unpaired low-dose ct denoising network based on cycle...

Research ArticleUnpaired Low-Dose CT Denoising Network Based onCycle-Consistent Generative Adversarial Network with PriorImage Information

Chao Tang Jie Li LinyuanWang Ziheng Li Lingyun Jiang Ailong CaiWenkun ZhangNingning Liang Lei Li and Bin Yan

PLA Strategy Support Force Information Engineering University Zhengzhou Henan Province 450001 China

Correspondence should be addressed to Bin Yan ybspacehotmailcom

Received 1 July 2019 Revised 2 September 2019 Accepted 16 September 2019 Published 7 December 2019

Guest Editor Adam Konefal

Copyright copy 2019 Chao Tang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e widespread application of X-ray computed tomography (CT) in clinical diagnosis has led to increasing public concernregarding excessive radiation dose administered to patients However reducing the radiation dose will inevitably cause servernoise and affect radiologistsrsquo judgment and confidence Hence progressive low-dose CT (LDCT) image reconstruction methodsmust be developed to improve image quality Over the past two years deep learning-based approaches have shown impressiveperformance in noise reduction for LDCT images Most existing deep learning-based approaches usually require the pairedtraining dataset which the LDCT images correspond to the normal-dose CT (NDCT) images one-to-one but the acquisition ofwell-paired datasets requires multiple scans resulting the increase of radiation doseerefore well-paired datasets are not readilyavailable To resolve this problem this paper proposes an unpaired LDCT image denoising network based on cycle generativeadversarial networks (CycleGAN) with prior image information which does not require a one-to-one training dataset In thismethod cyclic loss an important trick in unpaired image-to-image translation promises to map the distribution from LDCT toNDCT by using unpaired training data Furthermore to guarantee the accurate correspondence of the image content between theoutput and NDCT the prior information obtained from the result preprocessed using the LDCT image is integrated into thenetwork to supervise the generation of content Given the map of distribution through the cyclic loss and the supervision ofcontent through the prior image loss our proposed method can not only reduce the image noise but also retain critical in-formation Real-data experiments were carried out to test the performance of the proposed methode peak signal-to-noise ratio(PSNR) improves by more than 3 dB and the structural similarity (SSIM) increases when compared with the original CycleGANwithout prior information e real LDCT data experiment demonstrates the superiority of the proposed method according toboth visual inspection and quantitative evaluation

1 Introduction

X-ray computed tomography (CT) is one of the most sig-nificant imaging modalities in modern hospitals and clinicsHowever the risk of radiation in CT induces genetic can-cerous and other diseases and has become a critical concernto patients and operators [1ndash3]] A common and effectivestrategy to alleviate the risk is to achieve low-dose CT(LDCT) imaging by reducing the tube current duringscanning and consequently decreasing the number ofphotons received by the detector e dose reduction

increases noise and artifacts in reconstructed CT imagesthereby severely degrading the image quality and jeopard-izing the clinical diagnosis To solve this problem re-searchers have proposed various noise-reduction strategiesincluding iterative reconstruction (IR) [4 5] sinogramdomain denoising [6ndash9] and image domain postprocessing[10ndash12]

Over the past decades researchers have focused ondeveloping new iterative algorithms for LDCT image re-construction In general these algorithms optimize an ob-jective function which incorporates a systemmodel [13 14]

HindawiComputational and Mathematical Methods in MedicineVolume 2019 Article ID 8639825 11 pageshttpsdoiorg10115520198639825

a statistical noise model and prior information in the imagedomain [4 15 16] Well-known image priors consist of totalvariation (TV) and its variants [17ndash19] dictionary learning[20 21] and wavelet frame [22] ese iterative re-construction algorithms exhibit satisfactory performance inimproving image quality but their computational burdenand sensitive parameters limit their practical applications

Image postprocessing is more computationally efficientcompared with iterative reconstruction which has spawneda lot of simple and effective methods Nonlocal means(NLM) filtering methods estimate noise components byusing multiple patches extracted at different locations in theimage [23] and have been widely used for CT [24] Moti-vated by compressed sensing methods an adaptive K-SVDmethod [25] was proposed to reduce artifacts in CT re-constructions e block matching 3D (BM3D) method isalso an outstanding method for image postprocessing in CTimaging fields [26 27] this method exploits similarities inimage blocks ese traditional postprocessing methodshave improved the quality of CT images however the resultsoften undergo edge blurring andor residual artifacts giventhe nonuniform distribution of reconstruction noise

More recently several supervised machine learningapproaches have been proposed for noise reduction inLDCT ese methods usually reveal a relation between thepixel value in the LDCT image and the pixel value at thesame location in a corresponding NDCT image by trainingwith paired images Chen et al [28] designed a deep con-volutional neural network (CNN) to map LDCT imagestoward its relative normal-dose counterparts in a patch-by-patch manner Kang et al [29] used a similar method butadopted CNN to directional wavelet transform of CTimagesen more complex networks were proposed to handle theLDCT denoising problem such as the residual encoder-decoder convolutional neural network (RED-CNN) in [30]which achieves competitive performance relative to state-of-the-art methods in clinical cases

Although the abovementioned networks presented im-pressive denoising results they all belong to the end-to-endnetwork which typically utilizes mean squared errors (MSE)between the network output and the ground truth as lossfunction However recent studies [31 32] indicated that thisper-pixel MSE often suffers from oversmoothed edges andloss of details MSE-based approaches tend to take the meanof high-resolution patches by using Euclidean distancerather than geodesic distance Given that the medical imagesusually lie in a highly nonlinear manifold [33] the algorithmis prone to neglect subtle details that are vital for clinicaldiagnosis when it tries to minimize per-pixel MSE Toovercome the limitations of per-pixel regression in noisereduction the generative adversarial network (GAN) [34]based on adversarial loss is introduced to medical imagereconstruction In 2017 Wolterink et al [35] were the first toapply the GAN for cardiac CT image reconstruction AndYang et al [36] utilized a GAN with Wasserstein distance(WGAN) In order to enhance the capability of noise re-duction perceptual loss is simultaneously used to optimizethe loss function Yi and Babyn [37] combined an adversarialtrained network and a sharpness detection network to

