https://doi.org/10.31449/inf.v43i3.2916 Informatica 43 (2019) 415 –420 415 
Super-resolution Reconstruction of Noisy Video Image Based on Sparse 
Representation Algorithm 
Tierui Zhang, Dandan Li, Yanxia Cai and Yanyan Xu 
Hengshui University, Hengshui, Hebei 053000, China 
E-mail: ddli_dan@yeah.net 
Keywords: sparse representation, super-resolution, image reconstruction, image denoising, video image, image 
processing 
Received: July 29, 2019 
In this paper, the image super-resolution reconstruction (SRR) based on sparse representation was 
studied. Firstly, the sparse representation algorithm was simply analyzed, and then applied to the SRR 
processing of single image. In noisy video images, the Lucy-Rechardson algorithm was used for denoising 
first, then Lucas Kanade + multi-scale autoconvolution (MSA) method was used to register video images, 
and finally SRR was processed by sparse representation algorithm. Three video images were taken as 
examples for analysis, and the peak signal to noise ratio (PSNR) value and the structural similarity index 
measurement (SSIM) value were used as image quality evaluation indexes. The results showed that the 
average PSNR value and average SSIM of the SRR processing method based on sparse representation 
were significantly higher than those of bicubic interpolation method; the quality of the processed image 
was higher and the super-resolution effect was better. The experimental results prove the reliability of the 
proposed method and make some contributions to the further application of the sparse representation 
algorithm in SRR processing. 
Povzetek: Predstavljena je metoda za rekonstrukcijo kvalitetne slike iz slabih posnetkov s kombiniranjem 
vrste algoritmov.  
1 Introduction 
In general, the higher the resolution of an image, the 
clearer the image and the stronger the ability to express 
details. After a certain imaging process for high-
resolution (HR) scenes, low-resolution (LR) images are 
obtained due to degradation processes such as blurring 
and noise, but LR images are required in many 
applications. At present, the commonly used methods to 
improve image quality include image denoising, 
restoration, enhancement, and image super-resolution 
reconstruction (SRR). SRR refers to a method of 
reconstructing an HR image through one or more LR 
images [1]. SRR technology is an ill-posed inverse 
problem [2, 3], which can acquire LR images without 
changing the hardware conditions, and it is of great value 
in the field of image processing. Sparse representation 
algorithms are also widely used in SRR processing [4]. 
In this paper, the application of sparse representation 
algorithm in SRR processing was studied, and a SRR 
processing method based on sparse representation of 
noisy video images was designed. The effectiveness of 
the proposed method was proved by an example analysis, 
which was beneficial to the better application of sparse 
representation algorithm in SRR processing and also 
provided some theoretical support for SRR processing of 
noisy video images. 
2 Related works 
Xing et al. [5] designed a novel neural network with 
barycentric weight function (BWFNN) method, and 
reconstructed image details through nonlinear center-of-
gravity weight functions, showing excellent efficiency in 
image reconstruction. Dai et al. [6] proposed an improved 
projections onto convex sets (POCS) method to obtain 
the initial estimation of HR images by iterative curvature-
based interpolation (ICBI). The experimental results of 
subjective evaluation and objective evaluation proved the 
effectiveness of this method. Chen et al. [7] designed a 
regularization model based on the anisotropic fractional 
order adaptive (AFOA) specification, applied it to SRR 
image processing, and found that the model could achieve 
adaptive removal of image noise and well protect image 
edges. The experimental results showed that the image 
quality obtained by this method was good. Wang et al. [8] 
created a series of nested neighborhoods to collect LR 
pixels and then estimate the HR pixel values. This is a 
non-iterative method, which does not encounter 
convergence problems, but also has high computational 
efficiency. 
3 Sparse representation algorithm 
3.1 Sparse representation 
The sparse representation of signal can be expressed as:
Da x st a = . , min
0
, 
where a
 
is sparse representation 
coefficient, D is over-complete dictionary, and 
0
. is the 
number of non-zero elements of a vector. Assuming that 
the limiting error must within  , the sparse 

416 Informatica 43 (2019) 415 –420 T. Zhang et al. 
representation problem can be written as:
  −
2 0
. , min Da x st a . 
3.2 Sparse coding 
The method to solve the sparse representation problem is 
sparse coding, also known as sparse decomposition, 
which can be expressed as:
x Da st a a
a
 = . , min arg
~
0
. 
In this paper, the 
orthogonal matching pursuit (OMP) algorithm is chosen 
to solve this problem. 
The original signal is expressed as y ,
 
and the given 
sparsity is k; initial margin y r =
0
, supporting index set
 =
0
I , and initial iteration number 1 = k .
 
