Optimizing Super-resolution Reconstruction using a Genetic Algorithm

Michal Kawulok

1,2

, Daniel Kostrzewa

1,2

, Pawel Benecki

1,2

and Lukasz Skonieczny

Future Processing, Bojkowska 37A, 44-100 Gliwice, Poland

Institute of Informatics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Keywords:

Genetic Algorithm, Image Processing, Super-resolution Reconstruction.

Abstract:

Super-resolution reconstruction (SRR) is aimed at increasing spatial resolution given a single image or multiple

images presenting the same scene. The existing methods are underpinned with a premise that the observed low

resolution images are obtained from a hypothetic high resolution image by applying a certain imaging model

(IM) which degrades the image and decreases its resolution. Hence, the reconstruction consists in applying an

inverse IM to recover the high resolution data. Such an approach has been found effective, if the IM is known

and controlled, in particular when the low resolution images are indeed obtained from a high resolution one.

However, in a real-world scenario, when SRR is performed from images originally captured at low resolution,

ﬁnding appropriate IM and tuning its hyperparameters is a challenging task. In this paper, we propose to

optimize the SRR hyperparameters using a genetic algorithm, which has not been reported in the literature so

far. We argue that this may substantially improve the capacities of learning the relation between low and high

resolution images. Our initial, yet highly encouraging, experimental results reported in the paper allow us to

outline our research pathways to deploy the developed techniques in practice.

1 INTRODUCTION

Effectiveness of a number of computer vision systems

which include some object detection or pattern recog-

nition tasks, strongly depends on spatial resolution of

the input images. In many cases, obtaining images of

sufﬁciently high resolution is difﬁcult and it is subject

to a number of trade-offs. They range from the cost

of image acquisition to accessibility and safety (e.g.,

for medical imaging). Overall, this motivated the re-

searchers to develop the algorithms that would allow

a high resolution image be reconstructed from a series

of images of lower spatial resolution—this process is

known as super-resolution reconstruction (SRR) and

it has gained considerable attention over the years.

Despite many advancements, in many cases the state-

of-the-art solutions are still insufﬁcient to deploy SRR

in practical applications.

1.1 Related Work

SRR was considered for a variety of computer vision

problems, including medical imaging (Yang et al.,

2015; Jiang et al., 2014), analysis of facial images

(Jiang et al., 2014), satellite imaging (Zhu et al.,

2016), document image processing (Capel and Zis-

serman, 2000), or microscopy imaging (Lukinavi

cius

et al., 2013). SRR can be executed (i) given a sin-

gle image (Demirel and Anbarjafari, 2011), (ii) from

a sequence of images acquired with some shifts in the

spatial domain (Li et al., 2008b), or (iii) by processing

hyper-spectral images (Qian and Chen, 2012).

For single-image SRR, example-based learn-

ing (Timofte et al., 2014) is usually employed, which

exploits a large collection of examples—the recon-

struction consists in matching image patches be-

tween images of low and high resolution. This al-

lows for achieving visually plausible results, but may

easily lead to introducing some artifacts. The re-

cent advancements in single-image SRR are attributed

mainly to deep learning, which is being actively ex-

ploited for this purpose. Dong et al. (2016) has

shown that a super-resolution convolutional neural

network of relatively simple architecture outperforms

the state-of-the-art example-based methods. Also,

much deeper architectures coupled with fast residual

training were found effective (Kim et al., 2016).

Deep networks have not been exploited for

multiple-image SRR, which is considered in the re-

search reported here. The existing methods usually

employ a parametrized imaging model (IM) that sim-

ulates the process of degrading a hypothetical high-

Kawulok, M., Kostrzewa, D., Benecki, P. and Skonieczny, L.

Optimizing Super-resolution Reconstruction using a Genetic Algorithm.

DOI: 10.5220/0006654305990605

In Proceedings of the 10th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2018) - Volume 2, pages 599-605

ISBN: 978-989-758-275-2

599

resolution image into a set of N observed low resolu-

tion ones—I

(l)

: i ∈ [1..N]

. In general, such

models include image warping, blurring, downsam-

pling and ﬁnally contamination with the noise (Nas-

rollahi and Moeslund, 2014). Some of the IM parame-

ters are speciﬁc to each I

(l)

—basically, they stand for

the differences within I

and they are concerned with

the noise distribution and subpixel shifts between I

(l)

SRR consists in determining these parameters given

, which is an ill-posed optimization problem—it

is usually solved by employing the Bayesian frame-

work (Villena et al., 2004) or other optimization tech-

niques with some regularization imposed to provide

appropriate balance between sharp edges and spatial

smoothness of the reconstructed high-resolution im-

age I

0(h)

(Yue et al., 2016). A thorough study on

the regularization in SRR has been reported by Pana-

giotopoulou and Anastassopoulos (2012). Another

fairly popular optimization technique applied here is

the projection onto convex sets (Akgun et al., 2005),

which consists in updating the high-resolution tar-

get image iteratively based on the error measured be-

tween I

(l)

and I

0(l)

—a downsampled version of the

reconstructed I

0(h)

, degraded using the assumed IM.