mitigate noise in LDCT and achieved satisfactory perfor-mance Hence a general framework for estimating gener-ative models by using an adversarial process has shownoutstanding performance in medical image reconstruction

e above-mentioned denoising networks usually re-quire spatially paired counterparts However in medicalimaging well-paired counterparts are difficult to obtainFor example in LDCT imaging continuously scanning apatient twice in normal and low dose is impossible undernormal circumstances e shortage of paired data has beenone of the factors that restrict the wide application of deeplearning in low-dose CT reconstruction Recently un-supervised variants of GANs such as CycleGAN [38] andDualGAN [39] have been proposed for mapping differentdomains without matching data pairs Motivated by theirsuccess in image processing unpaired GANs have beensuccessfully applied to CS-MRI reconstruction [40] and CTsynthesis based on MR images [41 42] For LDCT re-construction well-paired clinical scans acquired at differentdose levels are not readily available Even if we obtain thesame patient data at different dose levels the data are difficultto match perfectly due to physical activity and the inevitableslight movement of the scanning position which may affectthe denoising ability of the networks

In this study we propose an unpaired LDCT denoisingnetwork based on CycleGAN with prior image informationIn the proposed network the design of cycle-consistentstructure impels the network to learn the mapping re-lationship between the LDCT image collection and NDCTimage collection (Figure 1(a)) rather than an image pair ofan LDCT image and NDCT image (Figure 1(b)) ereforethe proposed network does not need a one-to-one corre-sponding training dataset and can learn with the unpaireddataset Meanwhile the prior image information extractedfrom the preprocessed image by using LDCT is introducedinto the network to supervise the generation of content andensure correspondence of the image content e map ofimage collections through cyclic loss and the supervision ofcontent through prior image loss confer our proposedmethod to produce results that have not only lower noise butalso accurate details

2 Methods

21 Noise ReductionModel In LDCT imaging serious noisetypically occurs in CT images as the number of photonsreceived by the detector decreases One of the effective waysto improve the image quality is designing a tailored networkto make the input LDCT images as close as possible to theNDCT images is process can be classified as an imagedenoising problem which can be described by the followingmodel

G x⟶ y (1)

where x isin RNtimesN denotes an LDCT image and y isin RNtimesN

denotes the corresponding NDCT image e goal of thenoise reduction process is to obtain a transformation G thatmaps x to y

2 Computational and Mathematical Methods in Medicine

In this process x can be seen as a sample from the LDCTdistribution Pl and y can be seen as a sample from theNDCT distribution Pn e denoising process transforms x

to a certain distribution Pg And the denoising process aimsto determine an optimal G to make Pg close to Pn Howeverin the reconstructed LDCT images noise is complicated anduniformly distributed over the whole image as such dis-tributions Pl and Pn have no explicit mathematical re-lationship up to date [36] e traditional methods usuallyhave difficulty in denoising LDCT images For deep learn-ing-based methods the uncertainty of a noise model can beignored due to the learning capability of high-level featuresand presentation of data distribution by the CNNereforedesigning a tailored CNN is an effective method to suppressnoise in LDCT and improve image quality

22 Introduction of CycleGAN In 2017 Zhu et al [38]proposed an unpaired network named CycleGAN whichhas gained extensive attention is network can capture thespecial characteristics of one image collection and figure outhow these characteristics could be translated into otherimage collection without using any paired training exam-ples this network has been successfully utilized in styletransfer object transfiguration season transfer and photoenhancement

Under the assumption that there is some underlyingrelationship between the source domain X and target do-main Y the goal of CycleGAN is to learn mapping G

X⟶ Y so that the distribution of image from G(x) isindistinguishable from the distribution of image from do-main Y is network includes two mapping functionsnamely G X⟶ Y and F Y⟶ X and also introducestwo discriminators namely DX and DY Discriminator DY

aims to distinguish between translated samples G(x) andreal samples y Discriminator DX aims to distinguish be-tween translated samples F(y) and real samples x In theoryadversarial training can identify mappings G and F thatproduce outputs identically distributed as target domains Y

and X [34] However with its large sufficient capacity anetwork can map the same set of input images to anyrandom permutation of images in the target domain whereany of the learned mappings can induce an output distri-bution that matches the target distribution ereforeadversarial loss alone cannot guarantee that the learnedfunction can map individual input x to desired y To furtherreduce the space of possible mapping functions the map-ping functions G and F should be cycle consistent As shownin Figure 2(a) for each image x from domain X the imagetranslation cycle should be able to bring x back to theoriginal image x⟶ G(x)⟶ F(G(x)) asymp x which isnamed as forward cycle consistency Similarly as demon-strated in Figure 2(b) for each image y from domain Y theimage translation cycle should be able to bring y back to theoriginal image y⟶ F(y)⟶ G(F(y)) asymp y which isnamed as backward cycle consistency e abovementionedbehavior can be incentivized by cycle-consistency loss

Lcyc(G F) ExsimPdata(x) F(G(x)) minus x11113858 1113859

+ EysimPdata(y) G(F(y)) minus y11113858 1113859(2)

where Pdata(x) is the distribution of x and Pdata(y) is thedistribution of y

In LDCTimaging although the projection data contain alot of noise it is usually complete erefore the recon-structed images still contain useful information that is ba-sically consistent with corresponding NDCT images isindicates that there is a close relationship between the LDCT

Paired

hellip

(b)

Unpairedxi xi yiyi

hellip hellip

(a)

Figure 1 Schematic diagram of (a) unpaired dataset and (b) paired dataset

Computational and Mathematical Methods in Medicine 3

image and NDCTimage and satisfies the basic assumption ofCycleGAN us this study considers using this unpairednetwork for LDCT image reconstruction

Based on its structure CycleGANmainly focuses on themap of distributions is network is better at the overallconversion of images and may overlook the correspon-dence of details However for LDCT noise reduction theoutputs should not only appear similar to an NDCT imagebut also retain details as much as possible more impor-tantly the output must not contain false informationwhich may cause misdiagnosis ese issues require ad-ditional supervision and restraint to the network in thetraining process to make it more suitable for LDCT re-construction In this study we consider incorporating priorimage information into the network to guarantee contentcorrespondence and prevent the generation of fake detailsduring denoising process

