calculation.

4.1 Simulated Noise Dataset
In this dataset, 239 normal dose CT images were downloaded from the National
Cancer Imaging Archive (NBIA). Each image has a size of 512 × 512 covering
different parts of the human body. A fan-beam geometry was used to transform
the image to the sinogram, utilizing 937 detectors and 1200 views.
The photons hitting the detector are usually treated as Possion distributed.
Together with the electrical noise which starts to gain prominence in low dose
cases and is normally Gaussian distributed, the detected signal can be expressed as:
N ∼ Poisson(N0 exp(−y)) + Gaussian(0, σe2 ),
(1)
where N0 is the X-ray source intensity or sometimes called blank flux, y is the
sinogram data, and σe is the standard deviation of the electrical noise [71, 37].
The blank scan flux N0 was set to be 1 × 105 , 5 × 104 , 3 × 104 , 1 × 104 to
simulate effect of different dose levels and the electrical noise was discarded for

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Xin Yi, Paul Babyn

Table 1: Detailed doses for the piglet and phantom datasets.
Dose level

Full

50%

25%

10%

5%

Tube current (mAs)

300

150

75

30

15

CTDIvol (mGy)

30.83

15.41

7.71

3.08

1.54

DLP (mGy-cm)

943.24

471.62

235.81

94.32

47.16

Effective dose (mSv)

14.14

7.07

3.54

1.41

0.71

(a) Doses used for the piglet dataset. In all 5 series, tube potential was 100
kV with 0.625 mm slice thickness. Tube currents were decreased to 50%, 25%,
10%, 5% of full dose tube current (300mAs) to obtained images with different
doses.

Scan series

Full

3.33%

Tube current (mAs)

300

10

CTDIvol (mGy)

26.47

0.88

(b) Doses used for the Catphan 600 dataset. In both series, tube potential is
120 kV with 0.625 mm slice thickness.

simplicity. Since the network used is fully convolutional, the input can be of
different size. Each image was further divided into four 256 × 256 sub-images
to boost the size of the dataset. 700 out of the resultant 956 sub-images were
randomly selected as the training set and the remaining 64 full images were
used as the test set. Some sample images are shown in the first column of
Figure 5. Note that the simulated dose here is generally lower than that of
[14].

4.2 Real Datasets
CT scans of a deceased piglet were obtained with a range of different doses
utilizing a GE scanner (Discovery CT750 HD) using 100 kVp source potential
and 0.625 mm slice thickness. A series of tube currents were used in the scanning to produce images with different dose levels, ranging from 300 mAs down
to 15 mAs. The 300 mAs served as the conventional full dose whereas the
others served as low doses with tube current reductions of 50%, 25%, 10% and
5% respectively. At each dose level we obtained 850 images of a size 512 × 512
in total. 708 of them were selected for training and 142 for testing. The training size of the real dataset was also boosted by dividing each image into four
256 × 256 sub-images, giving us 2832 images in total for training.

Title Suppressed Due to Excessive Length
convCT

σ = 0.5

σ = 1.0

11
σ = 1.5

σ = 2.0

Fig. 3: The output of the sharpness detection network. The upper row is
the convCT of a lung region selected from the piglet dataset and its blurred
versions with increasing amount of Gaussian blur (σ shown on top). The lower
row shows their corresponding sharpness map.

A CT phantom (Catphan 600) was scanned to evaluate the spatial resolution of the reconstructed image, using 120 kVp and 0.625mm slice thickness.
For this dataset, only two dose levels were used. The one with 300 mAs served
as the convCT and the one with 10mAs served as the LDCT. The detailed
doses is provided in Table 1.
Data Science Bowl 2017 is a challenge to detect lung cancer from LDCTs.
It contains over a thousand high-resolution low-dose CT images of high risk
patients. The corresponding convCTs and specific dosage level for each scan
are not available. We selected two patients’ scan to evaluate the generality of
the proposed SAGAN method on unseen doses.
Four experiments were conducted. In the first experiment, we evaluated
the effect of the generator and the sharpness loss by using the simulated noise
dataset. In the second experiment, we evaluated the spatial resolution with
the Catphan 600 dataset. In the third experiment the proposed SAGAN was
applied on the piglet dataset to test its effectiveness on a wide range of real
quantum noise. Finally in the last experiment, the SAGAN model trained on
the piglet dataset was applied to the clinical patient data in the Data Science
Bowl 2017. Two state-of-the-art methods: BM3D, K-SVD from two major
line of traditional image denoising methods were selected for the comparison.
For the real dataset, the available CT manufacture iterative reconstruction
methods, ASIR (40%) and VEO were also compared. All experiments on the
real datasets are trained on the full range DICOM image.

