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Bioengineering 2023, 10, 22. https://doi.org/10.3390/bioengineering10010022 www.mdpi.com/journal/bioengineering
Article
De-Aliasing and Accelerated Sparse Magnetic Resonance
Image Reconstruction Using Fully Dense CNN with
Attention Gates
Md. Biddut Hossain 1, Ki-Chul Kwon 1, Shariar Md Imtiaz 1, Oh-Seung Nam 1, Seok-Hee Jeon 2 and Nam Kim 1,*
1 School of Information and Communication Engineering, Chungbuk National University,
Cheongju-si 28644, Chungcheongbuk-do, Republic of Korea
2 Department of Electronics Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu,
Incheon 22012, Gyeonggi-do, Republic of Korea
* Correspondence: namkim@chungbuk.ac.kr; Tel.: +82-043-261-2482
Abstract: When sparsely sampled data are used to accelerate magnetic resonance imaging (MRI),
conventional reconstruction approaches produce significant artifacts that obscure the content of the
image. To remove aliasing artifacts, we propose an advanced convolutional neural network (CNN)
called fully dense attention CNN (FDA-CNN). We updated the Unet model with the fully dense
connectivity and attention mechanism for MRI reconstruction. The main benefit of FDA-CNN is
that an attention gate in each decoder layer increases the learning process by focusing on the rele-
vant image features and provides a better generalization of the network by reducing irrelevant ac-
tivations. Moreover, densely interconnected convolutional layers reuse the feature maps and pre-
vent the vanishing gradient problem. Additionally, we also implement a new, proficient under-
sampling pattern in the phase direction that takes low and high frequencies from the k-space both
randomly and non-randomly. The performance of FDA-CNN was evaluated quantitatively and
qualitatively with three different sub-sampling masks and datasets. Compared with five current
deep learning-based and two compressed sensing MRI reconstruction techniques, the proposed
method performed better as it reconstructed smoother and brighter images. Furthermore, FDA-
CNN improved the mean PSNR by 2 dB, SSIM by 0.35, and VIFP by 0.37 compared with Unet for
the acceleration factor of 5.
Keywords: aliasing artifacts; attention gate; deep learning; fully dense network; MRI reconstruction
1. Introduction
Magnetic resonance imaging (MRI) is a sophisticated and noninvasive medical im-
aging technique that has full control over data capture to visualize the anatomy and func-
tions of the human brain and body [1]. It plays a significant role in smart healthcare sys-
tems alongside medical research by providing high-quality reconstructed images without
exposure to harmful radiation [2]. However, the long image acquisition time (more than
30 min per patient) [3] is a disadvantage compared with X-ray, computed tomography
(CT), and photoacoustic tomography (PAT) imaging modalities. In MRI, frequencies are
acquired in the k-space rather than directly in the image space. Full k-space data are re-
quired for high-quality reconstructed images, but this prolongs the acquisition process.
This slow process causes the patient discomfort and generates motion artifacts due to pa-
tient movement. A common way to speed up MRI acquisition is by taking fewer scans
and reconstructing the image using a partially recorded k-space. However, this creates
blurring and aliasing artifacts in the images according to the Nyquist–Shannon principle
[4]. Hence, an effective acceleration technique is essential for MRI reconstruction. Parallel
imaging (PI) [5,6] applies coil sensitivity maps to speed up reconstruction, but the setup
Citation: Hossain, M.B.; Kwon,
K.-C.; Imtiaz, S.M.; Nam, O.-S.;
Jeon, S.
-H.; Kim, N. De-Aliasing and
Accelerated Sparse Magnetic
Resonance Image Reconstruction
Using Fully Dense CNN with
Attention Gates. Bioengineering 2023,
10, 22. https://doi.org/10.3390/
bioengineering10010022
Academic Editor: Or Perlman and
Efrat Shimron
Received: 25 November 2022
Revised: 19 December 2022
Accepted: 19 December 2022
Published: 22 December 2022
Copyright: © 2022 by the authors. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (https://cre-
ativecommons.org/licenses/by/4.0/).
Bioengineering 2023, 10, 22 2 of 18
process is complex and expensive. Compressed sensing (CS) MRI [7,8] uses sparse data to
reconstruct high-resolution images from randomly picked k-space data. However, the
sparsity of data produces aliasing artifacts, and the computing time required is quite high
for their iteration process.
Deep learning (DL) has been successfully adopted in medical image processing [9–
12] and deals with the obstacles of iterative CS reconstruction [13,14]. Efficient reconstruc-
tion can be performed without repeatedly processing after properly training a DL model.
Several post-processing strategies [15–18] based on generative adversarial networks
(GANs) have been used to improve image quality in the image domain, whereas some
approaches [19–22] estimate the unknown missing k-space frequencies in the sensor do-
main. Cross-domain techniques [23–29] operate in both the sensor and image domains.
