A Lightweight Secure Image Super Resolution using Network Coding

Quoc-Tuan Vien

1 a

, Tuan T. Nguyen

2 b

and Huan X. Nguyen

1 c

Faculty of Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, U.K.

School of Computing, Buckingham University, Hunter St., Buckingham MK18 1EG, U.K.

Keywords:

Image Communication, Deep Learning, Super-resolution, Network Coding.

Abstract:

Images play an important part in our daily life. They convey our personal stories and maintain meaningful ob-

jects, events, emotions etc. People, therefore, mostly use images as visual information for their communication

with each other. Data size and privacy are, however, two of important aspects whilst transmitting data through

network like internet, i.e. the time prolongs when the amount of data are increased and the risk of exposing

private data when being captured and accessed by irrelevant people. In this paper, we introduce a uniﬁed

framework, namely Deep-NC, to address these problems seamlessly. Our method contains three important

components: the ﬁrst component, adopted from Random Linear Network Coding (RLNC), to protect the shar-

ing of private image from the eavesdropper; the second component to remove noise causing to image data due

to transmission over wireless media; and the third component, utilising Image Super-Resolution (ISR) with

Deep Learning (DL), to recover high-resolution images from low-resolution ones due to image sizes reduced.

This is a general framework in which each component can be enhanced by sophisticated methods. Simulation

results show that an outperformance of up to 32 dB, in terms of Peak Signal-to-Noise Ratio (PSNR), can be

obtained when the eavesdropper does not have any knowledge of parameters and the reference image used in

the mixing schemes. Various impacts of the method are deeply evaluated to show its effectiveness in secur-

ing transmitted images. Furthermore, the original image is shown to be able to downscale to a much lower

resolution for saving signiﬁcantly the transmission bandwidth with negligible performance loss.

1 INTRODUCTION

Deep Learning (DL) has recently received increas-

ing attention and achieves impressive results across

a spectrum of domains such as medicine, automation,

transportation, security, and so forth. It is a speciﬁc

sub-ﬁeld of machine learning that uses neural network

with multiple layers. Each layer represents a deeper

level of knowledge. DL learns representations from

data through successive layers to increase meaningful

representations.

The reasons for the success of DL can be at-

tributed to two folds: ﬁrst, the feature learning (Good-

fellow et al., 2016) capacity of its hierarchical archi-

tecture allows for automatically extracting meaning-

ful features from data, in which lower layers identify

basic features, and deeper layers synthesize higher-

level features in terms of learned lower-level ones;

second, the development of high-performance com-

https://orcid.org/0000-0001-5490-904X

https://orcid.org/0000-0003-0055-8218

https://orcid.org/0000-0002-4105-2558

puters with Graphic Processing Units and Tensor Pro-

cessing Units enable to perform a large number of op-

erations in reduced CPU times. Moreover, with the in-

creasing digitisation transformation, the applicability

of DL is more pronounced as the bigger data become,

the larger DL architecture is expected, and vice versa,

to capture underlying patterns better.

Research has proven that DL is one of effective

techniques for Super Resolution (SR) tasks with the

development of multiple DL based architectures. SR

is the process of recovering a High-Resolution (HR)

image from a given Low-Resolution (LR) image (Kim

et al., 2016). An LR image is an image which has a

reduced dimension or contains noise or blurring re-

gions. The relationship between an HR image and an

LR image can be represented by a function which al-

lows us to invert the LR image back to the HR im-

age. If the invert function is known, the HR im-

age can be easily reconstructed from the LR image.

In reality, this is, however, not the case. The core

problem of the SR is to create a mapping between

the LR and HR images. Although there are a va-

riety of approaches, they can be grouped into four

Vien, Q., Nguyen, T. and Nguyen, H.

A Lightweight Secure Image Super Resolution using Network Coding.

DOI: 10.5220/0010212406530660

In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 4: VISAPP, pages

653-660

ISBN: 978-989-758-488-6

653

main architecture types (Wang et al., 2020) includ-

ing: i) Pre-upsampling with bi-cubic (Keys, 1981)

and bi-linear interpolation (Smith, 1981); ii) Post-

upsampling at the last learnable layer; iii) Progressive

Upsampling with Laplacian pyramid SR framework

(LapSRN) (Lai et al., 2017); and iv) Iterative Up and

Down Sampling SR with back-projection (Irani and

Peleg, 1991), DBPN (Haris et al., 2018) and SRFBN

(Li et al., 2019b).