23 Unpaired Denoising Network Based on CycleGAN withPrior Information Figure 3 shows an overview of ourproposed method e network contains forward andbackward cycles and two generators and discriminators Inorder to more clearly illustrate the training mechanism ofthe proposed network we randomly selected an LDCTimage from LDCT image collection and an NDCT imagefrom the NDCT image collection as the input-ground truthpair Note that the LDCT image is not corresponding to theNDCT image as shown in Figure 4

In the forward cycle generator GN is trained to generateimages that are as close to corresponding NDCT images aspossible (Figure 3(a)) Generator FL is trained to translatethe resulting image GN(x) back to the corresponding LDCTimage In the backward cycle generator FL is trained togenerate images that are as close to corresponding LDCTimages as possible (Figure 3(b)) Generator GN is trained totranslate the resulting image FL(y) back to the NDCTimageIn the training process of network the discriminators DN

and DL are used to estimate the probability that the sample is

from the real image rather than generating image At thesame time the generators GN and FL attempt to generateimages that are not easily distinguishable by the discrimi-nators is paper utilizes the adversarial loss [43] as theobjective function to train the ldquogamerdquo process

LGANNGN DN X Y( 1113857 Eysimpdata(y) logDN(y)1113858 1113859

+ Exsimpdata(x) log 1 minus DN GN(x)( 1113857( 11138571113858 1113859

LGANLFL DL X Y( 1113857 Exsimpdata(x) logDL(x)1113858 1113859

+ Eysimpdata(y) log 1 minus DL FL(y)( 1113857( 11138571113858 1113859

(3)

In order to reduce the feasible domain space of themapping functions the cycle consistency is introduced tofurther constrain the training process of the network so thatthe network can be trained under unpaired data

Lcyc GN FL( 1113857 ExsimPdata(x) FL GN(x)( 1113857 minus x

11113960 1113961

+ EysimPdata(y) GN FL(y)( 1113857 minus y

11113960 1113961(4)

For this cycle consistency network the performance of agenerator requires the indirect supervision through theresults of another generator For example in the forwardcycle in addition to discriminator DN the performance ofgenerator GN also needs to be supervised by the resultsFL(GN(x)) of another generator FL is mechanism doesnot guarantee the accuracy of the final input and may lead tothe occurrence of fake details For LDCT image re-construction the accuracy of the results is critical and iffalse information is generated it may cause misdiagnosisleading to serious consequences ese circumstances re-quire direct constraints to the generators especially togenerator GN which directly produces the desired outcomeerefore this paper incorporates the prior image in-formation into the network to directly supervise the gen-erator GN as shown in Figure 3(a) For fear of changing theunpaired property of the network the resulting images

G F

x

X Y

Forward cycle-consistency loss

DY DX

F G

y

Y

Backward cycle-consistency loss

(b)(a)

x

x

X

X

y

y

Y

Figure 2 Structure diagram of CycleGAN (a) Forward cycle-consistency loss (b) Backward cycle-consistency loss


processed by BM3D method utilizing LDCT images areregarded as prior images And the mean absolute error(MAE) between the prior image and the generated image isintroduced into the loss function to constrain the training ofthe network e adversarial loss of the forward cycle can bewritten as

Lp

GANNGN DN X Y( 1113857 Eysimpdata(y) logDN(y)1113858 1113859

+ Exsimpdata(x)1113876log 1 minus DN(x)( 1113857

+ α GN(x) minus Iprior_img

11113877

(5)

FL

GN ||GN (IL) ndash Iprior_img||1

||FL (GN (IL)) ndash IL||1

IL

GN (IL) DN

BM3D

ILIprior_img

FL (GN (IL))

(a)

IN

FL

DL

||GN (FL (IN)) ndash IN||1 FL (IN)

GN

GN (FL (IN))

(b)

Figure 3 Overview of the proposed method (a) Forward cycle (b) Backward cycle

Input-LDCT image Ground truth-NDCT image

Figure 4 One input-ground truth pair of the proposed unpaired network


where α is the weight of theMAE In the training process thegenerator GN tries to minimize the objective function (5)while the discriminator DN tries to maximize it that isminGN

maxDNL

p

GANN(GN DN X Y) We denote the pro-

posed network as CycleGAN-BM3Drough the above analysis the total loss function of our

proposed method is

L GN FL DN DL( 1113857 Lp

GANNGN DN X Y( 1113857

+ LGANLFL DL Y X( 1113857

+ λLcyc(G F)

(6)

where λ is a nonnegative parameter used to balance theweight of the cycle consistency loss e total objectivefunction of the proposed CycleGAN-BM3D is

GlowastN FlowastL arg min

GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)

24 Network Architecture In the proposed method thenetwork of the generator as shown in Figure 5(a) includesthree submodules encoder convertor and decoder eencoder extracts the features from the input image utilizingCNN e network of the encoder includes one 7times 7Convolution-InstanceNorm-ReLU layer with 64 filters andstride 1 denoted as c7s1-64 two 3times 3 Convolution-InstanceNorm-ReLU layers with k filters and stride 2 inwhich k equals to 128 and 256 respectively We denote thesetwo layers as d128 and d256 e convertor as shown inFigure 5(b) is used to convert feature vectors extracted fromthe source domain X to the target domain Y e convertorcontains six residual network (Resnet) blocks [44] and eachblock contains two 3times 3 convolutional layers with 256 filterson both layers e decoder includes three layers e firsttwo layers are 3times 3 fractional-strided-Convolution-Instan-ceNorm-ReLU layers with stride 12 and 64 and 32 filtersrespectively We denote the two layers as u64 and u32 ethird layer is a 7times 7 Convolution-InstanceNorm-ReLU with3 filters and stride 1 denoted as c7s1-3 e network of thediscriminator as shown in Figure 5(c) consists of fiveconvolution layers e first four layers are 4times 4 Convo-lution-InstanceNorm-LeakyReLU layers with stride 2 and64 128 256 and 512 filters respectively We denote them asC64 C128 C256 and C512 We use leaky ReLUs with slope02 In the last layer a 4times 4 convolution layer with 1 filterand stride 1 is utilized to produce a one-dimensional output