Recently, iterative unrolled optimization methods [30–34] have been used for sparse MRI
reconstruction to improve the learning of image features. However, when the k-space is
uniformly under-sampled, DL-based iterative methods cannot properly eliminate aliasing
artifacts.
The first multilayer perceptron [35] is applied to reduce aliasing artifacts in parallel
MRI. The multi-scale Unet structure [36] has been suggested to handle phase image re-
construction and scattered artifacts. The convolutional neural network (CNN)-based two-
dimensional (2D) phase-contrast MRI reconstruction method [37] encodes low-frequency
regions in the phase direction, while high-frequency regions store image edges. The GAN-
based de-aliasing method [38] combines adversarial and innovative content loss but cal-
culates fast Fourier transforms (FFTs) of magnitude images instead of raw MRI data. Re-
fineGAN [39] measures only the cyclic loss of the training dataset using an autoencoder.
Based on deep residual learning (DLR), the denoising technique [40] identifies and then
subtracts noise from noisy images. After modifying this DLR-based network, Ouchi et al.
[41] proposed a model to generate alias-free images by subtracting the predicted alias
components from them.
Here, we adopt a post-processing strategy and propose an efficient fully dense atten-
tion convolutional neural network (FDA-CNN) architecture to remove aliasing and ghost
artifacts from sparsely reconstructed 2D MRI images. The FDA-CNN method generates
aliasing-free images instead of prediction artifacts, which is a key difference from previ-
ous MRI de-aliasing techniques. Guan et al. [42] proposed fully dense Unet (FD-Unet) for
reducing artifacts from PAT images. We use the modified FD-Unet architecture for MRI
reconstruction by adding an attention gate (AG) to each decoder layer. FDA-CNN consists
of an AG [43] in each layer of the decoding path and dense connectivity (DC) [44] in both
the encoding and decoding layers. DC solves the vanishing gradient issue and improves
information flow, whereas the AG gives more attention to essential features that make the
network more generalized. Supplementarily, we implement a hybrid mixed center and
periphery under-sampling (MCP-US) mask in the phase [ reconstructs complex image tex-
tures and contents better than the two-dimensional (2D) and one-dimensional (1D) Gauss-
ian under-sampling patterns. The results of FDA-CNN were evaluated using three sub-
sampling masks using only 20% of the data. The simulation results were compared to both
the single- and multidomain networks along with traditional CS methods on three widely
used k-space datasets.
2. Methodology
The data obtained from an MRI scanner are known as the Fourier space or k-space
and can be represented as follows:
y
=
FT (1)
where T is the artifact-free image, F is the Fourier transform, and y represents the fully
sampled k-space data. The reconstruction of image x from the k-space can be performed
by applying the inverse Fourier transform.
Bioengineering 2023, 10, 22 3 of 18
x
=
F–1
y
(2)
The reconstruction of an image with n pixels requires at least n frequencies. However,
it takes more scan time to capture n frequencies, because the number of frequencies ac-
quired is linearly related to the length of the MRI scan. Acquiring only 1/5 of the frequen-
cies can reduce both the scan time and cost by a factor of 5, but aliasing artifacts are intro-
duced. Under-sampled k-space y is represented as
y
=
U
⊙
y
=
U
⊙
FT (3)
Figure 1 exhibits a reconstructed artifact xaliased image from the under-sampled k-
space. Here, U is a sub-sampling matrix filled with 0 s (black area) and 1 s (white line),
and ⊙ expresses the element-wise multiplication.
Figure 1. Reconstructed artifact image from sparsely sampled k-space.
Conventional CS methods recover images by solving the following optimization
problem:
|
y
–y
|2
2
T
min + λG
(
T
)
(4)
where ||.||2 is a generic data consistency term that assures the solution of the original
image (T) with every observation of y and G denotes the regularization term, where λ
expresses the regularization parameter. The challenge of traditional CS is that the regu-
larizer, G(T), must be manually encoded to represent the reconstructed MR images.
2.1. Deep Learning Framework
A DL-based method is applied to adjust the under-sampled image and reconstruct
an artifact-free image that is close to the actual image. This is called a supervised learning
strategy, which aims to find an appropriate reconstruction function that matches the given
image with the expected output. This can be expressed with the following equation:
R
=
{(NN)L(F–1(y
))} (5)
where R is the reconstructed image, NN is a DL-based neural network, and L measures
the loss between the original and reconstructed images.
As shown in Figure 2, the fully sampled k-space (y) is sub-sampled by means of ele-
ment-wise multiplication with the under-sampling mask (U). First, an image with aliasing
and ghost artifacts x is reconstructed using the inverse fast Fourier transform (IFFT) from
sub-sampled k-space y. Then, these artifacts are removed by FDA-CNN by decreasing the
loss (L) between the predicted image (R) and the target image (T). FDA-CNN attempts to
recover an image F-1(y) that is close to the target image using sub-sampled sensor data y
as input. Gradient descent is used to optimize the parameters of the loss function.