Nowadays, data transfer is a crucial part of our

daily life and in multiple areas. Multiple tech-

niques have been introduced to transmit data efﬁ-

ciently. Network coding (NC) is one of them. Its con-

cept (Ahlswede et al., 2000) has been well exploited

in a vast number of research work from networking

and communications perspective aiming to increase

the system throughput by allowing the intermediate

nodes to perform encoding the incoming data rather

than operating simply as store-and-forward switches.

Speciﬁcally, an algebraic approach of NC, namely

random linear NC (RLNC), was developed in (Koet-

ter and Medard, 2003) where the intermediate nodes

can perform random linear operations on the incom-

ing data packets from different transmission source

nodes. The sink nodes with a sufﬁcient number of

mixed data packets along with all RLNC coefﬁcients

can recover the data of all source nodes.

Digital images contain quite a lot of essential in-

formation and are widely used to communicate be-

tween people over internet. Several issues encounter

during transmission such as data privacy and reducing

amount of data transferred to lessen the transmission

time. Various methods are developed to protect them

such as stenography, encryption, and watermarking.

Stenography is a method to hide data inside an image.

In the encryption approach, one image is converted

into an encrypted image by using the secret key. The

core idea of the encrypted image is to turn understand-

able data into incomprehensible data which are hard

to realise. On the other hand, watermarking tech-

niques are to embed the signature into an image to

visualise or hide the ownership of the image.

In general, steganography and encryption are dif-

ferent but they serve one main purpose, protecting

necessary data from irrelevant people. Encryption is

more ﬂexible and secure (Xie et al., 2019; Guerrini

et al., 2020; Peng et al., 2020). Human, however, is

always curious and tries to see what messages when

they receive encrypted information. In such cases,

steganography is a better option because the hidden

message can be embedded so that the change of im-

age will not be noticed and does not draw attention

(Bender et al., 1996; Franz et al., 1996; Chen and

Lin, 2006). This technique nevertheless requires the

hidden message to have a smaller size than the cover

image’s, meaning that hiding an image into another

image is not easily achievable.

Different from multiple works solely focusing on

data security, or interested in data compression, our

work integrates both techniques together to gain a bet-

ter information protection. This aim is to develop a

simple yet efﬁcient method to conceal and reduce the

ﬁle size whilst transmitting image data through net-

work. When the data is received, it can be easily re-

covered at the other end. Inspired by the NC concept,

a secure Image SR (ISR) using DL and NC, namely

Deep-NC, is proposed and demonstrated in the sce-

nario for an image communication between Alice and

Bob.

In the proposed Deep-NC, the downscaled image,

i.e. LR version of the original image, is incorporated

with the reference image by RLNC encoding prior to

transmitting to Bob. Over noisy channel, the received

image at Bob is denoised, followed by RLNC decod-

ing using the shared reference image and VDSR for

recovering the original image of high resolution. The

performance of the proposed Deep-NC is evaluated

in terms of Peak Signal-to-Noise Ratio (PSNR) tak-

ing into account additive white Gaussian noise model.

The impacts of RLNC, shared image dataset, noise

and scaling factor on the performance are assessed

through simulation to validate the effectiveness of the

proposed scheme. Simulation results show that Bob

achieves a far better performance than Eve with the

employment of Deep-NC, especially when the Eve

has no knowledge of the reference image shared be-

tween Alice and Bob. Additionally, both VDSR and

bicubic interpolation are shown to provide a better

performance at Bob compared to Eve. Furthermore,

the proposed Deep-NC allows the image to be down-

scaled to a much lower resolution to save the trans-

mission bandwidth, while still maintaining a signiﬁ-

cantly higher performance than Eve.

2 SYSTEM MODEL

A typical secure image communication model is con-

sidered where Alice (A ) wants to send a private image

to Bob (B) in the existence of Eve (E ) trying to eaves-

drop the image.