3 Experiments and Results

31 Experimental Dataset and Performance Evaluationse CT images of a deceased piglet were selected as theexperimental dataset to verify the performance of the pro-posed network e images were scanned by a 64-slicemultidetector GE Healthcare scanner (Discovery CT750HD) by using 100 kV and 0625mm slice thickness Fivedifferent tube currents were set to yield CT images withdifferent dose levels e specific scanned parameters andeffective dose of different tube currents are listed in Table 1

In each dose level 906 images with size 512times 512 wereacquired As shown in Figure 6 we partitioned the slices bytaking oneʼs data and then skipping 10 slices We finallyobtained 360 images reconstructed by FBP using the pro-jection data of 5 dose as the noisy dataset that is sourcecollection X And 180 images were obtained for testing enormal dose dataset utilized consists of 360 images whichare corresponding to the noisy dataset and obtained from theNDCT images constructed by FBP e normal dose datasetis the target collection Y Given the unpaired property of theproposed network the training images and the ground truthdo not require a one-to-one correspondence e number oftwo image datasets can also be different In the training stagewe performed an unpaired operation for the inputs andlabels of the network In addition each image was dividedinto sixteen 128times128 images to enlarge the training datasetto 5760 images

For comparison we selected some representative tra-ditional methods and other networks

311 BM3D is method exhibits outstanding perfor-mance in noise reduction over other traditional imagedenoising methods

312 Original CycleGAN is network is trained withoutthe constraint of prior image to test the supervised effect ofthe prior image e input dataset and ground truth datasetare the same as the proposed method CyclGAN-BM3Dwhich are not one-to-one correspondence

Structural similarity (SSIM) [45] peak signal-to-noiseratio (PSNR) and normalized mean absolute distance(NMAD) are selected as measures of reconstruction qualityfor the quantitative assessment of the proposed network andabovementioned contrast algorithms Specifically PSNR andNMAD are defined as follows

PSNR 10 log10MAX2(f)

1N1113936Ni1 f(i) minus f0(i)

111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936

Ni1 f(i) minus f0(i)

11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)

where f and f0 represent the denoising image and idealimage respectively i is the pixel in the image and N is thetotal number of pixels in the image A higher PSNR indicatesthat the image is of higher quality e NMAD value close to0 indicates small differences between the ideal image and thereconstructed results In general SSIMle 1 and SSIM 1indicate the exact theoretical reconstruction

32 Implementation Details In the training process thenegative log likelihood objective of the first two items inLGANN

and LGANLis replaced by least squares loss to stabilize

the proposed model [46] After the replacement we train GN

to minimize


Exsimpdata(x) DN GN(x)( 1113857 minus 1( 11138572


11113876 1113877

(9)

We also train FL to minimize

minEysimpdata(y) DL FL(y)( 1113857 minus 1( 11138572

1113960 1113961 (10)

For discriminators DN and DL the objectives are

minEysimpdata(y) DN(y) minus 1( 11138572

1113960 1113961 + Exsimpdata(x) DN G(x)2

1113872 11138731113960 1113961

minExsimpdata(x) DL(x) minus 1( 11138572

1113960 1113961 + Eysimpdata(y) DL FL(y)2

1113872 11138731113960 1113961

(11)

For the setting of parameters λ is set as 10 Adam solverwith a batch size of 1 is selected as the optimizer to optimizethe networks We keep the same learning rate for the first

Table 1 CT scanning protocol for the experiment

Normal dose 50 dose 25 dose 10 dose 5 doseTube current (mAs) 300 150 75 30 15Effective dose (mSv) 1414 707 354 141 071

helliphellip

20 training slices 10 testing slices 20 training slices 10 testing slices

Skipped 10 slices Skipped 10 slices Skipped 10 slices Skipped 10 slices

Figure 6 Schematic diagram of data preparation e yellow rectangular blocks represent the training data the green rectangular blocksrepresent the test data and the white rectangular blocks represent the skipped slices

512 times 512 times 3 128 times 128 times 256 128 times 128 times 256c7

s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3

Encoder Convertor Decoder512 times 512 times 3

(a)Co

nv la

yer 1

hellip

128 times 128 times 256 128 times 128 times 256Resnet block 1 Resnet block 2 Resnet block 6

Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512

32 times 32 times 512

Conv

laye

r

Decision [0 1]

(c)

Figure 5 Network structure (a) Diagram of generatorrsquos network structure (b) Diagram of convertorrsquos network structure (c) Diagram ofdiscriminatorrsquos network structure


10000 epochs and linearly decay the rate to zero over thenext 10000 epochs e proposed network in this papertrained 40000 epochs α is an important parameter forcontrolling the weight of prior information during trainingWhen the value of α is too small the effect of prior in-formation will be negligible and cause minimal improve-ment in image quality By contrast a very large α willoveremphasize the role of prior information and to someextent limit the learning ability of the network itself In thispaper a series of networks was trained by setting differentvalues of α to determine a suitable value For the sake offairness each network has the same parametersrsquo settingexcept α We randomly selected 10 LDCT images to test theperformance of different networks e effect of α wasquantitatively determined by plotting the average SSIM andNMAD of the denoising images in Figure 7

From the curves of Figure 7 when α 10 the SSIMreaches the maximum indicating that the denoising imagesare most similar to the NDCT images in structure that isunder this circumstance the network has the greatest abilityto retain the details of the LDCT images NMAD reflects theaccuracy of denoising to some extent Smaller NMAD in-dicates that the noise in the LDCT images is removed morecompletely Considering the detail retention and noise re-duction of the network this paper set α as 10

To analyze the potential denoising capability of selectedalgorithms and networks two representative slices and thecorresponding zoomed regions of interest (ROIs) are shownin Figures 8ndash10 respectively

As shown in Figure 8 when using traditional methods(BM3D) or deep learning-based methods the noise that ap-pears in the LDCTimage is suppressed to varying degreeseclassic BM3D method has an outstanding noise suppressioneffect but makes the processed image oversmoothed so thatsome vital details disappear As indicated by the red arrows inROI the results of BM3D lose some information of the boneAlthough the result of the original CycleGAN is not over-smoothed it shows fake details connecting the unconnectedbones in the NDCT image e CycleGAN-BM3D whichintroduces prior image information does not have redundantdetails and retains the information that should be retained