Bioengineering 2023, 10, 22 4 of 18
Figure 2. Flowchart of the proposed de-aliasing technique.
2.2. Proposed FDA-CNN Architecture
The proposed MRI de-aliasing network architecture is presented in this section. We
designed an improved CNN model based on the Unet [45] architecture by combining
modified dense connectivity and AGs. We applied batch normalization [46] to accelerate
training compared with earlier Unet implementations.
The network structure shown in Figure 3 has two main sections: the down- and up-
sampling parts, and the skip connection part with the AGs. The down-sampling section
consists of convolution, dense block, and max-pooling layers, whereas up-sampling con-
sists of upscaling (2 × 2 deconvolution), dense block, and convolutional layers. Firstly, a
1-channel 3 × 3 convolutional operation is applied on a 256 × 256 input image with rectified
linear unit (ReLU) [47] activation function. Then, five consecutive dense blocks (DB) are
used. The first DB starts with 32 channels and gradually increases by 64, 128, 256, and 512.
Every DB consists of a series of 1 × 1 and 3 × 3 convolutions with padding 1, batch nor-
malization, and ReLU. Initially, hyperparameters km and fm are specified by the user;
for our method, we initialized k1
=
8 and f1 = 64. Then, km and fm are changed by km=
2m-1× k1 and fm= 2m-1× f1, respectively. The concatenation of the inputs and outputs from
every layer of the DB generates its final output. Except for the last DB of the encoding
section, a max-pooling operation is executed after each DB, which halves the size of the
input at each level and doubles the number of feature maps.
The decoding or up-sampling section restores the size of the feature maps and main-
tains a form symmetric to the encoding section. This symmetry enables the reuse of fea-
tures by concatenating feature maps at the same level and reduces the loss of information
caused by the encoding/decoding process. Before concatenation, the features of encoding
and decoding layers go through the AG to focus on target features from different spatial
information. Every layer of the decoding section executes a 1 × 1 convolution with pad-
ding 1 and ReLU before going into a DB. A 1-channel 1 × 1 convolution is executed before
generating the final output.
Bioengineering 2023, 10, 22 5 of 18
Figure 3. Proposed FDA-CNN architecture.
Moreover, dense connectivity generates deeper networks. For comparison, Unet has
23 layers, while FDA-CNN has 97 convolutional and deconvolutional levels. The vanish-
ing gradient problem arises because the gradient information must flow through different
layers and may disappear before it arrives at the succeeding layers. Dense connectivity
adds more links to enable the effective backpropagation of gradient information. This less-
ens the vanishing gradient issue and makes it easier to train the network.
2.3. Dense Block
Densely connected networks [48] maximize the capability of the network by reusing
features. The input of the succeeding layers is more varied and more effective when fea-
ture maps from various layers are combined. In our method, a dense block with a growth
rate, km, is used to learn different feature maps, fm, for each spatial level, m. Initially,
hyperparameters km and fm are specified by the user. Then, km and fm are changed by
km= 2m-1× k1 and fm= 2m-1× f1, respectively, at each spatial level to preserve computational
efficiency and ensure that each dense block has the same number of convolutional layers.
A total of nine dense blocks with four layers are used in the FDA-CNN approach.
As shown in Figure 4, the Lth layer of the dense block has an initial input with
F + × (L-1) feature maps and output with km feature maps, where F is the total number
of feature maps in the dense block’s initial input. Through a series of 1 × 1 and 3 × 3 con-
volutions with batch normalization plus ReLU activation function, features are learned.
Due to the increased computational complexity of the 3 × 3 convolution, the input dimen-
sion is decreased to F feature maps by applying a 1 × 1 convolution, which increases con-
vergence speed. Then, using a 3 × 3 convolution, km attribute maps are developed from
the compacted data. The concatenation of the inputs and outputs from every layer of the
dense block generates the dense block’s final output.
Figure 4. Last dense block with four layers of encoding part, where k5 = 128 and f5 = 512.
Bioengineering 2023, 10, 22 6 of 18
2.4. Attention Gate
Models trained with AGs [49] intuitively learn to emphasize prominent features that
are helpful for a particular task while suppressing irrelevant regions in an input image.
With no additional computational work, AGs may be quickly added to common CNNs,
such as Unet topologies, improving model sensitivity and prediction accuracy. Unet em-
ploys skip connections to merge spatial data from the up- and down-sampling paths.
Low-quality feature representation exists in the first few layers, which carries in several
redundant low-level feature extractions. By actively suppressing activations in unneces-
sary regions through the use of AGs at the skip connections, the number of redundant
features transferred is decreased. Every AG takes two inputs, g and x. The gating signal,
g, comes from the next lowest layer of the network. It has greater feature representation
because it originates from a deeper region of the network. The input features, x, come
from skipped connections. They have better spatial information because they originate
from the early stages.
We incorporate an AG with every decoding part in our fully dense Unet framework.