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Xin Yi, Paul Babyn

Table 2: Comparison of different generator architecture on the simulated
dataset. The input noise level in terms of PSNR and SSIM is shown in the top
row.
Generator
Archetecture

unet256
res9
derain
proposed

N0 = 10000

N0 = 30000

N0 = 50000

N0 = 100000

PSNR
18.3346

SSIM
0.7557

PSNR
21.6793

SSIM
0.7926

PSNR
23.1568

SSIM
0.8119

PSNR
24.8987

SSIM
0.8387

26.2549
25.9032
25.8094
26.6584

0.8384
0.8412
0.8376
0.8438

27.5819
26.7443
26.4167
27.3066

0.8598
0.8549
0.8505
0.8533

27.9269
27.8765
27.1724
27.8443

0.8646
0.8710
0.8562
0.8622

28.1243
28.8179
27.1307
28.1718

0.8711
0.8877
0.8570
0.8701

4.3 Implementation Details
4.3.1 Training of SAGAN
All the networks are trained on the Guillimin cluster of Calcul Quebec and the
Cedar cluster of Compute Canada. Adam optimizer [36] with β1 = 0.5 was used
for the optimization with learning rate 0.0001. The generator and discriminator
was trained alternatively across the training with k = 1 as similar in [23]. The
implementation was based on the Torch framework. The training images have
size of 256 × 256 whereas the testing is with full size 512 × 512 CT images. All
the networks here are trained to 200 epochs. λ1 was set to be 100 and λ2 to
0.001. For the simulated dataset, one SAGAN was trained for each simulated
dose. For the real dataset, one SAGAN was trained for the piglet and phantom
separately, with the training set of different doses of piglet combined.

4.3.2 Training of the sharpness detection network
The sharpness detection network follows the work of Yi et al. [70]. In that
work, Yi et al. used a non-differentiable analytic sharpness metric to quantify
the local sharpness of a single image. Here in this work, we trained a neural
network to imitate its behaviour. To be more specific, the defocus segmentation
dataset [55] that contains 704 defocused images was adopted for the training.
5 subimages of size 256 × 256 were sampled from the 4 corners and centre of
each defocus image to boost the size of the training set. For the training of
the sharpness detection network, the unet256 structure was adopted and the
sharpness map created by the local sharpness metric of [70] was used for regression. Adam optimizer [36] with β1 = 0.5 was also used for the optimization
with learning rate also 0.0001. Some sample images and their sharpness map
can be seen in Figure 3.

Title Suppressed Due to Excessive Length

LDCT

convCT

unet256

13

res9

derain

proposed
generator

Fig. 4: Evaluation of the generator architecture. LDCT is with N0 = 10000.
5 Results
5.1 Analysis of the generator architecture
A variety of generator architectures were evaluated, including unet256 [53],
res9 [33], Derain [73]. In the analysis, only the architecture of the generator
was modified. The discriminator was fixed to be the patchGAN with patch size
of 70×70 [31]. The sharpness network was not incorporated in this experiment
for simplicity.
The quantitative results are shown in Table 2. As can be seen that the performance generally improves when lowering the noise level (increase of N0 ) no
matter what architecture has been used. For every single noise level, the listed
generators achieved comparative results since all of them optimized the PSNR
as part of their loss function. However, the visual results shown in Figure 4
have shed some light on the architectural differences. Comparing the unet256
with the proposed, we can see that the proposed recovered the low contrast
zoom region much sharper. It shows the benefits of maintaining the spatial
size during the first stage of feature extraction. The major difference of res9
and the proposed one is the long skip connection. We can see by comparing
results of the two that this connection can help recovering small details. As for
the derain architecture, the training was not stable and some grainy artifacts
can be observed. We attribute this to the small size of the feature dimension
of the bottleneck layer (only 1 in this case) which is not sufficient to encode
the global features.