Among other methods, adaptive Wiener ﬁlter (Hardie,

2007) and random Markov ﬁelds (Li et al., 2008a)

were used to specify the imaging model. Importantly,

an IM is controlled with a set of hyperparameters that

are common for all low-resolution images.

A commonly adopted way to evaluate the outcome

of SRR is to degrade a high-resolution image I

(h)

us-

ing an IM deﬁned on a theoretical basis to obtain the

set I

(Farsiu et al., 2004). Subsequently, SRR is

employed to reconstruct I

0(h)

from I

, and its qual-

ity is assessed based on the similarity between I

0(h)

and I

(h)

, measured with peak signal-to-noise ratio

(PSNR) or structure similarity index (SSIM) (Wang

et al., 2004). Such a scenario makes it possible to

evaluate the optimization process, but it does not ver-

ify whether the assumed IM is appropriate. The latter

is often done only qualitatively—SRR is performed

for camera-captured images and the outcome is as-

sessed visually (rather than quantitatively). Overall,

the problem of selecting IM and tuning its hyperpa-

rameters has not been deeply studied in the literature

and it remains an open issue.

1.2 Contribution

Our contribution consists in proposing a genetic al-

gorithm (GA) to optimize the hyperparameters of an

SRR process (including the IM), so as to increase its

accuracy in recovering high resolution image data.

Learning the relation between the images that have

been captured at different native resolution is in con-

trast to many works, in which the IM is assumed a

priori and it is used to generate the validation data.

In the work reported here, we initially verify the pro-

posed concept—we validate our new algorithm (GA-

SRR) by using it to optimize the hyperparameters of a

well-established SRR method (Farsiu et al., 2004) ap-

plied to reconstruct artiﬁcially degraded images. Im-

portantly, our proposed framework is fairly generic

and extendable, and we outline our intended research

pathways to deploy it in a realistic scenario.

1.3 Paper Structure

In Section 2, we present the SRR algorithm, which

we exploit to validate our concept, and we explain

the hyperparameters that we optimize. Our GA-SRR

is demonstrated and discussed in Section 3 and our

initial experimental results are reported in Section 4.

Finally, in Section 5, we conclude the paper and we

outline the goals of our ongoing research.

2 SRR FROM MULTIPLE

IMAGES

The majority of multiple-image SRR methods assume

that any observed image I

(l)

could be obtained from

an image of higher resolution I

(h)

by applying the fol-

lowing generic degradation model (Yue et al., 2016):

(l)

= D

(h)

+ n

, (1)

where W is the warp matrix (it includes translation

and rotation), B is the blur matrix, D downscales

the image, and n stands for the additive noise. Im-

portantly, if the observed images are captured by the

same sensor, it may be assumed that B and D are

common for all the images in the series (thus, they do

not depend on i). Hence, the differences among the

observed images are resulting from translations and

rotations, as well as from the additive noise.

A super-resolved image is found based on maxi-

mum a posteriori (MAP) theory as a solution (X ) of

a minimization problem:

0(h)

= argmin

∑

i=1



(l)

, DBW



+ λU(X ),

(2)

where ρ(·) is an image similarity metric and U(·)

is the regularization term. The existing SRR meth-

ods present different approaches towards deﬁning the

degradation matrices, regularization terms and opti-

mization techniques.