As shown in Figure 5, input features xi
l perform 1 × 1 × 1 convolutions with stride 2 × 2 to
lessen the size of the dimensions (H × W) by half, and gating signals gi
l+1 perform 1 × 1 ×
1 convolutions with stride 1 × 1. As a result, the spatial geometry of the modified input
features and gating signals is the same. The ReLU function activates them through ele-
ment-wise summation and maps them by Wint
T into a smaller-dimensional space for gat-
ing operations. The sigmoid function levels the vector in (0, 1), with coefficients closer to
1 denoting more pertinent features. Then, a trilinear up-sampler is used to restore the size
of attention weight matrix αi
l to correspond to the pixel density of the input features. The
output of the AG, xi
l, is generated by means of element-wise multiplication between at-
tention weight matrix αi
l and input features xi
l and then is transmitted as usual through
the residual connections.
Figure 5. Schematic diagram of an attention gate.
3. Deep Learning Implementation
3.1. Datasets and Under-Sampling Masks
We used fully sampled brain k-space data from BraTs-2020 [50], fastMRI [51,52], and
IXI [53]. We used the cross-sectional T1-weighted BraTS-2020 dataset for both the training
and testing of all the networks. On the other hand, the T1-weighted axial fastMRI and T2-
weighted coronal IXI datasets were only used for testing. Each volume possessed both the
fully acquired k-space data and the associated reconstructed images of the same size (256
× 256). As we concentrated on the correlation between the number of k-space slices and
FDA-CNN performance, no data augmentation was used in training. Images were recon-
structed sequentially from every k-space.
During training, the sub-sampled zero-filled (ZF) noisy and artifact images were
used as the network input along with the fully sampled images as target images. Our new
MCP-US pattern was used for training and compared with 2D Gaussian under-sampling
(2DG-US) and 1D Gaussian under-sampling (1DG-US) distributions. Mostly, 2D-US and
1DG-US focus on the central low frequencies of the k-space. However, low-spatial-fre-
quency data, which determine the overall contrast, brightness, and form of the image, are
located in the center of the k-space. On the other hand, high-spatial-frequency data deter-
mining the image edges and details are located in the periphery of the k-space. As the k-
Bioengineering 2023, 10, 22 7 of 18
space has a symmetric nature, our MCP-US takes both the low and high frequencies.
Among the total sampled data (S) of each k-space, MCP-US constantly samples 50% of
the center (sc) and 25% of the periphery (sp) and randomly chooses 25% of data (sr) fre-
quencies, except for center and periphery data. It can be expressed as follows:
S = sc+sp+sr
where sc=
S
2%, sp=
S
4%, sr=
S
4%
In both training and testing, we took only 20% of data of each k-space for all three sub-
sampling patterns, where white spaces were replaced with zero, as shown in Figure 6.
Figure 6. Several sampling patterns: (a) fully sampled; (b) 2D Gaussian pattern; (c) 1D Gaussian
pattern; (d) mixed center and periphery under-sampling pattern.
Among the sampled data (S), our MCP-US non-randomly takes 10% of sc from the
middle position and 5% of sp from the zero position and randomly chooses 5% of sr be-
tween the sc and sp areas. As we concentrated on the correlation between the number of
training images and FDA-CNN performance, no data augmentation was used in training.
3.2. Loss Function
The disparity between the sub-sampled aliasing image and the fully sampled alias-
ing-free image was evaluated using the loss function. The optimum objective of FDA-
CNN is to minimize the value of the loss function. Smaller values between the under-
sampled and fully sampled images ensure better reconstruction. We used the mean square
error (MSE) as the loss function to calculate pixel-wise disparity and update the network
parameters, which can be expressed as follows:
LossMSE = 1
N
∑
(Ti
N
i = 1 –Ri)2 (6)
where N indicates the number of voxels (or pixels) in the image, and Ti and Ri represent
the target and reconstructed MR images, respectively.