The 
supporting index is calculated in the k -th
 
cycle:
i k
N i
k
d r , min arg
1
, , 2 , 1
−
=
=

 , then the support set is
k k k
I I   =
−1
. The residual is updated:
( ) y D D D D y r
T T
k
k k k k
   
1 −
− = . After loop iteration for
k times, when   − Da y , the sparse coefficient
( ) y D D D D a
T T
k k k k
   
1 −
=
 
is output. 
4 SRR processing of noisy video 
images under sparse 
representation 
4.1 SRR processing of single image 
It is assumed that the sparse coefficients of image blocks 
are the same under HR dictionary
h
D
 and LR dictionary 
l
D
.  In SRR processing, the HR image is firstly degraded 
to LR image, and the training sample pair composed of 
HR image block and LR image block is obtained. After 
training 
h
D
and
l
D
, the sparse coefficient
a
of LR image 
block
l
x
is calculated on 
l
D
, and the reconstructed HR 
image block is obtained through a D x
h h
= . 
The mapping relationship between HR image block 
and LR image block is represented by a sparse dictionary, 
and the single dictionary training model is established as 
follows:
N i d st D X D
i
D
 , 2 , 1 , 1 . , min arg
2
2 1
2
2
=   +  − =


(1) 
where  
M
x x x X , , ,
2 1
 =
 
represents an image 
block, M represents the total number of samples, 
 
M
a a a , , ,
2 1
 = 
 
represents a sparse coefficient 
matrix, N represents the number of dictionary atoms, and 
 is a Lagrangian multiplier used for balancing fidelity 
and sparsity. 
In the image SRR, the two dictionaries can be 
expressed as: 
1
2
2
min arg  +  − =


h h
D
h
D X D
h
 
,        (2) 
1
2
2
min arg  +  − =


l l
D
l
D Y D
l
 
,            (3) 
where 
h
X
and 
l
Y
are training sample matrices 
composed of HR image blocks and LR image blocks 
respectively. 
The two dictionaries are trained jointly and expressed 
as: 
 
1
2
2
2
2
, ,
1 1 1 1
min 








+ +  − +  −

Q P
D Y
Q
D X
P
l l h h
D D
l h

(4) 
where P
 
and Q
 
represent the sample number of 
HR and LR image blocks respectively. 
The training model of the dictionary can be 
expressed as: 
 












=












=  +  −

l
h
l
h
D
D
Q
D
P
D
Y
Q
X
P
X D X
1
1
,
1
1
, min
1
2
2
,

.(5)
 
4.2 Video image SRR processing 
SRR was performed on video images on the basis of SRR 
for single image. The process was mainly divided into 
two steps: (1) registering LR sequence images; (2) 
obtaining HR image by SRR processing of image. 
4.2.1 Motion estimation 
In this paper, a hybrid non-display motion estimation 
method combining Lucas Kanade and multi-scale 
autoconvolution (MSA) was used to achieve image 
registration. Firstly, the initial motion of the image block 
was estimated by MSA, and then Lucas Kanade method 
was used for further registration to achieve accurate 
calculation of motion displacement. The steps of the 
hybrid method are as follows. 
The current frame image is represented by f , the 
previous frame is represented by 1 + f , and the next 
frame is represented by 1 − f . The image f is divided 
into blocks with the size of 
1 1
n m  , and the position of 
the current frame image block R is expressed as 
( ) y x   , .
 
The position ( )
1 1
, y x   of the image blocks 
corresponding to the front and rear frames was calculated 
by MSA method, and the search range is 
2 1
s s  , then the 
average motion displacement ( )
2 2
, y x   of the image 
blocks of three frames was calculated by using the motion 
displacement ( )
1 1
, y x   . The image block M of 
2 2
n m 
 
is intercepted in R , and the corresponding 
image blocks ' M
 
and ' ' M
 
before and after frames are 
intercepted by motion displacement. The motion 
displacement of the image blocks ' M
 
and ' ' M
 

Super-resolution Reconstruction of Noisy Video Image...  Informatica 43 (2019) 415 –420 417 
matched with 
M can be expressed as 
( ) ( )
2 2 1 1
, , y x y x   +   . 
4.2.2 SRR processing 
LR video sequence is set as
    ,
~
,
~
,
~
,
1 1 + − k k k
I I I
, and up-
sampling video sequence as     , , , ,
1 1 + − k k k
I I I . After 
registration, the image block of each frame is 
( )   , , , ,
1 1 + − k k k
x x x ,
 