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

600

For our proof of concept, we selected the method

proposed by Farsiu et al. (2004). They exploit the L

norm to measure the similarity ρ, B matrix imple-

ments the Gaussian blur, and for regularization, the

total variation method (Rudin et al., 1992) is com-

bined with a bilateral ﬁlter:

U(X ) =

∑

l=−P

∑

m=−P

|m|+|l|



X − S



, (3)

where S

and S

shift an image by l and m pix-

els in horizontal and vertical direction, respectively,

and 0 < α < 1 is a parameter of spatial decay. The

reconstructed image is obtained by minimizing the

term (2), which is done with the iterative steepest gra-

dient descent—the update is obtained as

n+1

= X

− β



dρ

) +λ

)



, (4)

where

dρ

) =

∑

i=1

Dsgn(DBW

− I

(l)

(5)

) =

∑

|m|+|l|

sgn(X

− S

), (6)

= 1 − S

−m

−l

. (7)

Overall, the SRR process is controlled with (i) a sin-

gle parameter (σ) that deﬁnes the width of the Gaus-

sian kernel used in B, (ii) P used in the regulariza-

tion (3), and (iii) the remaining hyperparameters re-

lated to the optimization process (4)–(7), namely: α,

β, λ and the number of gradient descent iterations (Γ).

It is worth noting that Farsiu et al. (2004) applied their

SRR method to several images, for each of which dif-

ferent values of the hyperparameters were found op-

timal. The parameters speciﬁc to every single pre-

sented image I

(l)

∈ I

are concerned with the W

matrix, and they are determined by subpixel registra-

tion of the images within each I

. This is done prior

to the SRR process and the values in W

remain ﬁxed

afterwards.

3 GENETIC ALGORITHM TO

OPTIMIZE SRR

SRR algorithms are controlled with a number of hy-

perparameters, which severely inﬂuence the quality

of the reconstructed image, and the problem of their

tuning has been paid little attention in the literature so

far. Therefore, we expect a framework for optimizing

these hyperparameters to improve the capacities of

existing SRR methods, and hopefully this may lead to

developing adaptive IMs that could better reﬂect the

relation between images of low and high spatial reso-

lution. Motivated by that, we explore the possibilities

of applying a GA to optimize the SRR hyperparam-

eters. In the research reported here, we demonstrate

that the proposed GA-SRR algorithm is successful in

optimizing a well-established SRR technique (Farsiu

et al., 2004). Importantly, the essential components of

our framework are though to be highly generic, hence

we intend to embrace other SRR methods, which is

discussed later in Section 5.

3.1 Outline of GA-SRR

The pseudocode of the proposed algorithm is pre-

sented in Alg. 1. A population P of N

individuals

is initialized (line 1)—a chromosome of each indi-

vidual deﬁnes the values of hyperparameters which

control the SRR process (these values are initialized

randomly within an allowed range speciﬁc to each hy-

perparameter). Subsequently, each individual in P is

considered for mutation with the probability P

and

the selected individuals (P

) are excluded from the

individuals selected for crossover (P

) (lines 3–4).

The individuals in P

are paired and crossed over to

create an offspring population P

of the same size as

, hence #P

= #P

. During crossover (line 5) of

two individuals p

and p

, each parameter value of

the child p

a+b

is copied either from p

or p

with

equal probability. For each individual selected for

mutation, one value in the chromosome is selected

and modiﬁed within the allowed range (line 6). The

existing population P is appended with the mutated

individuals P

and those created during the crossover

)—this creates a new population P

(line 7). Fit-

ness η of each new solution is retrieved (this is ex-

plained later in Section 3.2) to select the N

ﬁttest in-

dividuals (line 11). When the stop condition is met

(line 13), the best solution p

is returned (line 14),

which conﬁgures the SRR method.

3.2 Computing the Fitness

The process to retrieve the ﬁtness η of an individ-

ual p

is illustrated in Fig. 1a. Basically, this process

requires a set of M high-resolution images, each of

which is coupled with a set of low-resolution counter-

parts I

—an example is presented in Fig. 1b (here,

four low-resolution images in I

present the same re-

gion as a high-resolution image I

(h)

To evaluate the ﬁtness η of an individual p

, the

hyperparameters deﬁned by its chromosome are used

to conﬁgure the SRR process, which is run to pro-

Optimizing Super-resolution Reconstruction using a Genetic Algorithm

601

M sets of

low-resolution

images I

M sets of

low-resolution

images I

SRR process

(run for each I

)

SRR process

(run for each I

)

SRR process

(run for each I

)

Reconstructed

images I

0(h)

Reconstructed

images I

0(h)

Reconstructed

images I

0(h)

Similarity between

0(h)

and I

(h)

Similarity between

0(h)

and I

(h)

Similarity between

0(h)

and I

(h)

M ground-truth

high-resolution

images I

(h)

M ground-truth

high-resolution

images I

(h)

M ground-truth

high-resolution

images I

(h)

Individual p

Fitness η(p

)

(h)

(l)

Figure 1: The process of computing the ﬁtness η(p

) of an individual p

(a) along with an example of input images of low

(l)

) and high (I

(h)

) resolution (b).