Figure 9 shows the overall second slice of differentmethods and the corresponding absolute difference imagesbetween NDCT images and the resulting images In thedifference images the darker the color is the smaller theerror will be It can be clearly observed that the result ofCycleGAN-BM3D has the smallest difference

For further analysis of image details two regions wereselected as ROIs which are shown in Figure 10 In ROI I thetissue pointed by red squares is smeared out in the BM3Dimages but is easily identifiable in the CycleGAN andCylceGAN-BM3D images As marked by the yellow ellipsesin ROI II the three black holes in the results of BM3D andCycleGAN are blurred and inseparable but are recognizablein the result of CycleGAN-BM3D Furthermore the smootharea below the ROI II of CycleGAN-BM3D is the mostsimilar to the NDCT image

Based on the visual effect the proposed networkCycleGAN-BM3D can not only better suppress noise but

also retain more details than the other networks Moreimportantly after adding the constraint of prior in-formation CycleGAN-BM3D can effectively prevent thegeneration of fake details compared with the originalCycleGAN without prior information

For quantitative analysis the average of PSNR SSIMand NMADwas calculated for 180 slices in the test dataset tomeasure performance of the proposed method and the othercompared methods (Table 2)

In each evaluation item the results with the best per-formance are marked black CycleGAN-BM3D ranks first interms of SSIM even with the unpaired training dataset Assuch the results of CycleGAN-BM3D are the most struc-turally similar to the NDCT images In terms of PSNR andNMAD CycleGAN-BM3D also exhibits satisfactory per-formance indicating that the noise removal is relativelyclean Compared with the other algorithms CycleGANshows the worst performance because it mainly focuses onmapping the data distribution from the LDCTto NDCT andcyclic loss may not be enough to supervise the generation ofdetails and suppression of noise is method needs to addsupervision during training to improve image quality eintroduction of prior information in CycleGAN-BM3Denhances the constraints to the image content at is in theproposed CycleGAN-BM3D method cyclic loss plays a rolein distributionmapping and prior information loss is used toguarantee the relevance of the content erefore theproposed method demonstrates good performance in noisesuppression and detail preservation We note that the nu-merical results of BM3D are in the front rank From thevisual effect the noise removal of BM3D is complete and themain information of the image is basically retained as muchBM3D has a high quantitative evaluation result at findingis the reason why we choose the result of BM3D as the priorinformation

4 Discussion and Conclusion

In the modern CT imaging field the hidden risk of radiationdose has increased the demand for LDCT However LDCT

0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD

1 10 10001The values of alpha

Figure 7 Average SSIM and NMAD of 10 images in differentvalues of α e blue line indicates the SSIM curve and the orangeline represents the NMAD curve


ROI

(a) (b) (c) (d) (e)

Figure 8 Results of (a) NDCT (b) LDCT (c) BM3D (d) CycleGAN and (e) CycleGAN-BM3D respectivelye display widow is [800 1300]

(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II

Figure 10 Zoomed-in ROIs of slice 2 e first column is the NDCT (a) e following columns are the results from (b) LDCT (c) BM3D(d) CycleGAN and (e) CycleGAN-BM3D respectively e display widow is [800 1300]


images often suffer from serious noise which degradesimage quality and troubles clinical diagnosis In the past twoyears deep neural network provides a new idea for LDCTnoise reduction Most of the existing neural networks forLDCT reconstruction usually require well-matched datasetsfor network training However the well-matched CT imagesof different dose levels are difficult to obtain is may affectthe performance of networks and lead to blurred details orfake information in the resulting images

To improve the quality of LDCT image and broaden theapplication of neural networks in LDCTnoise reduction thispaper proposed an unpaired network based on CycleGANwith prior image information In contrast to existingdenoising networks the proposed network can be trained byunpaired datasets thereby alleviating the limitation of paireddataset requirement Most GANs used to reduce noisemainly focus on the distribution mapping from LDCT toNDCT and this process may overlook the accurate contentcorrespondence To enhance the constraint to the contentand prevent producing fake details we incorporate the priorimage processed by BM3D into CycleGAN to supervise thegeneration of image content In the experiment of real datavisual inspection demonstrated that the proposed methodcan suppress noise in the LDCT image and prevent thegeneration of fake details e result of quantitative evalu-ations indicated that after incorporating prior informationthe PSNR improvedmore than 3 dB and SSIM also increasedcompared with the original CycleGAN without prior in-formation e results of qualitative and quantitative eval-uations indicated that the proposed method exhibitsreasonable performance and outperforms the originalCycleGAN when applied to LDCT reconstruction

e validity of prior information affects the performanceof the proposed method In this work the LDCT imagesprocessed by traditional methods are obtained as prior in-formation which is a simple and efficient way In the futurewe intend to explore other representative shared featuresbetween LDCT and NDCT images as prior information tofurther improve the performance of the proposed networksuch as the sparsity or sharpness information

Data Availability

e data used in the study can be obtained from httphomepageusaskcasimxiy525publicationsagan

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Chao Tang and Jie Li contributed equally to this work

Acknowledgments

is study was funded by the National Natural ScienceFoundation of China (grant no 61601518) and the NationalKey RampD Program of China (grant no 2018YFC0114500)

References

[1] D J Brenner and E J Hall ldquoCancer risks from CTscans nowwe have data what nextrdquo Radiology vol 265 no 2pp 330-331 2012

[2] O W Linton and F A Mettler ldquoNational conference on dosereduction in CT with an emphasis on pediatric patientsrdquoAmerican Journal of Roentgenology vol 181 no 2 pp 321ndash329 2003

[3] D J Brenner and E J Hall ldquoComputed tomographymdashanincreasing source of radiation exposurerdquo New EnglandJournal of Medicine vol 357 no 22 pp 2277ndash2284 2007

[4] I A Elbakri and J A Fessler ldquoStatistical image reconstructionfor polyenergetic X-ray computed tomographyrdquo IEEETransactions on Medical Imaging vol 21 no 2 pp 89ndash992002

[5] JWang T Li and L Xing ldquoIterative image reconstruction forCBCT using edge-preserving priorrdquo Medical Physics vol 36pp 252ndash260 2009

[6] P J L Riviere J Bian and P A Vargas ldquoPenalized-likelihoodsinogram restoration for computed tomographyrdquo IEEETransactions on Medical Imaging vol 25 no 8 pp 1022ndash1036 2006