Let I

denote the original image of size M × N

that Alice wants to send. Considering typical colour

images with three channels, i.e. red, green and blue,

can be deﬁned as an M × N × 3 array, i.e.

: f (x

) → R

, (1)

where f (x

) ∈ R is the intensity of the image pixel

at point (x

). Over the transmission media, the

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

654

noise is inevitable, which causes image degradation.

Generally, Gaussian noise model has been regarded

as the best ﬁt in representing the additive noise in the

undesired signal at the receiver in most of commu-

nication systems due to its simplicity with dominant

central limit theorem.

Considering additive noise model, the image re-

ceived at node X , X ∈ {B ,E}, is given by

= I

+ N

, (2)

where N

, X ∈ {B,E}, is additive white Gaussian

noise (AWGN) at X having mean µ

and variance σ

In order to denoise an image with AWGN, a deep

neural network can be employed, e.g. a pretrained

DnCNN network (Zhang et al., 2017).

3 PROPOSED SECURE ISR

Our proposed approach is shown in the ﬂowchart,

Fig. 1, which consists of the following main steps:

3.1 Downscaling at Alice

In order to save the transmission bandwidth, a LR ver-

sion of the original image is ﬁrstly generated using

bicubic interpolation. The bicubic ﬁlter is employed

for downscaling due to its low computational com-

plexity, while preserving image details with smooth

interpolated surface.

After downscaling the original image, i.e. I

, from

Alice, we have a LR image I

having size dM/δe ×

dN/δe × 3 where δ denotes the scaling factor and dxe

denotes the ceiling function of x.

3.2 RLNC Encoding at Alice

Following the concept of RLNC (Koetter and Medard,

2003), in the proposed scheme, the downscaled im-

age at Alice is linearly mixed with a reference image

using random scalar coefﬁcients, a.k.a. RLNC coefﬁ-

cients. The reference image is acquired from an im-

age datastore which is assumed to be shared between

users as a common image dataset.

Note that common blocks at Bob and Eve to represent

the same steps are combined in the following discussion.

There exist different downscaling methods, e.g. Box

sampling, Nearest-neighbour interpolation, Lanczos Filter-

ing (Duchon, 1979), or CNN based downscaling like (Li

et al., 2019a); however, we do not need a sophisticated

downscaling method in this work.

Notice that only RLNC coefﬁents and the index of the

reference image are shared between Alice and Bob prior to

transmission as private keys in key-agreement protocols.

In order to mix two images, the shared image is

ﬁrst downscaled to the same size of the original LR

image. Let I

and I

denote the HR and LR shared

image, respectively. I

should have the same size of

, i.e. an dM/δe × dN/δe × 3 array.

The mixing of the original image and the shared

image can be realised as follows:

= α

+ α

, (3)

where I

denotes the transmitted image at Alice, α

and α

are RLNC coefﬁcients having α

> 0, α

≥ 0

and α

+ α

= 1. Here, α

and α

represent the

fractions of original image and shared image, respec-

tively, in the mixed image.

Remark 1 (Image Decodability-security Tradeoff)

A higher α

results in a better performance at Bob

with an enhanced image decodability, while a higher

helps secure the original image from Eve. In fact,

a higher α

means more information of the original

image in the mixed image, and thus Bob can recover

the desired image with higher decodability. However,

Eve also overhears the same amount of information

to be able to extract the original image, which means

more information at the same time is leaked to Eve.

On the other hand, a higher α

, i.e. a lower α

, causes

degradation of the image decodability at Bob, but it

helps improve the secrecy of the image communica-

tions due to less information of the original image in

the image mixture. Therefore, it is crucial to ﬁnd α

(or α

) to balance the tradeoff between the image de-

codability and security.

3.3 Denoise at Bob and Eve

Over the noisy channel, the image transmitted from

Alice is deteriorated caused by Gaussian noise. It is

assumed that Eve experiences the same noisy envi-

ronment as Bob.

The images received at B and E over Gaussian

noise model can be obtained as in (2), i.e.

= I

+ N

, (4)

where X ∈ {B,E} and I

is the transmitted image

at Alice given by (3). Both B and E then remove

the Gaussian noise using the same pretrained DnCNN

network.