5.2 Analysis of the sharpness loss
In this experiment, we evaluated the effectiveness of the sharpness loss on the
denoised result. Table 3 shows quantitive results before and after applying
the sharpness detection network. The values in term of PSNR and SSIM are
comparable to each other with slight differences that can be explained by

14

Xin Yi, Paul Babyn

Table 3: Quantitive evaluation of the sharpness-aware loss.
N0 = 10000

Methods

N0 = 30000

N0 = 50000

N0 = 100000

PSNR
18.3346

SSIM
0.7557

PSNR
21.6793

SSIM
0.7926

PSNR
23.1568

SSIM
0.8119

PSNR
24.8987

SSIM
0.8387

w/o sharpness loss
w sharpness loss (SAGAN)

26.6584
26.7766

0.8438
0.8454

27.3066
27.5257

0.8533
0.8571

27.8443
27.7828

0.8622
0.8620

28.1718
28.2503

0.8701
0.8708

BM3D
K-SVD

24.0038
21.9578

0.8202
0.7665

25.6046
24.0790

0.8485
0.8167

26.0913
25.0425

0.8589
0.8379

26.7598
26.0902

0.8726
0.8620

LDCT

convCT

w/o sharp loss

w sharp loss
(SAGAN)

BM3D

K-SVD

Fig. 5: Visual examples to evaluate the effectiveness of the proposed sharpness
loss with N0 = 10000. Row 1 and 3 are two examples with zoomed region
shown below.

the competition of the data fidelity loss and the sharpness loss. However,
visual examples shown in Figure 5 clearly demonstrates that the sharpness
loss excels at suppressing noises on small structures without introducing too
much blurring.

5.3 Denoising results on simulated dataset
As can be also seen from Table 3 and Figure 5, the performance of SAGAN
in terms of PSNR and SSIM is better than BM3D and K-SVD in all noise
levels. For the visual appearance, SAGAN is also sharper than BM3D and K-

Title Suppressed Due to Excessive Length

15

SVD and can recover more details. K-SVD could not remove all the noise and
sometimes make the resultant image very blocky. For example, in the zoomed
region of row 1 of Figure 5, the fat region of SAGAN is the sharpest among
the comparators. In row 2, we have shown that the low contrast vessel can
be faithfully reconstructed by SAGAN whereas missed by the other methods.
The streak artifact is another problem faced by BM3D in high quantum noise
level as has already been pointed out by many works [14, 34]. We recommend
the reader to zoom in for better appreciation of the results.

5.4 Denoising results on Catphan 600
Figure 6 gives the denoised visual result for the CTP 528 21 line pair high
resolution module of the Catphan 600. The 4 and 5-line pairs is clearly distinguishable for LDCT and we can observe these line pairs equally well on
SAGAN reconstructed images which suggests that the amount of spatial resolution loss is very small. 6-line pairs is distinguishable from the convCT but
not the case for LDCT and all the reconstruction methods, which highlights
the gap between the reconstruction methods and the convCT. Figure 7 shows
the line profile along the line drawn across the 4 and 5-line pairs. 30 points
were sampled along the drawn line. SAGAN is the one among the comparative
methods that achieves the highest spatial resolution. K-SVD behaves slightly
better than BM3D and VEO demonstrates the lowest spatial resolution.

5.5 Denoising results on the real piglet dataset
Here we plotted a line graph of the PSNR and SSIM against the dosage in Figure 9 for all the comparator methods. It can be seen that all methods except
VEO have their performance improved with the increase of dose in terms of
PSNR. SSIM is less affected because it penalizes structural differences rather
LDCT

convCT

SAGAN

VEO

BM3D

KSVD

4-lp
5-lp
6-lp

Fig. 6: Visual comparison of the spatial resolution on the CTP 528 high resolution module of the Catphan 600. Images are trained and tested on the full
range DICOM image. Display window is [40, 400] HU.

16

Xin Yi, Paul Babyn
800

m
p/c

5-l

CT Number (HU)

4-lp/cm

CT Number (HU)

600

400

200

4-lp/cm

0
0

10

400

200

0
20

30

5-lp/cm
0

Point

VEO

(a)

LDCT

10

20

30

Point

ConvCT

BM3D

SAGAN

K-SVD

(b)

Fig. 7: (a) shows the convCT of the CTP 528 high resolution module of the
Catphan 600. (b) shows the line profile for the 4-line pair per centimeter and
5-line pair per centimeter of different reconstruction methods. 30 data points
were sampled along the red line as marked in (a).