[7] J Wang T Li H Lu and Z Liang ldquoPenalized weighted least-squares approach to sinogram noise reduction and imagereconstruction for low dose X-ray computed tomographyrdquoIEEE Transactions on Medical Imaging vol 25 no 10pp 1272ndash1283 2006

[8] Y Zhang J Zhang and H Lu ldquoStatistical sinogramsmoothing for low-dose CT with segmentation-based adap-tive filteringrdquo IEEE Transactions on Nuclear Science vol 57no 5 pp 2587ndash2598 2010

[9] Q Xie D Zeng Q Zhao et al ldquoRobust low-dose CTsinogrampreprocessing via exploiting noise-generating mechanismrdquoIEEE Transactions on Medical Imaging vol 36 no 12pp 2487ndash2498 2017

[10] A M R Schilham B van Ginneken H Gietema andM Prokop ldquoLocal noise weighted filtering for emphysemascoring of low-dose CT imagesrdquo IEEE Transactions onMedical Imaging vol 25 no 4 pp 451ndash463 2006

[11] A Borsdorf R Raupach T Flohr and J Hornegger ldquoWaveletbased noise reduction in CT-images using correlation anal-ysisrdquo IEEE Transactions on Medical Imaging vol 27 no 12pp 1685ndash1703 2008

[12] Y Chen Z Yang Y Hu et al ldquooracic low-dose CT imageprocessing using an artifact suppressed large-scale nonlocalmeansrdquo Physics in Medicine and Biology vol 57 no 9pp 2667ndash2688 2012

[13] B D Man and S Basu ldquoDistance-driven projection andbackprojection in three dimensionsrdquo Physics in Medicine andBiology vol 49 no 11 pp 2463ndash2475 2004

[14] R M Lewitt ldquoMultidimensional digital image representationsusing generalized Kaiser-Bessel window functionsrdquo Journal of

Table 2 Quantitative evaluation of results by different algorithmson 180 slices in the test dataset

PSNR SSIM NMADLDCT 276514plusmn 13862 08698plusmn 00375 01124plusmn 00174BM3D 322185plusmn 09599 09271plusmn 00245 00681plusmn 00087CycleGAN 290833plusmn 08661 09059plusmn 00263 00890plusmn 00096CycleGAN-BM3D 343577 plusmn 01475 09798 plusmn 00041 00583 plusmn 00012


the Optical Society of America A vol 7 no 10 pp 1834ndash18461990

[15] B R Whiting P Massoumzadeh O A Earl J A OrsquoSullivanD L Snyder and J F Williamson ldquoProperties of pre-processed sinogram data in X-ray computed tomographyrdquoMedical Physics vol 33 no 9 pp 3290ndash3303 2006

[16] S Ramani and J A Fessler ldquoA splitting-based iterative al-gorithm for accelerated statistical X-ray CT reconstructionrdquoIEEE Transactions on Medical Imaging vol 31 no 3pp 677ndash688 2012

[17] E Y Sidky and X Pan ldquoImage reconstruction in circularcone-beam computed tomography by constrained total-variation minimizationrdquo Physics in Medicine and Biologyvol 53 no 17 pp 4777ndash4807 2008

[18] Y Liu J Ma Y Fan and Z Liang ldquoAdaptive-weighted totalvariation minimization for sparse data toward low-dose X-raycomputed tomography image reconstructionrdquo Physics inMedicine and Biology vol 57 no 23 pp 7923ndash7956 2012

[19] Z Tian X Jia K Yuan T Pan and S B Jiang ldquoLow-dose CTreconstruction via edge-preserving total variation regulari-zationrdquo Physics in Medicine and Biology vol 56 no 18pp 5949ndash5967 2011

[20] Q Xu H Yu X Mou L Zhang J Hsieh and GWang ldquoLow-dose X-ray CT reconstruction via dictionary learningrdquo IEEETransactions on Medical Imaging vol 31 no 9 pp 1682ndash1697 2012

[21] Y Zhang X Mou G Wang and H Yu ldquoTensor-baseddictionary learning for spectral CT reconstructionrdquo IEEETransactions on Medical Imaging vol 36 no 1 pp 142ndash1542017

[22] J K Choi B Dong and X Zhang ldquoLimited tomographyreconstruction via tight frame and simultaneous sinogramextrapolationrdquo Journal of Computational Mathematicsvol 34 no 6 pp 575ndash589 2016

[23] A Buades B Coll and J M Morel ldquoA review of imagedenoising algorithms with a new onerdquoMultiscale Modeling ampSimulation vol 4 no 2 pp 490ndash530 2005

[24] Z Li L Yu J D Trzasko et al ldquoAdaptive nonlocal meansfiltering based on local noise level for CTdenoisingrdquoMedicalPhysics vol 41 no 1 Article ID 011908 2014

[25] M Aharon M Elad and A Bruckstein ldquoK-SVD an algo-rithm for designing overcomplete dictionaries for sparserepresentationrdquo IEEE Transactions on Signal Processingvol 54 no 11 pp 4311ndash4322 2006

[26] P F Feruglio C Vinegoni J Gros A Sbarbati andR Weissleder ldquoBlock matching 3D random noise filtering forabsorption optical projection tomographyrdquo Physics in Med-icine and Biology vol 55 no 18 pp 5401ndash5415 2010

[27] D Kang P Slomka R Nakazato et al ldquoImage denoising oflow-radiation dose coronary CT angiography by an adaptiveblock-matching 3D algorithmrdquo in Proceedings of the MedicalImaging Image Processing International Society for Opticsand Photonics March 2013

[28] H Chen Y Zhang W Zhang et al ldquoaLow-dose CT viaconvolutional neural networkrdquo Biomedical Optics Expressvol 8 no 2 pp 679ndash694 Prague Czech Republic 2017

[29] E Kang J Min and J C Ye ldquoA deep convolutional neuralnetwork using directional wavelets for low-dose X-ray CTreconstructionrdquo Medical Physics vol 44 no 10 pp e360ndashe375 2017