3.3. Performance Evaluations Metrics
To evaluate the network performance, we summarized the findings using four pa-
rameters: structural similarity index measure (SSIM) [54], peak signal-to-noise ratio
(PSNR), normalized root mean squared error (NRMSE), and pixel visual information fi-
delity (VIFP) [55]. The SSIM is a perceptual index that utilizes the mutual dependencies
among adjacent pixels to measure the similarity of two images, such as brightness, con-
trast, and structural properties. The following expression gives the SSIM between the net-
work output (R) and the desired output (T):
SSIM
(
T, R
)
=
2µTµR+c1
(
2σTR+c1
)
µT
2+µR
2+c1
σT
2+σR
2+c1
(7)
where µT and µR represent the mean values of T and R, respectively; and σT
2 and σR
2
denote the corresponding pixel variance values. The covariance value is also shown by
σTR. To stabilize the division, c1 and c2 have the following definitions:
Bioengineering 2023, 10, 22 8 of 18
c1
=
(0.01P)2, c2
=
(0.03P)2
where P = max(T)– min(T)
The PSNR calculates the ratio of the signal’s highest potential power (image intensity
throughout a volume) to its fidelity-affecting distorting noise power. This can be ex-
pressed as
PSNR(T, R) = 10log10
⎝
⎛
255
1
N
∑
(Ti
N
i = 1 –Ri)2
⎠
⎞
(8)
The ground truth and the pixel differences in network output images are compared
by the NRMSE, which can be expressed as
NRMSE
(
T, R
)
=
1
N
∑
(Ti
N
i = 1 –Ri)2
max
(
T
)
– min
(
R
)
(9)
The human viewer’s perceptual evaluation approach, VIFP, measures image infor-
mation by computing two mutual information quantities from the reference and distorted
images. This can be defined as
VIFP
(
T,R
)
=
∑
I
C→N,j; R→N,j
sN,j
j
∈
subbands
∑
I
C→N,j; T→N,j
sN,j
j
∈
subbands
(10)
where R→N,j, and T→N,j represent the sub-bands of the reconstructed and target images,
respectively; SN,j defines a realization for a specific image; and C→N,j expresses N ele-
ments of random field Cj that specifies the coefficient of the sub-band, j. The evaluation
result of VIFP is indicated as values between 0 and 1, similar to the SSIM.
These criteria were chosen as they are typically used to evaluate image reconstruc-
tion. Higher values of SSIM, PSNR, and VIFP indicate better results, while smaller values
of the NRMSE define better reconstructions. Moreover, the reconstruction time for each
image indicates the transformation of MRI raw data into pictures. The reconstruction time
of each method was calculated using the MCP-US pattern.
3.4. Experimental Setup
The training and testing of FDA-CNN were executed on an Intel Core i7-9800X 3.80
GHz processor and 128 GB memory with NVIDIA GeForce RTX 2080 Ti GPU running on
Windows 10 Pro 64 bit. This model was implemented in Python 3.8 with the DL open-
source libraries TensorFlow v2.4 and Keras v2.4 in the PyCharm environment. We used
the Adam optimizer with momentum values of β1 = 0.9 and β2 = 0.999 to reduce the loss
function. The starting learning rate was 1e-4, and it declined with a decay factor of 0.95
every 20 epochs. A small batch size of 8 was chosen, and 2000 epochs were executed for
the training of our network. Figure 7 illustrated the training and validation losses of the
proposed network, where the regularizing impact of extensive connectivity lessens the
possibility of overfitting the training data.
Bioengineering 2023, 10, 22 9 of 18
Figure 7. Training and validation losses of proposed FDA-CNN.
4. Result and Discussion
The performance of our network was compared to classical CS total variation (TV)
[56], wavelet [57] denoising algorithms, and DL-based state-of-the-art (image and dual
domain) reconstruction methods. Lightweight autoencoder (LAE) [58], basic Unet [46],
projection-based cascade Unet (PBCU) [59], and DRL-based MRI (DRL-net) [41] recon-
structions are image-domain DL networks. LAE uses an autoencoder framework, and
PBCU uses five cascade Unets for MRI reconstruction. DRL-net subtracts the predicted
artifacts from the under-sampled aliased images. The multidomain MRI reconstruction
strategy (Wnet) [60] uses two Unets: one for the k-domain and another for the image do-
main. SSIM, PSNR, and NRMSE were used for quantitative analysis, where VIFP was used
to evaluate the perception of the de-aliased images of a human viewer. The average re-
construction times were calculated using the MCP-US pattern. All results were generated
in the same environment.
4.1. BraTs 2020-T1 Dataset
The T1-weighted axial brain Brats-2020 dataset was used for both the training and
testing of all the networks. In an ideal dataset, the training and test data are very well
correlated, providing an opportunity to acquire, from the training data, most of the fea-
tures that are required to perform effectively during testing. The efficiency of CNNs can
be compared in this ideal situation without being affected by the data. This BraTS-2020
dataset was obtained using a clinical 3T multimodal MR scanner. Among 150 k-spaces,
100 k-spaces were used for training; 30 k-spaces were used for validation; and 20 k-spaces
were used for testing. Each k-space contained 155 axial cross-sectional T1-weighted (256
× 256) images. In the training, validation, and test sets, there was no duplication of the
same k-space.
In this experiment, the same MRI sequence was used for both training and testing,
with 25% of the training data being used for validation to increase the reliability of the
results. The learning potential of FDA-CNN to eliminate artifacts was measured by ad-
justing the hyperparameters (feature maps and growth rate) of the dense block. Compar-
ative DL methods were trained using the MCP-US pattern and evaluated on the associated
datasets with each under-sampling mask. The efficiencies of all CNNs in terms of elimi-
nating artifacts were compared using various sub-sampling masks for an acceleration fac-
tor of 5. In general, the CNN produced a better image with minimal artifacts. As seen in
Table 1, the proposed FDA-CNN produced higher average SSIM, PSNR, and VIFP with a
lower average NRMSE than traditional CS and the autoencoder and Unet-based methods.