than the pixel-wise difference. The average SSIM measure in the lowest dose
level for SAGAN is 0.95 which is slightly higher than that of the second highest dose level for FBP. Figure 8 shows some visual examples from different
anatomic region (from head to pelvis) at the lowest dose level and their reconstruction by all the comparator methods. We can see clearly that SAGAN
produces results that are more visually appealing than the others.
Figure 9 also shows the mean standard deviation of CT numbers on 42 hand
selected rectangular homogeneous regions as a direct measure of noise level.
The red horizontal dashed line is the performance of the convCT and serves
as reference and it can be seen that the available commerical methods do not
surpass the reference line. In general, the mean standard deviation of SAGAN
results are pretty constant across all dose levels and very close to the convCT. It implicitly shows that SAGAN can simulate the statistical properties
of convCT. BM3D and K-SVD on the other hand obtained smaller numbers
by over-smoothing the result images. At the highest noise level, the measure
was 25.35 for FBP and 8.80 for SAGAN, corresponding to a noise reduction
factor of 2.88. Considering both the quantitative measures and the visual appearance, SAGAN is no doubt the best method among the comparators in the
highest noise level.

5.6 Denoising results on the clinical patient data with unknown dose level

1

Figure 10 shows the results on the clinical patient data with unknown dose
levels. The dose level of these data are unlikely to coincide with the dose level
of our training set but we can see that it performs reasonable well on these
images with increased CNR.
1

Testing code is available at https://github.com/xinario/SAGAN

Title Suppressed Due to Excessive Length
LDCT

convCT

SAGAN

17
VEO

ASIR

BM3D

K-SVD

Fig. 8: Visual examples for the denoised images on the piglet dataset. Rows
are 3 selected samples from pelvis to head each with a zoomed up local region.
The first column is the LDCT (5% of full dose reconstructed by FBP, 0.71
mSv). The second column is the convCT (100% dose reconstructed by FBP,
14.14 mSv). The last 5 columns are results from different denoising methods.
Display window is [40, 400].

6 Discussion
These quantitative results demonstrate that SAGAN excels in recovering underlying structures in great uncertainty. The adversarially trained discriminator guarantees the denoised texture to be close to convCT. This is an advantage over VEO, which produces a different texture. The sharpness detection
network guarantees that the generated CT is with similar sharpness as the
convCT. Another advantage is time efficiency. Neural network based methods, including SAGAN only need one forward pass in the testing and the task
could be accomplished in less than a second. BM3D showed better denoising
at the highest dose, however SAGAN was better at lower doses. BM3D and
K-SVD also had evident streak artifacts across the image surface at low doses
as seen in Figure 3.

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Xin Yi, Paul Babyn

35

Mean Standard Deviation (HU)

0.98

SSIM

PSNR

0.96

0.94

30
0.92

102

103

102

DLP (mGy-cm)

VEO

20

10

102

103

ASIR

FBP

103

DLP (mGy-cm)

DLP (mGy-cm)

BM3D

SAGAN

K-SVD

Fig. 9: The left two figures show the PSNR and SSIM plotted against doselength product (DLP) for different reconstruction methods for the piglet
dataset. The rightmost figure gives the mean standard deviation of image
noise against dose-length product (DLP) for different reconstruction methods.
Red dashed line refers to the standard deviation of the FBP reconstructed
convCT.
LDCT (17.06)

(a)

SAGAN (8.72)

LDCT (22.98)

SAGAN (9.83)

(b)

Fig. 10: SAGAN denoising results on the clinical patient data (from the Kaggle
Data Science Bowl 2017) with unknown dose levels. Image pairs of (a), (b)
come from 2 different patients. The noise level of the liver in (a) and lung
nodule in (b) were shown below the images. Display window of is [40, 400] HU
for (a) and [-700, 1500] HU for (b). Numbers in the braces are the noise level
computed from 20 homogeneous regions selected from the patient scan.