The trained dictionary 
l
D
 
and 
h
D
 
are used to solve the sparse problem, the block 
h
k
x
 
of the current frame after SRR is obtained, and the whole 
video sequence is restored. 
5 Image quality evaluation index 
It is assumed that a N M  noisy video image is ( )
j i f , , 
and the image processed by SRR is ( ) j i f , . The 
indicators for evaluating the quality of the image 
processed by SRR are: 
(1) Peak signal to noise ratio (PSNR): 
𝑃 𝑆𝑁 𝑅 = 10 𝑙𝑜𝑔
10
{
25 5
2
1
𝑀 × 𝑁 ∑ ∑ [ 𝑓 ( 𝑖 , 𝑗 ) − 𝑓 ̄
( 𝑖 , 𝑗 ) ]
2
𝑁 𝑗 = 1
𝑀 𝑖 = 1
} 
the larger the PSNR value, the better the image quality. 
(2) Structural similarity ratio (SSIM): 
𝑆𝑆𝐼 𝑀 =
( 2 𝜇 𝑥 𝜇 𝑦 + 𝐶 1
) ( 2 𝜎 𝑥𝑦
+ 𝐶 2
)
( 𝜇 𝑥 2
+ 𝜇 𝑦 2
+ 𝐶 1
) ( 𝜎 𝑥 2
+ 𝜎 𝑦 2
+ 𝐶 2
)
, where
x
 and 
y

 
are the 
mean values of the two images, 
x
 and
y

 
represent the 
standard deviation, 
xy

 
represents covariance, and 
1
C
 
and 
2
C
 
are small positive numbers with denominators of 
0 or close to 0 [9]. The closer the SSIM value to 1, the 
higher the similarity between the processed image and the 
original image, and the better the image quality. 
6 Case analysis 
6.1 Noise video image preprocessing 
In this paper, three road monitoring video were taken as 
examples to analyze the performance of the SRR method 
designed in this paper, and randomly selected some frame 
from the video image, as shown in Figure 1. 
As can be seen from Figure 1, the video had a low 
resolution and some noises. The noise in the video image 
needed to be removed before SRR is performed. In this 
paper, Lucy-Rechardson algorithm was used, and its 
iteration expression is: 
( ) ( )
( )
















=
+
h
h f
g
f f
k
k k 1
,               (6) 
where g
 
is degraded images, f
 
is the estimation of 
the original undegraded image, h
 
is a known point 
spread function, 
 
is convolution, 
 
is related 
operations, and k
 
is the number of iterations. 
Lucy-Rechardson algorithm and wiener filter [10] 
are used for denoising, and the comparison results is 
shown in Figure 2. 
Figure 3 is the local details of the image in Video 1, 
they are the original noisy image, the Lucy-Rechardson 
denoised image and the Wiener filtering denoised image, 
from left to right. Combined with Figure 2 and Figure 3, 
it can be found that the Lucy-Rechardson had better 
denoising effect than the Wiener filtering, which could 
better remove the noise in the image and retain the image 
details. 
 
Figure 1: Noisy video images. 

418 Informatica 43 (2019) 415 –420 T. Zhang et al. 
6.2 SRR processing results of video image 
The HR and LR dictionaries were obtained by training 
the denoised video image sequence, then the image 
registration was realized by Lucas Kanade+MSA. The 
sparse coefficient was solved according to the 
registration image block, then the HR image blocks were 
restored by the obtained sparse coefficients, and the 
reconstructed HR video image sequences were obtained. 
The results are shown in Figure 4. 
By comparing Figure 4 and Figure 1, it can be found 
that the quality of the video image after SRR processing 
was obviously improved, and the image details were 
more clear. To further understand the performance of the 
proposed method in this paper, it was compared with the 
bicubic interpolation method (a reconstruction method 
that obtains HR pixels from LR pixels by weighted 
averaging of the nearest sixteen sample points in a 
rectangular grid) [11] and ten consecutive frames of 
images in each video were taken. Video 1 was used as an 
example, and its PSNR value and SSIM value of video 1 
are shown in Figure 5. 
According to Figure 5 and 6, it can be found that the 
PSNR value of the video image reconstructed by this 
method was significantly higher than that of the bicubic 
interpolation method, and the SSIM value was closer to 
1, indicating that the reconstructed image had better 
super-resolution effect. The average values of the three 
video indicators were compared, and the results are 
shown in the Table 1. 
 
 
  
Figure 2: Comparison of denoising results. 
 
Figure 3: Local contrast 
 
Figure 4: SRR results. 