[30] H Chen Y Zhang M K Kalra et al ldquoLow-dose CT with aresidual encoder-decoder convolutional neural network(RED-CNN)rdquo IEEE Transactions on Medical Imaging vol 36no 12 pp 2524ndash2535 2017

[31] J Johnson A Alahi and L Fei-Fei ldquoPerceptual losses for real-time style transfer and super-resolutionrdquo in Proceedings of theEuropean Conference on Computer Vision pp 694ndash711Springer Amsterdam e Netherlands October 2016

[32] C Ledig L eis F Huszar et al ldquoPhoto-realistic singleimage super-resolution using a generative adversarial net-workrdquo 2016 httpsarxivorgabs160904802

[33] D Wu K Kim F G El et al ldquoIterative low-dose CT re-construction with priors trained by artificial neural networkrdquoIEEE Transactions on Medical Imaging vol 36 no 12pp 2479ndash2486 2017

[34] I Goodfellow ldquoNips 2016 tutorial generative adversarialnetworksrdquo 2016 httpsarxivorgabs170100160

[35] J M Wolterink T Leiner M A Viergever and I IsgumldquoGenerative adversarial networks for noise reduction in low-dose CTrdquo IEEE Transactions on Medical Imaging vol 36no 12 pp 2536ndash2545 2017

[36] Q Yang P Yan Y Zhang et al ldquoLow dose CT imagedenoising using a generative adversarial network with Was-serstein distance and perceptual lossrdquo IEEE Transactions onMedical Imaging vol 37 no 6 pp 1348ndash1357 2017

[37] X Yi and P Babyn ldquoSharpness-aware low-dose CTdenoisingusing conditional generative adversarial networkrdquo Journal ofDigital Imaging vol 31 no 5 pp 655ndash669 2018

[38] J Y Zhu T Park P Isola and A A Efros ldquoUnpaired image-to-image translation using cycle-consistent adversarial net-worksrdquo in Proceedings of the 2017 IEEE International Con-ference on Computer Vision (ICCV) pp 2242ndash2251 VeniceItaly October 2017

[39] Z Yi H Zhang P Tan and M Gong ldquoDualGAN un-supervised dual learning for image-to-image translationrdquo inProceedings of the 2017 IEEE International Conference onComputer Vision (ICCV) pp 2868ndash2876 Venice Italy Oc-tober 2017

[40] T M Quan T Nguyen-Duc and W K Jeong ldquoCompressedsensing MRI reconstruction using a generative adversarialnetwork with a cyclic lossrdquo IEEE Transactions on MedicalImaging vol 37 no 6 pp 1488ndash1497 2018

[41] J M Wolterink A M Dinkla M H F Savenije et al ldquoDeepMR to CT synthesis using unpaired datardquo in Simulation andSynthesis in Medical Imaging pp 14ndash23 Springer BerlinGermany 2017

[42] C-B Jin H Kim W Jung et al ldquoDeep CT to MR synthesisusing paired and unpaired datardquo 2018 httpsarxivorgabs180510790

[43] I Goodfellow J Pouget-Abadie M Mirza et al ldquoGenerativeadversarial netsrdquo in Proceedings of the Advances in NeuralInformation Processing Systems 27 (NIPS 2014) MontrealQuebec Canada 2014

[44] K He X Zhang S Ren and J Sun ldquoDeep residual learningfor image recognitionrdquo in Proceedings of the 2016 IEEEConference on Computer Vision and Pattern Recognition(CVPR) pp 770ndash778 Las Vegas NV USA June 2016

[45] Z Wang A C Bovik H R Sheikh and E P SimoncellildquoImage quality assessment from error visibility to structuralsimilarityrdquo IEEE Transactions on Image Processing vol 13no 4 pp 600ndash612 2004

[46] X Mao Q Li H Xie R Y Lau and Z Wang ldquoMulticlassgenerative adversarial networks with the L2 loss functionrdquo2016 httpsarxivorgabs161104076v1


Stem Cells International

Hindawiwwwhindawicom Volume 2018


MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine


Behavioural Neurology

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

a statistical noise model and prior information in the imagedomain [4 15 16] Well-known image priors consist of totalvariation (TV) and its variants [17ndash19] dictionary learning[20 21] and wavelet frame [22] ese iterative re-construction algorithms exhibit satisfactory performance inimproving image quality but their computational burdenand sensitive parameters limit their practical applications

Image postprocessing is more computationally efficientcompared with iterative reconstruction which has spawneda lot of simple and effective methods Nonlocal means(NLM) filtering methods estimate noise components byusing multiple patches extracted at different locations in theimage [23] and have been widely used for CT [24] Moti-vated by compressed sensing methods an adaptive K-SVDmethod [25] was proposed to reduce artifacts in CT re-constructions e block matching 3D (BM3D) method isalso an outstanding method for image postprocessing in CTimaging fields [26 27] this method exploits similarities inimage blocks ese traditional postprocessing methodshave improved the quality of CT images however the resultsoften undergo edge blurring andor residual artifacts giventhe nonuniform distribution of reconstruction noise

More recently several supervised machine learningapproaches have been proposed for noise reduction inLDCT ese methods usually reveal a relation between thepixel value in the LDCT image and the pixel value at thesame location in a corresponding NDCT image by trainingwith paired images Chen et al [28] designed a deep con-volutional neural network (CNN) to map LDCT imagestoward its relative normal-dose counterparts in a patch-by-patch manner Kang et al [29] used a similar method butadopted CNN to directional wavelet transform of CTimagesen more complex networks were proposed to handle theLDCT denoising problem such as the residual encoder-decoder convolutional neural network (RED-CNN) in [30]which achieves competitive performance relative to state-of-the-art methods in clinical cases