Figure 2: Images used to train GA-SRR.

Algorithm 1 A genetic algorithm for optimizing SRR

hyperparameters (GA-SRR).

1: Initialize population P = {p

} of size N

;

2: repeat

3: P

← SELECTFORMUTATION(P, P

);

4: P

← P \ P

;

5: P

← CROSSOVER(P

);

6: P

← MUTATE(P

);

7: P

← P ∪ P

∪ P

;

8: for all {p

} ∈ P

9: η(p

) ← FITNESS(p

);

10: end for

11: P ← SELECT(P

, N

);

12: p

← argmax

∈P

{η(p

)};

13: until STOPCONDITION;

14: return (p

);

cess each I

and reconstruct a high-resolution image

0(h)

. Quality of the reconstruction is assessed based

on the similarity between I

0(h)

and I

(h)

, measured

with SSIM. The ﬁnal ﬁtness η(p

) is obtained as the

mean of M similarity scores—basically, the better the

SRR is, the more similar is the reconstructed image

to the ground truth, and this similarity is expected to

increase during the evolutionary optimization.

4 EXPERIMENTAL VALIDATION

In order to verify the capacities of the proposed ap-

proach to optimize the SRR hyperparameters, we

have run an experiment in a controlled environment

for M = 10 artiﬁcially degraded satellite images of

200 × 200 pixels, presented in Fig. 2. Each high-

resolution image I

(h)

was subject to a small transla-

tion, followed by the Gaussian blur, and downsam-

pled to 100×100 pixels—for each I

(h)

, we generated

N = 25 downsampled images I

(l)

. From these im-

ages, we reconstruct the high-resolution image using

the algorithm by Farsiu et al. (2004), whose hyper-

parameters are optimized with GA-SRR. The values

of the hyperparameters were initialized in the follow-

ing ranges, set based on the results reported in the

paper (Farsiu et al., 2004): α ∈ (0, 1), β ∈ (0, 200),

λ ∈ (0, 0.2), Γ ∈ [1, 20], σ ∈ (0, 5) and P ∈ [1, 5]. We

implemented the algorithms in C++ (using OpenCV

library) and we ran the experiments on an Intel Xeon

3.2 GHz computer with 16 GB RAM.

As our goal here was to verify the behavior of

the genetic algorithm, we observed the ﬁtness (i.e.,

the average SSIM for M samples) in subsequent iter-

ations of the GA optimization. We ran the process

10 times and we stop the optimization after 10 iter-

ations (which we found sufﬁcient to verify the con-

cept). Average and best ﬁtness in subsequent itera-

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

602

a) I

(h)

b) I

0(h)

, SSIM = 0.344 c) I

0(h)

, SSIM = 0.670

d) I

(l)

e) I

0(h)

, SSIM = 0.711 f) I

0(h)

, SSIM = 0.843

Figure 4: Examples of an image from the training set: a) I

(h)

, I

(l)

and reconstructed I

0(h)

using different hyperparameters.

6 8 10 12

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7 8 9 10

Fitness

Iteration

Average fitness

Fitness of the best individual

Figure 3: Average and best ﬁtness in subsequent genera-

tions of GA-SRR.

tions along with the standard deviation are presented

in Fig. 3. It may be seen that the SRR quality grows

during the optimization and the standard deviation of

the best ﬁtness decreases, which conﬁrms the conver-

gence capabilities of the proposed GA. In addition,

we inspected the results qualitatively—an example of

the reconstruction improvement during the GA opti-

mization is presented in Fig. 4. The ﬁgure presents the

input I

(h)

and I

(l)

images (a, d) alongside four exam-

ples of I

0(h)

obtained within a single run of GA-SRR

(b, c, e, f). It may be seen that during the optimiza-

tion process, the reconstruction quality improves both

quantitatively and qualitatively. For low SSIM val-

ues (b, c), it may be concluded that the regularization

is too strong, which results in observing less details

than in the input low-resolution image I

(l)

. Impor-

tantly, the ﬁnal image (f) contains much more details

than I

(l)

, though still less than the original I

(h)

im-

age (a)—however, this is obtained after only 10 gen-

erations of the GA. It is worth noting that the ranges

of hyperparameter values are based on the results re-

ported in the literature—overall, this indicates high

sensitivity of the reconstruction process to its param-

eters and conﬁrms that determining their optimal val-

ues is not a trivial task.