Let us denote the denoised images at B and E af-

ter ﬁltering by

and

, respectively.

3.4 RLNC Decoding at Bob

Given the index of the reference image in the shared

image datastore and RLNC coefﬁcients, i.e. α

or α

A Lightweight Secure Image Super Resolution using Network Coding

655

Figure 1: Proposed Deep-NC for secure ISR.

Bob can recover the image transmitted from Alice as



− α



, (5)

where I

is the LR version of the shared image and

is the decoded image at B.

3.5 RLNC Estimation at Eve

Trying to decode the image shared from Alice, Eve

however does not know the RLNC coefﬁcients, i.e.

and α

, and the index of the image in the shared

datastore, i.e. I

, which was used at Alice for mixing

it with the original image. Therefore, Eve has to esti-

mate the RLNC parameters and select the right image

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

656

in the datastore to recover the image.

The RLNC coefﬁcients estimated at Eve can be

written by

= α

± ε

, (6)

= 1 −

, (7)

where

and

are estimated RLNC coefﬁcients of

and α

, respectively, and ε

denotes the estimation

error of α

at Eve knowing the fact that

= 1.

In addition to the RLNC coefﬁcients, Eve needs to

predict the image in the shared datastore that was used

for encoding at Alice. Letting

denote the predicted

image, Eve can decode the image following the same

method at Bob in Subsection 3.4.

3.6 VDSR at Bob and Eve

To be able to recover original images from decoded

images by RLNC, the VDSR framework, mentioned

in (Kim et al., 2016), was implemented. VDSR

was, then, trained with a public available IAPR TC-12

Benchmark dataset. We use simiar hyper-parameters

described in (Kim et al., 2016). More speciﬁc, the

training used batches of size 64, 100 epochs. The

learning rate is initially 0.1 and decreased by a fac-

tor of 10 every 10 epochs. The VDSR was trained

with the scaling factor δ = 4.

Then, the decoded images by RLNC decoding at

Bob, i.e.

, and at Eve, i.e.

, are fed into VDSR

model to obtain the upscaled images at Bob and Eve,

denoted by

and

. respectively. The upscaled im-

ages at Bob and Eve can be written by

= V DSR(

), (8)

= V DSR(

), (9)

respectively, where V DSR(·) denotes the operator

function to reconstruct the images with the scaling

factor δ trained before.

It is worth to mention that other SR methods can

be exploited to replace VDSR.

4 EVALUATION METHOD OF

THE PROPOSED DEEP NC

In order to evaluate the effectiveness of the proposed

Deep-NC for secure VDSR, Peak Signal-to-Noise Ra-

tio (PSNR) is presented in this section as a perfor-

mance metric to compare the quality of the recovered

image at Bob and Eve, i.e.

and

, with the original

HR image transmitted from Alice, i.e. I

The peak signal-to-noise ratio (PSNR) is the ra-

tio between a signal’s maximum power and the power

of the signal’s noise. Engineers commonly use the

PSNR to measure the quality of reconstructed images

that have been compressed. Each picture element

(pixel) has a color value that can change when an im-

age is compressed and then uncompressed. Signals

can have a wide dynamic range, so PSNR is usually

expressed in decibels, which is a logarithmic scale.

As a well-known image comparison metric, the

PSNR is considered to evaluate the loss of the image

quality. In the proposed secure ISR, the loss is due to

not only the noise at Bob, but also the lack of details

in the LR downscaled image and the training loss in

the VDSR network.

The PSNR, in dB, of the recovered image

Bob with respect to the original image I

is deﬁned

PSNR , 10log

MSE

, (10)

where MSE is the mean square error between

and

given by

MSE , E



−



. (11)

Here, E[·] denotes the expectation operator.

Considering RGB colour images having size M ×

N with three RGB values per pixel, the MSE can be

calculated by

MSE =

3MN

∑

x=1

∑

y=1

∑

z=1



(x,y,z) −

(x,y,z)



(12)

Note that the PSNR at Eve is also evaluated using

(10). However, the quality of the recovered image is

further degraded due to the unknown reference image

and the lack of the information of RLNC coefﬁcients

which are only shared between Alice and Bob.

