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Received August 1, 2018, accepted September 21, 2018, date of publication October 2, 2018, date of current version October 29, 2018.

Digital Object Identifier 10.1109/ACCESS.2018.2873484

Multi-Contrast Brain MRI Image Super-Resolution

With Gradient-Guided Edge Enhancement

HONG ZHENG

1,2

, KUN ZENG

, DI GUO

, JIAXI YING

, YU YANG

, XI PENG

FENG HUANG

, ZHONG CHEN

, AND XIAOBO QU

Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Department of Electronic Science, College of Physical Science and Technology,

Xiamen University, Xiamen 361005, China

Key Laboratory of Intelligent Processing of Image and Graphics, School of Computer Science and Information Security, Guilin University of

Electronic Technology, Guilin 541004, China

School of Computer and Information Engineering, Fujian Provincial University Key Laboratory of Internet of Things Application Technology, Xiamen

University of Technology, Xiamen 361024, China

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China

Neusoft Medical System, Shanghai 110179, China

Corresponding author: Xiaobo Qu ([email protected])

This work was supported in part by the National Key R&D Program of China under Grant 2017YFC0108703, in part by the National

Natural Science Foundation of China under Grant 61571380, Grant 61871341, Grant 61811530021, Grant U1632274, Grant 61672335,

and Grant 61601389, in part by the Natural Science Foundation of Fujian Province of China under Grant 2018J06018 and

Grant 2016J05205, in part by the Fundamental Research Funds for the Central Universities under Grant 20720180056,

and in part by the Science and Technology Program of Xiamen under Grant 3502Z20183053.

ABSTRACT In magnetic resonance imaging (MRI), the super-resolution technology has played a great

role in improving image quality. The aim of this paper is to improve edges of brain MRI by incorporating

the gradient information of another contrast high-resolution image. Multi-contrast images are assumed to

possess the same gradient direction in a local pattern. We proposed to establish a relation model of gradient

value between different contrast images to restore a high-resolution image from its input low-resolution

version. The similarity of image patches is employed to estimate intensity parameters, leading a more

accurate reconstructed image. Then, an iterative back-projection ﬁlter is applied to the reconstructed image

to further increase the image quality. The new approach is veriﬁed on synthetic and real brain MRI images

and achieves higher visual quality and higher objective quality criteria than the compared state-of-the-art

super-resolution approaches. The gradient information of the multi-contrast MRI images is very useful.

With a proper relation model, the proposed method enhances image edges in MRI image super-resolution.

Improving the MRI image resolution from very low-resolution observations is challenging. We tackle this

problem by ﬁrst modeling the relation of gradient value in multi-contrast MRI and then performing fast

supper-resolution methods. This relation model may be helpful for other MRI reconstruction problems.

INDEX TERMS MRI, image reconstruction, super-resolution, multi-contrast images.

I. INTRODUCTION

In magnetic resonance imaging (MRI), the low-resolution

(LR) is usually encountered due to acquisition constrains

such as limited sampling time or moving subjects. These

LR may seriously affect the post-processing and medical

diagnosis. To recover a high-resolution (HR) image from

its low-resolution version [1], super-resolution technologies

have been widely used in MRI [2]–[11].

Super-resolution methods can be roughly grouped into

two main categories: Interpolation and non-interpolation.

Interpolation approaches, e.g., the bicubic and bi-spline, are

usually fast but frequently generate over-smooth images.

Non-interpolation methods incorporate various image priors,

e.g., sparse representation [3]–[6], [11] non-local recon-

struction [7], [10] and total variations [8], [9], leading to

more attractive super-resolved images. However, these non-

interpolation methods usually require time-consuming iter-

ation processing and do not pay special attention to edge

information.

Edge structures of medical images have a particularly sig-

niﬁcant impact on visual scenes to detect suspicions, classify

malformations and make diagnosis [15]. Thus, it is valu-

able to consider edge factor in image super-resolution. For

example, edges are preserved pretty well in a contrast-guided

interpolation (CGI) approach [16]. Edges are also sharpened

by considering gradient features [2], [12]. These methods,

57856

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VOLUME 6, 2018

H. Zheng et al.: Multi-Contrast Brain MRI Image Super-Resolution With Gradient-Guided Edge Enhancement

only explore the information from a single target image in the

low resolution, thus a faithful super-resolution may be hard to

achieve since the available information is very limited.

Other prior information beyond a single image is expected

to improve the image resolution [5], [7], [13], [14], [17], [18].

For example, non-local similarity of image patches is intro-

duced as the prior information [5], [7], [13], [14], [17]. These

methods also require time-consuming iteration processing.