Although the abovementioned networks presented im-pressive denoising results they all belong to the end-to-endnetwork which typically utilizes mean squared errors (MSE)between the network output and the ground truth as lossfunction However recent studies [31 32] indicated that thisper-pixel MSE often suffers from oversmoothed edges andloss of details MSE-based approaches tend to take the meanof high-resolution patches by using Euclidean distancerather than geodesic distance Given that the medical imagesusually lie in a highly nonlinear manifold [33] the algorithmis prone to neglect subtle details that are vital for clinicaldiagnosis when it tries to minimize per-pixel MSE Toovercome the limitations of per-pixel regression in noisereduction the generative adversarial network (GAN) [34]based on adversarial loss is introduced to medical imagereconstruction In 2017 Wolterink et al [35] were the first toapply the GAN for cardiac CT image reconstruction AndYang et al [36] utilized a GAN with Wasserstein distance(WGAN) In order to enhance the capability of noise re-duction perceptual loss is simultaneously used to optimizethe loss function Yi and Babyn [37] combined an adversarialtrained network and a sharpness detection network to

mitigate noise in LDCT and achieved satisfactory perfor-mance Hence a general framework for estimating gener-ative models by using an adversarial process has shownoutstanding performance in medical image reconstruction

e above-mentioned denoising networks usually re-quire spatially paired counterparts However in medicalimaging well-paired counterparts are difficult to obtainFor example in LDCT imaging continuously scanning apatient twice in normal and low dose is impossible undernormal circumstances e shortage of paired data has beenone of the factors that restrict the wide application of deeplearning in low-dose CT reconstruction Recently un-supervised variants of GANs such as CycleGAN [38] andDualGAN [39] have been proposed for mapping differentdomains without matching data pairs Motivated by theirsuccess in image processing unpaired GANs have beensuccessfully applied to CS-MRI reconstruction [40] and CTsynthesis based on MR images [41 42] For LDCT re-construction well-paired clinical scans acquired at differentdose levels are not readily available Even if we obtain thesame patient data at different dose levels the data are difficultto match perfectly due to physical activity and the inevitableslight movement of the scanning position which may affectthe denoising ability of the networks

In this study we propose an unpaired LDCT denoisingnetwork based on CycleGAN with prior image informationIn the proposed network the design of cycle-consistentstructure impels the network to learn the mapping re-lationship between the LDCT image collection and NDCTimage collection (Figure 1(a)) rather than an image pair ofan LDCT image and NDCT image (Figure 1(b)) ereforethe proposed network does not need a one-to-one corre-sponding training dataset and can learn with the unpaireddataset Meanwhile the prior image information extractedfrom the preprocessed image by using LDCT is introducedinto the network to supervise the generation of content andensure correspondence of the image content e map ofimage collections through cyclic loss and the supervision ofcontent through prior image loss confer our proposedmethod to produce results that have not only lower noise butalso accurate details

2 Methods

21 Noise ReductionModel In LDCT imaging serious noisetypically occurs in CT images as the number of photonsreceived by the detector decreases One of the effective waysto improve the image quality is designing a tailored networkto make the input LDCT images as close as possible to theNDCT images is process can be classified as an imagedenoising problem which can be described by the followingmodel

G x⟶ y (1)

where x isin RNtimesN denotes an LDCT image and y isin RNtimesN

denotes the corresponding NDCT image e goal of thenoise reduction process is to obtain a transformation G thatmaps x to y













Paired

hellip

(b)

Unpairedxi xi yiyi

hellip hellip

(a)













(3)



11113960 1113961


11113960 1113961(4)


G F

x

X Y


DY DX

F G

y

Y


(b)(a)

x

x

X

X

y

y

Y




Lp




11113877

(5)

FL



IL

GN (IL) DN

BM3D

ILIprior_img

FL (GN (IL))

(a)

IN

FL

DL


GN

GN (FL (IN))

(b)






maxDNL

p



proposed method is




+ λLcyc(G F)

(6)



GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)











111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936


11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)





to minimize




11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






























Paired

hellip

(b)

Unpairedxi xi yiyi

hellip hellip

(a)













(3)



11113960 1113961


11113960 1113961(4)


G F

x

X Y


DY DX

F G

y

Y


(b)(a)

x

x

X

X

y

y

Y




Lp




11113877

(5)

FL



IL

GN (IL) DN

BM3D

ILIprior_img

FL (GN (IL))

(a)

IN

FL

DL


GN

GN (FL (IN))

(b)






maxDNL

p



proposed method is




+ λLcyc(G F)

(6)



GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)











111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936


11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)





to minimize




11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





























(3)



11113960 1113961


11113960 1113961(4)


G F

x

X Y


DY DX

F G

y

Y


(b)(a)

x

x

X

X

y

y

Y




Lp




11113877

(5)

FL



IL

GN (IL) DN

BM3D

ILIprior_img

FL (GN (IL))

(a)

IN

FL

DL


GN

GN (FL (IN))

(b)






maxDNL

p



proposed method is




+ λLcyc(G F)

(6)



GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)











111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936


11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)





to minimize




11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















Lp




11113877

(5)

FL



IL

GN (IL) DN

BM3D

ILIprior_img

FL (GN (IL))

(a)

IN

FL

DL


GN

GN (FL (IN))

(b)






maxDNL

p



proposed method is




+ λLcyc(G F)

(6)



GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)











111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936


11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)





to minimize




11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















maxDNL

p



proposed method is




+ λLcyc(G F)

(6)



GNFL

maxDNDL

L GN FL DN DL( 1113857 (7)











111386811138681113868111386811138681113868111386811138682

⎛⎝ ⎞⎠

NMAD 1113936


11138681113868111386811138681113868111386811138681113868

1113936Ni1|f(i)|

(8)





to minimize




11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















11113876 1113877

(9)



1113960 1113961 (10)




1113872 11138731113960 1113961



1113872 11138731113960 1113961

(11)




helliphellip





s1-6

4

d128

d256

Resn

et b

lock

1

Resn

et b

lock

2

Resn

et b

lock

6

u64

u32

c7s1

-3


(a)Co

nv la

yer 1

hellip


Conv

laye

r 2

Conv

laye

r 1

Conv

laye

r 2

Conv

laye

r 2

+ + +

Conv

laye

r 1

(b)

C64

C128

C256

C512


Conv

laye

r

Decision [0 1]

(c)















0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of































0972

0974

0976

0978

098

0982

SSIM

005

0055

006

0065

007

0075

NM

AD




ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















ROI

(a) (b) (c) (d) (e)


(a) (b) (c)

ROI I

ROI II

(d) (e)

2000

1800

1600

1400

1000

1200

800

600

400

200

0


(a) (b) (c) (d) (e)

ROI I

ROI II






Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















Data Availability






Acknowledgments


References
























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of

























































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















unpaired low-dose ct denoising network based on cycle...

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