5 SIMULATION RESULTS

In this section, we present the simulation results of the

proposed Deep-NC in terms of PSNR. We ﬁrst com-

pare the performance at Bob with that at Eve when

employing either bicubic interpolation or VDSR

for

converting the received LR images to the original HR

images. The impacts of shared image dataset, Gaus-

sian noise, RLNC coefﬁcients and scaling factor on

the performance are then sequentially evaluated to

show the enhancement of the proposed scheme in se-

curing the private image from the Eve. The results

In this work, the image is in double-precision ﬂoating-

point data type having maximum possible pixel value of 1.

It is worth to notice that the VDSR is selected as a typ-

ical ISR to validate the effectiveness of the proposed Deep-

NC in securing the image. A comparison of different ISR

schemes is beyond the scope of this work.

A Lightweight Secure Image Super Resolution using Network Coding

657

Figure 2: Images for evaluation of the proposed Deep-NC.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Noise variance (

)

-10

-5

PSNR [dB]

Bicubic (at Bob)

VDSR (at Bob)

Bicubic (at Eve) (known reference image)

VDSR (at Eve) (known reference image)

Bicubic (at Eve) (15th)

VDSR (at Eve) (15th)

Bicubic (at Eve) (16th)

VDSR (at Eve) (16th)

At Eve

Figure 3: PSNR versus noise variance with respect to dif-

ferent shared images at Eve.

are obtained by simulation in MATLAB. The training

is performed on an image dataset of the IAPR TC-12

benchmark with 20,000 still natural images which are

available free of charge and without copyright restric-

tions (Grubinger et al., 2006). In the following exper-

iment, the scaling factor is set as δ = 4, unless other-

wise stated. For validation of the proposed scheme,

20 undistorted images of the Image Processing Tool-

box in MATLAB are used as shown in Fig. 2 in which

the last image is selected as a reference image.

5.1 Impacts of Shared Image Dataset

In order to decode the original image, apart from the

RLNC coefﬁcients, the reference image in the datas-

tore is required to be known at the receiver. Consid-

ering the scenario when Eve may not know the ref-

erence image used at Alice or may use the incorrect

image, Fig. 3 plots the PSNR of the proposed scheme

as a function of the noise variance, i.e. σ

, with re-

spect to different shared images at Eve including the

15th, 16th and 20th reference images. Here, the 20th

image is used for the RLNC encoding at Alice. Bicu-

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Noise variance (

)

-5

PSNR [dB]

Bicubic (at Bob)

VDSR (at Bob)

Bicubic (at Eve)

VDSR (at Eve)

Figure 4: PSNR versus noise variance in Gaussian white

noise model.

bic interpolation and VDSR are employed as typical

ISR for upscaling. It can be observed in Fig. 3 that

the PSNR at Eve is considerably degraded when the

wrong reference image is selected for decoding. For

instance, in the noise-free environment with VDSR

upscaling, the PSNR at Eve decreases by 7 dB when

using the 15th or 16th image instead of the 20th im-

age. A further notice is the fact that, without knowl-

edge of the RLNC coefﬁcient, Eve can only achieve

a close performance to Bob even with the right refer-

ence image. This accordingly reﬂects the effective-

ness of the proposed scheme in securing the origi-

nal image. Furthermore, as shown in Fig. 3, Bob

achieves a much better performance than Eve of up

to 32 dB when Eve implements only bicubic interpo-

lation. This is due to the fact that no SR is involved in

the image processing at Eve in this case along with es-

timation error of RLNC coefﬁcient and the unknown

reference image.

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

658

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

RLNC coefficient of original image (

)

PSNR [dB]

v = 0.1 (at Bob)

v = 0.1 (at Eve)

v = 0.2 (at Bob)

v = 0.2 (at Eve)

Figure 5: PSNR versus RLNC coefﬁcient of original image.