Bioengineering 2023, 10, 22 10 of 18
Table 1. Average SSIM, PSNR, NRMSE, and VIFP values and reconstruction time of state-of-art
methods on BraTs-T1 axial brain data using several sampling patterns.
Sampling
Metrics
Zero Filling
TV
Wavelet
LAE
Unet
Wnet
PBCU
DRL-Net
FDA-CNN
2DG-US
SSIM 0.31 0.32 0.36 0.78 0.79 0.77 0.82 0.83 0.89
PSNR 34.11 35.90 36.13 35.16 35.31 35.29 35.55 35.84 36.22
NRMSE 0.09 0.07 0.06 0.08 0.08 0.07 0.07 0.06 0.04
VIFP 0.60 0.50 0.65 0.87 0.92 0.93 0.90 0.80 0.94
1DG-US
SSIM 0.52 0.58 0.62 0.68 0.69 0.68 0.69 0.69 0.70
PSNR 33.20 33.23 33.25 33.23 33.26 33.10 33.15 33.40 33.59
NRMSE 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.11 0.10
VIFP 0.25 0.21 0.27 0.42 0.38 0.44 0.38 0.41 0.45
MCP-US
SSIM 0.76 0.77 0.76 0.96 0.95 0.96 0.96 0.95 0.97
PSNR 36.70 36.47 36.73 38.92 38.78 38.97 38.74 38.97 40.55
NRMSE 0.05 0.06 0.06 0.03 0.04 0.03 0.04 0.03 0.02
VIFP 0.52 0.41 0.50 0.90 0.91 0.91 0.89 0.85 0.93
Reconstruction time (seconds) 0.97 0.5 0.30 0.30 0.39 0.33 0.31 0.30
The classical CS methods required almost 0.5 s and 0.97 s in reconstruction time for
each slice, and the dual-domain network required approximately 0.4 s. In contrast, the
single-domain post-processing methods required approximately 0.30 s to 0.33 s. Our pro-
posed method generated better images than Unet within the same reconstruction time of
0.30 s for each slice.
As shown in Figure 8, the under-sampled image contained noise and aliasing arti-
facts. Basic Unet improved the image quality by reducing these artifacts, although some
artifacts remained. Our method effectively removed most of the artifacts and recon-
structed the images close to the reference images from the BraTs testing dataset. The per-
formance of three under-sampling masks on BraTs testing data is shown in Figure 9,
where MCP-US generated better PSNR and SSIM than other under-sampling patterns,
except for VIFP using 2DG-US.
Figure 8. Reconstructed MRI images from the BraTs testing dataset (slice No. 140) using zero filling,
Unet, and FDA-CNN: (a) 2D Gaussian distribution; (b) 1D Gaussian distribution; (c) mixed center
and peripheral mask; (d) fully sampled ground truth image.
Bioengineering 2023, 10, 22 11 of 18
Figure 9. Comparison of three sampling patterns using FDA-CNN.
4.2. FastMRI and IXI Datasets
The second experiment used the fastMRI and IXI datasets to test the CNNs after they
had been trained on the BraTs dataset. This represents a scenario using different training
and test datasets that are not perfectly matched. For testing, fastMRI comprised 2560 T1-
weighted axial brain images from 160 k-spaces, while IXI comprised the same number of
T2-weighed coronal brain images from 10 k-spaces. BraTs and fastMRI have many simi-
larities, such as features and MR sequences. On the other hand, BraTs and IXI have dis-
tinctly dissimilar features and are not compatible due to their MR sequences. This exper-
iment was performed to assess how well the CNN performs and generalizes when the
training and testing datasets are different. The results of FDA-CNN and other methods
without fine-tuning the fastMRI dataset are shown in Table 2.
Table 2. Average SSIM, PSNR, NRMSE, and VIFP values and reconstruction time of state-of-art
methods on fastMRI-T1 axial brain data using several sampling patterns.
Sampling
Metrics
Zero Filling
TV
Wavelet
LAE
Unet
Wnet
PBCU
DRL-Net
FDA-CNN
2DG-US
SSIM 0.52 0.49 0.51 0.70
0.72 0.72 0.76 0.80 0.81
PSNR 35.87 35.65 35.89 35.16
35.28 35.13 35.51 35.40 36.23
NRMSE 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.07 0.06
VIFP 0.78 0.56 0.79 0.84 0.80
0.85 0.82 0.81 0.88
1DG-US
SSIM 0.57 0.54 0.57 0.61 0.64 0.63 0.65 0.66 0.71
PSNR 32.64 32.62 32.64 32.89 33.08 32.71 33.03 33.18 34.29
NRMSE 0.14 0.14 0.14 0.13 0.13 0.14 0.13 0.11 0.09
VIFP 0.43 0.29 0.42 0.64 0.62 0.69 0.64 0.56 0.64
MCP-US
SSIM 0.78 0.76 0.78 0.88 0.87 0.88 0.88 0.88 0.91
PSNR 36.76 36.40 36.76 37.79 37.93 37.88 37.76 37.81 40.88
NRMSE 0.06 0.06 0.06 0.05 0.04 0.04 0.05 0.04 0.02
VIFP 0.56 0.40 0.54 0.75 0.77 0.82 0.80 0.73 0.75
Reconstruction time (seconds) 1.52 1.3 0.46 0.49 0.95 0.82 0.47 0.44
With the 2DG-US mask, the CS methods slightly improved image quality, but under
the other two Cartesian samplings, these methods did not perform well. The CNNs re-
moved the artifacts and improved the image quality using all three sub-sampling patterns.