Although we have not run multi-fold cross-

validation tests at this stage of our research, we

applied the hyperparameters obtained at subsequent

GA-SRR iterations (we exploited the best run out of

the 10 performed) to reconstruct images that were not

included in the data set used for training. This allowed

Optimizing Super-resolution Reconstruction using a Genetic Algorithm

603

a) I

(h)

b) I

0(h)

, η = 0.551, SSIM = 0.611 c) I

0(h)

, η = 0.701, SSIM = 0.733

d) I

0(h)

, η = 0.693, SSIM = 0.790 e) I

0(h)

, η = 0.794, SSIM = 0.875 f) I

0(h)

, η = 0.857, SSIM = 0.925

Figure 5: Example of the SRR applied to an image not included in the training set: ground-truth I

(h)

(a) and ﬁve reconstructed

0(h)

obtained using different hyperparameters obtained during GA-SRR process (b–f).

us to initially verify the universality of the optimized

hyperparameters. An example of such an image is

presented in Fig. 5. It is worth noting that the values

of SSIM measured between the original I

(h)

and re-

constructed I

0(h)

present the same tendency as the ﬁt-

ness η. Importantly, the best reconstruction result (f)

presents similar detail level to that visible in the orig-

inal image (a), rendering SSIM = 0.925.

5 CONCLUSIONS AND FUTURE

WORK

In this paper, we report our initial study on using GAs

for optimizing the SRR hyperparameters. This is an

important problem, as both the IM assumed for recon-

struction, as well as the reconstruction process itself

are sensitive to their parameters. Here, we demon-

strated that the proposed GA-SRR framework is ca-

pable of optimizing a well-established SRR method.

Although the tests were run for artiﬁcially degraded

images rather than for images originally captured at

different resolution (still, such validation scenario is

commonly adopted in the state-of-the-art works on

SRR), the obtained results conﬁrm that the general

idea standing behind our approach is correct. This,

in turn, allows us to outline the further research steps

towards addressing more realistic scenarios.

The main goal of our ongoing research is to ex-

ploit the proposed framework to conﬁgure both an

IM, so that it reﬂects the relation between images

originally captured at low and high resolution, as well

as the hyperparameters of an SRR method which is

based on that IM. This will allow us to adapt an IM

given a training set of low and high-resolution images,

captured using two different sensors (e.g., Sentinel-

2 and SPOT satellites, respectively)—afterwards, the

learned IM would be suitable for increasing the res-

olution of images having similar characteristics as

those in the training set (i.e., Sentinel-2 images, re-

ferring to the given example). Obviously, the ground-

truth high-resolution images will be required only for

training to deﬁne the IM.

Creating such a solution will require solving sev-

eral problems. First of all, we will make the IM more

conﬁgurable (at this stage only the width of the Gaus-

sian kernel is considered) to make it capable of mod-

eling the real-life downsampling process. As a conse-

quence, appropriate SRR method needs to be selected

that will be appropriate to optimize the IM parameters

for each presented sample. Another important issue is

concerned with measuring the similarity between I

(h)

and I

0(h)

. In the reported study, I

0(h)

is reconstructed

from the set I

, obtained from I

(h)

, which is used as

the ground truth, hence the differences between I

(h)

and I

0(h)

originate only from applying the IM fol-

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

604

lowed by the reconstruction process. While simple

measures (like PSNR or SSIM) are sufﬁcient here, it

is much more challenging to measure the similarity

between images that have been captured using differ-

ent sensors, at various spatial resolution. An example

of such images was shown earlier in Fig. 1b—I

(h)

and

(l)

were captured by different satellites, and certainly

the reconstructed image would be visually different

from I

(h)

. Importantly, the differences related to the

detail level may be negligible compared with those

incurred by the global variations. We have found the

keypoint detectors to be quite promising here (Kawu-

lok et al., 2017) and we will consider employing them

to evaluate the ﬁtness. Overall, we currently explore

how to exploit the proposed framework to adapt an IM

alongside an SRR technique to images acquired by a

given sensor, which will be an important step towards

deploying SRR in real-life scenarios.

ACKNOWLEDGEMENTS

The reported work is a part of the SISPARE project

run by Future Processing and funded by European

Space Agency. In addition, the authors were partially

supported by Institute of Informatics funds no. BK-

230/RAu2/2017 (MK) and BKM-509/RAu2/2017

(DK).

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