In addition, Zheng et al. [18] introduced a fast interpolation

approach using the local weight similarity (ILWS) between

multi-contrast brain images to improve the resolution of the

LR MRI image. But, it does not perform satisfactorily when

the LR image is too smooth.

Recently, an effective interpolation method that establish-

ing gradient relations between the LR image and HR ref-

erence image with different contrast was proposed [19] in

the remote sensing. This method has a simple but effective

non-iterative linear model, and does not require training sets.

Image edges were interpolated much well according to the

reported results [19]. This model is called as the Super-

Resolution of using Gradient Relations (SRGR) model here.

The SRGR provides a promising direction to model rela-

tionship between the multi-contrast images due to its fast

computing and attractive performance. The SRGR, as far as

we know, has not been applied for MRI. What is more, to ﬁt

for the multi-contrast MRI interpolation, SRGR should be

carefully modiﬁed since the images in MRI are very different

from those in remote sensing [19]. This aim of this work is

to model the gradient relations of multi-contrast MRI images

and improve MRI super-resolution.

In this work, we propose a new gradient linear relation

model for multi-contrast brain MRI super-resolution, which

is inspired by SRGR. The gradient information on edges

of a HR reference is used to guide the interpolation of a

LR MRI image. To further improve the resolution, the non-

local similarity of image patches is employed to robustly

estimate the intensity parameter of the model and the Iterative

Back-Projection (IBP) ﬁlter is enforced. Experimental results

will verify more promising results for our method than the

compared MRI interpolation approaches.

This paper is structured as follows. Section II gives a brief

review of the related work. Section III presents the proposed

approach. Section IV provides experimental results followed

by discussions in Section V. Finally, we summarize this work

in Section VI.

II. BACKGROUND AND RELATED WORKS

A. MULTI-CONTRAST IMAGES IN MRI

Multi-contrast images are frequently acquired in

MRI [1], [20] and the commonly acquired ones are T1w

and T2w. Plentiful edge structures are visible in these two

contrast images of the same subject (Fig. 1). According to the

MRI physics [21], the image S

(

)

of T1w or T2w is generated

as follows:

(

)

∝ ρ

(

)



1 − e

−TR/T

(

)



−TE/T

(

)



, (1)

FIGURE 1. Multi-contrast MRI brain images: (a) a T1w image;

(b) a T2w image.

where ρ

(

)

is the proton density at spatial location Er,

TR refers to the repetition time and TE denotes the echo

time. By setting different values of TR and TE, multi-contrast

images will be acquired. Yet, these images share the proton

density of the subject and hence they largely share similar

anatomical structures but with different contrasts in regions.

The shared information between inter-contrast images was

previously considered to proﬁt the super-resolution [18] and

other image reconstruction tasks [22]–[24].

B. BRIEF REVIEWS OF SRGR MODEL

The SRGR model was proposed in super-resolution of remote

sensing images [19]. Its basic idea is described below.

Suppose that a LR image

of its target HR image

(Fig. 2(a)) and a HR reference image

R (Fig. 2(b)) are avail-

able while

X and

R have same size. SRGR consists two

steps: 1) A pre-interpolated image X (Fig. 2(c)), that is with

the same size of

X, is obtained with some classic interpola-

tion methods; 2) Gradient information from

R is applied to

update X.

To improve the interpolation, the same gradient direction

is assumed between the multi-contrast images

X and

R. The

relationship of gradient is modeled as [19]

i,j

)

i,j

)

= λ

, (2)

where g

(

)

is a second order gradient function,

i,j

is the pixel

i,j

is the pixel of

R and λ

is a parameter that models

this relationship ideally.

Assuming that an adjustment parameter δ

i,j

is added to the

(i, j) pixel X

i,j

of a pre-interpolated image X, the SRGR model

is formulated as [19]

min

i,j

{[g(X

i,j

+ δ

i,j

) − λg(

i,j

)]

+ [g

⊥

i,j

+ δ

i,j

) − λ

⊥

(

i,j

)]

} (3)

by considering a gradient direction l (Fig. 2(d)) and its normal

direction, also called edge direction, l

⊥

(Fig. 2(d)).

Now, we are prepared to discuss the essential parts

in Eq. (

3). First, the gradient functions g(X

i,j

+ δ

i,j

) and

⊥

i,j

+ δ

i,j

) are deﬁned as

g(X

i,j

+ δ

i,j

) = X

i+1,j−1

+ X

i−1,j+1

− 2(X

i,j

+ δ

i,j

)

⊥

i,j

+ δ

i,j

) = X

i−1,j−1

+ X

i+1,j+1

− 2(X

i,j

+ δ

i,j

) (4)

VOLUME 6, 2018 57857

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