Instead of VIFP, our method produced better average PSNR, SSIM, and NRMSE than the
multidomain (Wnet) network in two cases. As shown in Figure 10, FDA-CNN effectively
removed most of the artifacts and generated a better image than Unet. The performances
of three under-sampling masks on the fastMRI dataset are shown in Figure 11. MCP-US
produced better PSNR and SSIM than other under-sampling patterns, except for VIFP us-
ing the 2D random sampling pattern.
Bioengineering 2023, 10, 22 12 of 18
Figure 10. Reconstructed MRI images from the fastMRI dataset (slice No. 01) using zero filling, Unet,
and FDA-CNN: (a) 2D Gaussian distribution; (b) 1D Gaussian distribution; (c) mixed center and
peripheral mask; (d) fully sampled ground truth image.
Figure 11. Comparison of three sampling patterns on fastMRI dataset using FDA-CNN.
The test results of FDA-CNN and other methods on the IXI dataset are shown in
Table 3. In this case, the CS methods improved some quantitative values but decreased
the VIFP values. FDA-CNN performed significantly better and yielded high-quality im-
ages by eliminating unwanted artifacts compared with other networks using all masks.
However, Wnet generated better VIFP in two Cartesian samplings than our method. The
goal of this experiment was to determine whether it is feasible to test CNNs on unknown
testing datasets to remove artifacts from anatomically accurate MR images using various
sampling patterns.
Bioengineering 2023, 10, 22 13 of 18
Table 3. Average SSIM, PSNR, NRMSE, and VIFP values and reconstruction time of state-of-the-art
methods on the IXI -T2 coronal dataset using several sampling patterns.
Sampling
Metrics
Zero Filling
TV
Wavelet
LAE
Unet
Wnet
PBCU
DRL-Net
FDA-CNN
2DG-US
SSIM 0.46 0.48 0.50 0.67 0.70 0.71 0.73 0.76 0.77
PSNR 33.97 33.46 33.98 34.25 34.85 34.71 35.02 34.75 35.47
NRMSE 0.15 0.07 0.07 0.10 0.08 0.08 0.08 0.07 0.06
VIFP 0.69 0.70 0.67 0.89 0.86 0.90 0.86 0.75 0.97
1DG-US
SSIM 0.50 0.52 0.56 0.64 0.66 0.66 0.68 0.71 0.79
PSNR 33.38 33.47 33.67 33.43 33.63 33.34 33.64 34.14 35.02
NRMSE 0.12 0.12 0.12 0.12 0.11 0.12 0.11 0.09 0.07
VIFP 0.35 0.19 0.32 0.58 0.57 0.60 0.55 0.56 0.51
MCP-US
SSIM 0.70 0.72 0.72 0.82 0.81 0.82 0.83 0.83 0.89
PSNR 35.74 35.40 35.40 36.36 36.58 36.44 36.52 36.65 37.70
NRMSE 0.07 0.08 0.08 0.06 0.06 0.06 0.06 0.05 0.04
VIFP 0.44 0.25 0.25 0.71 0.73 0.77 0.73 0.68 0.68
Reconstruction time (seconds) 0.9 0.91 0.33 0.33 0.43 0.33 0.32 0.32
As shown in Figure 12, FDA-CNN effectively reconstructed a better image, which
was close to the reference image from different MRI sequence data, than Unet. The per-
formances of three under-sampling patterns on the IXI dataset are shown in Figure 13.
MCP-US performed better than other under-sampling patterns, except for VIFP using
2DG-US.
Figure 12. Reconstructed MRI images from IXI dataset (slice No. 75) using zero filling, Unet, and
FDA-CNN at a sampling rate of 20%: (a) 2D Gaussian distribution; (b) 1D Gaussian distribution; (c)
mixed center and peripheral under-sampling; (d) fully sampled ground truth image.
Bioengineering 2023, 10, 22 14 of 18
Figure 13. Comparison of three sampling patterns on IXI dataset using FDA-CNN.
The average NRMSEs of the BraTs test dataset slices are displayed in Figure 14. The
NRMSEs exhibited a recognizable pattern over the middle slices. The borders of the brain con-
tain a lower number of frequencies that produce more unspecified and inconsistent images.