Another phenomenon we have observed is that the SAGAN can also help
to mitigate the streak artifacts. As can be seen from the first row of Figure 5,
the lower half of the convCT had mild streak artifacts but was less evident
in the SAGAN result (4th column). The reason we think is that the discriminator discriminates patches and the number of patches containing artifacts is

Title Suppressed Due to Excessive Length

19

significantly smaller than the number of normal ones. Therefore these patches
were considered as outliers in the discrimination process. A straightforward
extension of this work would be for limited view CT reconstruction.
The proposed generator here adopts the Unet[53, 31] architecture and incorporates the residual connection for the ease of training. We have empirically
demonstrate its effectiveness on the denoising task and have observed much
more stable training statistics than the comparators in the adversarial training
scheme.
The sharpness-aware loss proposed here is similar to the methodology of the
content loss as used in [33, 38] but differs in the final purpose. The similarity
lies in that we both measure the high-level features of the generated and input
image. In their work, the high-level features are from the middle layer of the
pre-trained VGG network [58] and used to ensure the perceptual similarity. On
the contrary, the high-level features used here are extracted from a specifically
trained network and directly correspond to the visual sharpness.
The work of Wolterink et al. [66] and Yang et al. [69] also employed GAN for
CT denoising and some technical differences from ours have been highlighted
in section 2. Here we also want to emphasize two of their weaknesses. These two
works either centered on cardiac CT or abdominal CT. It is not clear whether
their trained model can be applied to CTs of different anatomies. Our work
considered a wider range of anatomic regions ranging from head to pelvis and
has demonstrated that a single network in cGAN setting would be sufficient
to denoise CT of the whole body. Moreover, their work only employed a single
dose level in the training whereas ours covered a wider range of dose levels.
We have also empirically shown that the trained model not only suitable for
denoising images with the training dose level but also applicable to unseen
dose levels as long as the noise level is within our training range.
The dose reduction achieved by SAGAN is very high. According to the
measurement of PSNR and SSIM, SAGAN reconstructed result in the lowest
dose level has a measurement almost equivalent to the CT in the second highest
dose level (7.07 mSv), corresponding to a dose reduction of 90%. Meanwhile if
we measure the dose reduction factor with respect to the mean standard deviation of attenuation, SAGAN’s result in the lowest dose level (0.71 mSv) has a
noise level similar to that of the convCT (14.14 mSv), corresponding to a dose
reduction of 95%. Each measurement has their own strengths and weaknesses
in measuring the CT image quality. PSNR and SSIM take into consideration
the spatial information but would penalize a lot of the texture difference even
with similar underlying image content. For example, although VEO has been
shown to have superior performance in many clinical studies than ASIR and
FBP and has received clearance released by the Food and Drug Administration of the USA, it obtained the worst PSNR and SSIM measurements. On the
other hand, mean standard deviation of attenuation direct measures the noise
level, but completely discarded the spatial information. Therefore, we reported
both results for the sake of fair comparison. The work of Suzuki et al. [59] reported a dose reduction of 90% from 1.1 mSv to 0.11 mSv with MTANN. Their
network is patched based and need to train multiple networks corresponding to

20

Xin Yi, Paul Babyn

different anatomic regions. It is unclear how much dose reduction was achieved
for the other deep learning based approaches [68, 34, 14, 66].
We evaluated the spatial resolution of the reconstructed image using the
Catphan 600 high resolution module. This analysis was generally missed for
the other deep learning based approaches. These methods could achieve high
PSNR and SSIM by directly treat them as the optimization objective but at the
cost of losing spatial resolution. GAN based methods, including ours mitigate
this problem by incorporating the adversarial objective. We think it is crucial
to bring the spatial resolution into assessment for the deep learning based
approaches when PSNR and SSIM become less effective. An alternative way
of quantifying the denoising performance would be to measure the performance
of subsequent higher level tasks, e.g. lung nodule detection, anatomical region
segmentation. We would like to leave this to the future work.
7 Conclusion
In this paper, we have proposed sharpness aware network for low dose CT
denoising. It utilizes both the adversarial loss and the sharpness loss to leverage the blur effect faced by image based denoising method, especially under
high noise levels. The proposed SAGAN achieves improved performance in
the quantitative assessment and the visual results are more appealing than
the tested competitors.
However, we acknowledge that there are some limitations of this work that
are waiting to be solved in the future. First of all, the sharpness detection
network is trained to compute the sharpness metric of [70] which is not very
sensitive to just noticeable blur. This could limit the final sharpness of the
denoised image, especially some small low contrast regions.
Second, for all the deep learning based methods, the network need to be
trained against a specific dosage level. Even though we trained our method on
a wild range of doses and have applied it to clinical patient data, the analysis
is mostly centred on the visual quality assessment of the denoised image. The
image diagnosis performance in clinical practice remains to be evaluated.
Acknowledgements The authors would like to thank Troy Anderson for the acquisition
of the piglet dataset.

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