Super-resolution Reconstruction of Noisy Video Image...  Informatica 43 (2019) 415 –420 419 
Index Video 1 Video 2 Video 3 
Average PSNR (dB) Bicubic interpolation 27.8557 26.4525 27.2154 
Method of this paper 29.4528 28.8745 29.4854 
Average SSIM Bicubic interpolation 0.8638 0.8542 0.8624 
Method of this paper 0.9445 0.9369 0.9486 
Table 1: Image quality evaluation results. 
According to the results of Table 1, it can be found 
that in the three video images, the average PSNR value 
and the average SSIM value of the proposed method were 
higher than those of the bicubic interpolation. Taking 
Video 1 as an example, the average PSNR value of the 
image obtained by using the bicubic interpolation was 
27.8557 dB, and the average SSIM value obtained by this 
proposed method was 29.4528 dB, which was obviously 
higher. The average SSIM value obtained by bicubic 
interpolation was 0.8638, and that of proposed method 
was 0.9445.  According to the results of image quality 
evaluation, the SRR based on sparse representation 
designed in this paper had a higher super-resolution effect 
and image quality, which proved the reliability of the 
proposed method. 
7 Discussion 
SRR technology has important application value in many 
fields. In the aspect of entertainment, SRR technology 
can be used to recover low-resolution films and other 
influential materials from the 1980s to 1990s; in the 
aspect of medicine, it can improve the details of medical 
images such as Magnetic Resonance Imaging (MRI) [12], 
which can provide reliable basis for doctors' diagnosis 
[13]; in satellite remote sensing imaging, the LR image 
obtained by SRR is conducive to target recognition and 
provide reliable information for military investigation 
and environmental monitoring, etc. [14]. The application 
of SRR technology involves various fields of production 
and life, so it is of great practical significance to study 
SRR technology. 
At present, the methods for image SRR processing 
mainly include interpolation-based algorithms, image 
sequence-based algorithms, maximum posterior 
probability methods, regularization methods [15] and so 
on. The sparse representation algorithm can reduce the 
amount of data in the calculation process, improve the 
quality of image reconstruction, and effectively avoid 
over-fitting and under-fitting, so it has a good application 
in SRR processing. This paper first designed a SRR 
processing method based on sparse representation for a 
single image and then carried out SRR processing for the 
noisy video image. In the video image, the Lucy-
Rechardson algorithm was firstly used to remove the 
noise in the video image, and then combined with Lucas 
Kanade algorithm and MSA algorithm to register the 
video image, and then SRR processing was carried out. 
According to the results of case analysis, it can be found 
that the SRR processing method based on sparse 
representation designed in this paper had high reliability. 
Firstly, from the results of image preprocessing, the 
denoising effect of the Lucy-Rechardson algorithm was 
better than that of Wiener filtering (Figure 2 and 3), 
which proved the reliability of the denoising algorithm in 
this paper. Then from the results of SRR processing, it 
can be seen from the comparison between Figure 1 and 
Figure 4 that, after SRR processing based on sparse 
representation designed in this paper, the resolution of the 
image was obviously improved, the image was clearer, 
and the details were more obvious. Taking PSNR and 
SSIM as image quality evaluation indexes, the method in 
this paper was compared with the bicubic interpolation 
method, and the results showed that the PSNR value and 
SSIM value of the method in this paper are both higher. 
In the three video images, the PSNR values of the images 
obtained by proposed method were 29.4528 dB, 28.8745 
dB and 29.48854 dB, and the SSIM values were 0.9445, 
0.9369 and 0.9486, respectively, which are significantly 
higher than that of the bicubic interpolation method. The 
results showed that the image obtained by SRR 
processing under the sparse representation designed in 
this paper had better super-resolution effect, which 
proves the reliability of this method. 
SRR is an important part of image processing. 
Although some achievements have been obtained from 
the research on SRR processing under sparse 
representation algorithm in this paper, further research is 
needed, such as the research on denoising video image, 
the research on motion estimation method, the research 
on how to reduce the amount of SRR calculations, etc. 
  
Figure 5: Comparison of PSNR.   Figure 6: Comparison of SSIM 

420 Informatica 43 (2019) 415 –420 T. Zhang et al. 
8 Conclusion 
Based on the sparse representation algorithm, the SRR 
processing of noisy video images was studied in this 
paper. Super-resolution reconstruction of image was 
carried out through sparse representation, and registration 
of video image was realized by Lucas Kanade+MSA 
hybrid algorithm. The results of the case analysis showed 
that the PSNR value and SSIM value of the reconstructed 
image obtained by the method designed in this paper were 
both higher, which proves the effectiveness of the sparse 
representation algorithm in SRR processing and is 
conducive to the further development of image SRR 
processing. 
9 Acknowledgement 
This study was supported by Research on the reform of 
theoretical teaching methods of Arts in Hengshui 
University-Taking the course of history of modern world 
design as an example under grant number jg2018085. 
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