Figure 14. Average NRMSE variation across the slices. Edge slices have larger errors.
FDA-CNN performed better in artifact removal and image restoration than the reg-
ular Unet-based CNN and CS techniques according to the described test results. The two
3 × 3 convolutions in Unet are replaced by a dense block in FD-CNN. The input and output
of all of the convolutional layers are comparatively small, although the dense block has
eight distinct convolutional layers (four 1 × 1 and four 3 × 3). Therefore, the computational
cost of the dense block-based convolutional layer is less expensive than that of Unet. Ad-
ditionally, the regularizing impact of extensive connectivity lessens the possibility of over-
fitting the training data. The effectiveness of the CNN is heavily reliant on the accuracy of
the MRI spatial frequencies, which is a drawback of post-processing techniques such as
FDA-CNN. CNN reconstruction is likely to restore image features inaccurately if they are
heavily obscured. Some of the lower frequencies may be recoverable if the CNN is directly
employed to restore the sensor data. Furthermore, FD-CNN is more generalized than
other state-of-the-art methods, as it generated higher average SSIM and PSNR, and lower
average NRMSE on both the fastMRI and IXI datasets.
Bioengineering 2023, 10, 22 15 of 18
5. Conclusions
This article presents an efficient and effective deep learning-based method for MRI
reconstruction from a sparsely sampled k-space using a fully dense attention convolu-
tional neural network. In the proposed approach, edge information and geometry struc-
ture are restored more effectively from zero-filled MRI images. This network has the com-
petency to extract realistic features and reconstruct 2D images that are virtually similar to
the original. Dense connectivity remarkably promotes feature reuse and improves infor-
mation flow within the network. Furthermore, AGs combine lower and higher spatial in-
formation to pick up more useful features, so the model needs a smaller number of pa-
rameters than the more complex Unet. This makes the network more generalized. Alt-
hough network training requires many hours, reconstruction can be performed fast after
training. Compared with CS-based iterative existing approaches, the proposed network
needs less reconstruction time.
Compared with existing DL-based denoising and de-aliasing methods, the proposed
network shows outstanding performance with regard to quantitative and qualitative hu-
man vision indexes, and reconstruction time. Furthermore, the correlations between the
acquired image quality and several under-sampling patterns were evaluated. Future re-
search will focus on recovering unmeasured frequencies in the k-domain. Moreover, we
will implement our approach for real-time interactive temperature-based MRI.
Author Contributions: Conceptualization, M.B.H.; methodology, M.B.H.; software, M.B.H.; valida-
tion, M.B.H. and K.-C.K.; formal analysis, M.B.H., K.-C.K., and N.K.; investigation, M.B.H. and K.-
C.K.; resources, M.B.H. and S.M.I.; data curation, M.B.H.; writing—original draft preparation,
M.B.H.; writing—review and editing, M.B.H., K.-C.K., S.M.I., O.-S.N., S.-H.J., and N.K.; visualiza-
tion, M.B.H. and K.-C.K.; supervision, K.-C.K. and N.K.; project administration, K.-C.K. and N.K.;
funding acquisition, N.K. M.B.H. and K.-C.K. are co-first authors. All authors have read and agreed
to the published version of the manuscript.
Funding: This work was supported by Institute for Information and Communications Technology
Promotion (IITP), funded by the Korean government (MSIP) (No. 2021-0-00490; Development of
precision analysis and imaging technology for biological radio waves).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The datasets are available at https://www.med.up-
enn.edu/cbica/brats2020/registration.html, https://fastmri.med.nyu.edu/ and https://brain-develop-
ment.org/ixi-dataset/. The source code of this manuscript is available at https://github.com/bid-
dut2j8/FDA-CNN (Last accessed on 20 December 2022).
Acknowledgments: We thank Shahinur Alam and Rupali Shinde for validating the proposed
method from a deep learning perspective.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
1D One-dimensional
1DG-US 1D Gaussian under-sampling
2D Two-dimensional
2DG-US 2D Gaussian under-sampling
AG Attention gate
CNN Convolutional neural network
CS Compressed sensing
CT Computed tomography
DB Dense block
DC Dense connectivity
DL Deep learning
DRL Deep residual learning
Bioengineering 2023, 10, 22 16 of 18
FDA-CNN
Fully dense attention CNN
FFT Fast Fourier transform
GAN Generative adversarial network
IFFT Inverse fast Fourier transform
LAE Lightweight autoencoder
MCP-US Mixed center and periphery under-sampling
MRI Magnetic resonance imaging
MSE Mean square error
NRMSE Normalized root mean squared error
PAT Photoacoustic tomography
PBCU Projection-based cascade Unet
PI Parallel imaging
PSNR Peak signal-to-noise ratio
ReLU Rectified linear unit
SSIM Structural similarity index measure
TV Total variation
VIFP Pixel visual information fidelity
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