5.2 Impacts of Noise

Considering AWGN model in image communication

over wireless medium, Fig. 4 plots the PSNR of the

proposed scheme versus noise variance, i.e. σ

with

the assumption that Bob and Eve experience the same

noise model. Two typical upscaling schemes, i.e. the

bicubic interpolation and VDSR, are employed at Bob

and Eve. The reference image shared to Bob is also

leaked to Eve. Intuitively, it can be seen that the

PSNR decreases as the noise variance increases. Over

the wireless medium, the VDSR is shown to be bene-

ﬁcial providing a higher PSNR than the bicubic inter-

polation. Similarly, Bob is shown to achieve a better

performance than Eve over the whole range of noise

variance with both bicubic interpolation and VDSR,

though the performance gap is smaller in the more

lossy environment. For instance, with the VDSR up-

scaling, the PSNR at Bob is 3 dB and 2 dB higher than

that at Eve, while a considerable enhancement of 14

dB and 13 dB can be achieved with the bicubic inter-

polation when σ

= 0.1 and σ

= 0.2, respectively.

5.3 Impacts of RLNC Coefﬁcients

Investigating the impacts of RLNC coefﬁcients on the

performance of the proposed scheme, Fig. 5 plots the

PSNR of the proposed scheme versus the RLNC co-

efﬁcient of the original image, i.e. α

, with respect to

different noise variances at Bob and Eve. Speciﬁcally,

two noise variances, i.e. σ

= σ

= {0.1,0.2},

are considered. It can be seen that Bob achieves a bet-

ter performance than Eve for all RLNC coefﬁcients.

Also, the PSNR at both Bob and Eve increases as α

increases. This is due to the fact that there is more

information of the original image in the mixed im-

age. As noted in Remark 1, the RLNC coefﬁcients

should be selected so as to restrict Eve from recover-

ing the original image, while maintaining the higher

image decodability at Bob. For instance, α

should

be less than 0.5 to limit the PSNR at Eve by 14 dB

when σ

= 0.1. The PSNR coefﬁcients should be

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Noise variance (

)

PSNR [dB]

VDSR (at Bob) - scale=4

VDSR (at Bob) - scale=10

VDSR (at Eve) - scale=4

VDSR (at Eve) - scale=10

At Bob

At Eve

Figure 6: PSNR versus noise variance with respect to dif-

ferent scaling factors.

thus selected depending also on the noise variance.

As shown in Fig. 5, with the same requirement of the

maximal PSNR at Eve by 14 dB, α

should not be

greater than 0.5 and 0.7 when σ

= 0.1 and σ

= 0.2,

respectively.

5.4 Impacts of Scaling Factor

The impacts of scaling factor are shown in Fig. 6

where the PSNR at Bob and Eve of the proposed

scheme is plotted against noise variance in AWGN

model, i.e. σ

, with different scaling factors, i.e. δ = 4

and δ = 10. VDSR is considered with the same set-

tings as in Fig. 4. It can be seen in Fig. 6 that the

PSNR at Bob decreases considerably in the noiseless

environment as the scale increases, while there is not

much difference in the PSNR in the noisy environ-

ment. For instance, 4 dB is reduced when σ

= 0,

while less than 1 dB when σ

> 0.1. This means that

over the noisy medium, the image can be downscaled

with a higher scaling factor to save the bandwidth

with negligible performance loss.

6 CONCLUSIONS

In this paper, we have proposed a Deep-NC pro-

tocol for secure ISR communication between Alice

and Bob taking into account Gaussian noise model.

Speciﬁcally, RLNC has been adopted to protect the

secret image from Eve. It has been shown that Bob

achieves a much higher PSNR than Eve of up to 32

dB with the proposed Deep-NC protocol. Addition-

ally, an enhanced performance has been shown to

achieve at Bob over the whole range of noise vari-

ance in Gaussian model. Furthermore, the Deep-NC

protocol enables the original image to be downscaled

to a much lower resolution prior to transmitting over

the lossy environment, which accordingly implies the

effectiveness of the proposed scheme in saving the

transmission bandwidth.

A Lightweight Secure Image Super Resolution using Network Coding

659

ACKNOWLEDGMENT

This work was supported in part by a UKIERI grant,

ID ‘DST UKIERI-2018-19-011’, and in part by an

Institutional Links grant, ID 429715093, under the

Newton Programme Vietnam partnership.

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