Satoshi ITO^{1} and Tsukasa SAITO^{1}
^{1}Utsunomiya University, Utsunomiya, Japan
Synopsis
Aliasfree image
reconstruction is feasible in phase scrambling Fourier transform imaging. When
small downscaling factor is used in that method, the size of reconstructed
images become small and aliased image are separated in the scaled space. In
this work, a new fast imaging method in which aliasing artifacts due to
undersampling of signal is removed 2steps; one is downscaled space
introduced by aliasfree reconstruction and the second is the denoising using
deep convolution network. It was shown that proposed method provide higher PSNR
images compared to random sampling compressed sensing and has an advantage in
low sampling rate image acquisition.
Introduction
When
the size of imaging object is larger than the fieldofview in magnetic
resonance imaging, aliasing artifacts
will appear on the reconstructed image. We have proposed a new image
reconstruction technique, in which images at optional scaling can be obtained
and hence aliasfree images can
be reproduced from the data that occur aliasing artifact in Fourier
transform image reconstruction technique ^{[1,2]}. Since aliasfree image is realized by expanding
the pseudo FOV, the spatial resolution of that image must be reduced. In this work, we propose
a new faster imaging method in which equispaced undersampling is adopted and
aliasing artifacts are removed by aliasing control in the scaled space
introduced by aliasfree reconstruction, and following deep convolutional neural network.Method
Phasescrambling
Fourier transform imaging (PSFT) ^{[3] }is adopted in proposed method,
$$v(k_x,k_y)=
\int \hspace{2.0mm} \int^{\infty}_{\infty}
\left\{ \rho(x,y) e^{j q (x^2+y^2)} \right\} e^{j(k_x x+k_y y)}dxdy
...(1),$$
$$
\rho_\alpha(x',y')= \alpha^2 \rho(\alpha x, \alpha y)
e^{j c \left(\frac{\alpha1}{\alpha} \right) \left[ (\alpha x)^2 + (\alpha
y)^2 \right]}
...(2), $$
where
$$$\rho(x,y)$$$ represents the spin density distribution in the subject, $$$c$$$
is the coefficient of quadratic phase shifting. The coefficient $$$c$$$ is
normalized as $$$c=\alpha (\pi/N)$$$, where phase changes with neighboring
pixel become $$$\pi$$$ at the end of image space when $$$\alpha =1.0 $$$ (N:
matrix size of image).
Figure
1 shows the application of aliasfree reconstruction (AFR) ^{[1,2]}. Most of aliasing
artifacts are removed, however, the spatial resolution is reduced due to the
shrinkage of image to fit in the size of signal matrix as shown in Fig.1(b).
Regarding
to $$$\alpha$$$, optional value can be used in reconstruction process
irrespective of actual parameter used in the data acquisition and in that time scaling of images will
be realized.When AFR is executed in a high downscaling
factor using a zerofilled undersampled signal (Fig.1(c)), main image
components and aliasing components will be separated in the scaled space as
shown in Fig.1(e). After removal of main aliasing components shown as red squared
line and followed by the inverse of aliasfree reconstruction, almost aliasing
artifacts are removed as shown in Fig.1(f). Since some aliasing artifacts are
still remained on the image, deep convolutional neural network (CNN) is adopted
to remove the remained artifacts. Deep CNN^{ [4]} we utilized was known as high dealiasing performance
without sacrificing spatial resolution.
Results and Discussions
In
simulation experiments, PSFT signal is calculated using the MR volunteer image
data according to the Eq. (1). Calculated signals were undersampled at an
equal interval to be 2x, 3x and 4x acceleration factor. Imaging
parameters are set as $$$\alpha_{true}=1.0$$$ for data acquisition, and $$$\alpha$$$
for reconstruction is listed in Fig.3 The
structure of deep CNN ^{[4]}
is as follows; depth: 17, receptive field size: 35, 17 layer, filter size:
3x3x64. 50 images were used for learning of deep CNN network. Figures (a), (e), (i) are
downscaled images using aliasfree reconstruction for 2x, 3x, 4x factor. Most
of the aliasing artifacts were
removed by replacing these separated aliased images surrounded by red dashed
line with zero data. Obtained reduce aliased images shown in Figs (b), (f), (j)
were used as the input images of deep CNN network. Obtained images by CNN are shown in Fig.3 (c),(g),(k).
Figs. (b),(f),(j) show that remained artifacts are clearly removed by deep CNN network
without conspicuous degradation of spatial resolution. Figure 4 shows the PNSR
characteristics with reference to signal reduction factor using 20 phase varied
images. Proposed method are compared with CS iterative reconstruction using
PSFT signal using random sampling (PSFTCS) ^{[5]} and CS iterative reconstruction (FTCS). Figure
4 indicates that proposed method shows higher PSNR especially for lower
sampling rate, 25% and 33%. The reason is that 1) aliasing artifacts are
separated and they can be removed effectively by AFR, 2) spatial resolution is
not severely
sacrificed by undersampling since equispace sampling is executed, 2) remained
aliasing artifacts are fairly removed by deep CNN.
Figure
4 shows the results of application to experimentally obtained PSFT signal.
Fully scanned signal was acquired using 0.2T MRI and then the obtained signal
was undersampled. Imaging parameters are the same as Fig.3. Figure (b) shows
the fully scanned image, and (c), (d), (e) show the image with acceleration
factor 2x, 3x and 4x, respectively. Even though aliasing artifacts were slightly
remained on the images, high resolution images are obtained even acceleration
factor 4x case (e).
Conclusion
A
new fast imaging method equispaced undersampled signal in PSFT is proposed.
Aliasing artifacts are removed using aliasfree reconstruction and deep CNNAcknowledgements
This
study was supported in part by JSPS KAKENHI(16K06379). We would like
to thank Canon Medical Systems.References
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