1. Simultaneous multi-slice imaging provides
robust slice-level motion tracking, estimation
and DWI reconstruction by covering the 3D
anatomy at multiple coupled image planes
3.3. Ball-and-Stick Model [2]
Introductio
Motion-Robust Reconstruction based on Simultaneous Multi-Slice
Registration for Diffusion-Weighted MRI of Moving Subjects
Bahram Marami1, Benoit Scherrer, Onur Afacan, Simon K.Warfield, Ali Gholipour2
1,2 {Bahram.Marami,Ali.Gholipour}@childrens.harvard.edu
•Simultaneous multi-slice (SMS) echo-
planar imaging has had a huge impact on the
acceleration of diffusion-weighted MRI
(DWI) in neuroimaging studies.
•These scans are still lengthy with vibration
which are not easily tolerated by non-
cooperative patients, children and newborns.
•A novel registration-based motion tracking
technique is proposed in this paper that takes
advantages of SMS acquisition to enable
robust reconstruction of neural
microstructures in moving subjects.
•Our technique has three main components:
1. Detection and rejection of through-
slice motion-corrupted images
2. Tracking and estimation of motion
using SMS registration
3. Robust reconstruction of diffusion
tensors and multi-compartment models
from motion-corrected DWI data
An SMS DWI scan is performed by
interleaved 2D echo-planar imaging with two
(or more) multi-band excitations. Two rigidly-
coupled slices provide a multi-plane coverage
of the anatomy and mitigate ill-posedness of
slice-to-volume registration.
Fig. 1: Two same-color arrows point at through-slice motion artifacts
seen in simultaneously acquired slices in a 2-band axial SMS DWI
Closing Filter
Input
Image
1. Through-slice motion detection
A morphological closing filter along the slice
select direction is used to detect inter-slice
intensity discontinuity.
Input
Image
Subtractor
Output
Image
Fig. 2: through-slice motion detection
A rule-based motion detection technique:
2. Slice-level motion tracking and
estimation
• Stochastic state-space model:
xk is the vector of motion parameters (three
rotations and three translations)
The distribution of measurement noise is NOT
fixed a priori. It is updated based on the
sequential observations through estimating its
covariance Sk at any time step k.
•multi-slice to volume registration:
yk is the set of simultaneous (coupled) slices
acquired at time step k.
• Multi-slice to volume registration and outlier-robust Kalman filter-based
motion states estimation [1]
3. Robust diffusion model reconstruction
from motion-corrected images
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. , NO., JULY 2015
Algorithm 1 Pseudo-code of the outlier-robust motion esti-
mation for each slice
Input: I3D, yk, xk 1
Output: xk
1: slice-to-volume-registration:
2: zk max
p
f (I2D(p), yk); p0 = xk 1
3: predict states:
4: xk xk 1 , xk xk
5: Pk Pk 1 + Q , Pk Pk
6: repeat
7: update noise:
8: = zk xk
9: ⇤k = (sR + T
+ Pk)/(s + 1)
10: update states:
11: Kk = (Pk + ⇤k) 1
Pk
12: xk = xk + KT
k (zk xk )
13: Pk = KT
k ⇤kKk + (I Kk)T
Pk (I Kk)
14: until converged
15: return xk
system ⌦0(x, y, z) fixed to the base b=0 image. Similarly,
⌦0,i(x, y, z) represents the coordinate system of the ith b=0
image (1iNb=0). To reconstruct the ˜B0 in ⌦0(x, y, z), any
point in the coordinates of every b=0 image, i.e. ⌦0,i(x, y, z),
is mapped to the coordinate of the ˜B0 through registering ˜B0
to each b=0 image slice using the explained outlier-robust
motion estimation method.
The isotropic 3D base image ˜B0 is reconstructed in an
iterative process. Since there is no ˜B0 for the registration
at the beginning, we choose the b=0 image volume with
least motion as the reference image and register this image
to slices in other b=0 image volumes. Then, an isotropic 3D
image is reconstructed in the coordinates of the selected b=0
image using image information of all b=0 based on scattered
data interpolation (SDI). The reconstructed ˜B0 image at each
iteration, is used as the reference image in the next iteration
to reconstruct a final ˜B0 image. Our experiments on various
image data showed that the iterative reconstruction algorithm
converges after 2-3 iterations. As shown in Fig. 2 in a 2D
representations, in order to compute the image intensity at the
center of the regular grid points of the ˜B0 image, all scattered
points around the center grid in a 3⇥3⇥3 neighborhood
are considered. The scattered points in the neighborhood
are mapped from the coordinates of the all b=0 images
(⌦0,i(x, y, z), 1iNb=0) to the coordinates of the ˜B0 image
(⌦0(x, y, z)).The gray-scale intensity at each center gird is
computed as
˜B0,regular =
Pn
i=1 wiB0,scattered
Pn
i=1 wi
(10)
where wi is a weight computed based on a Gaussian kernel
ri
Fig. 2: Scattered data interpolation in the 3
reconstruction
centered at the regular grid point (star in Fig.
wi =
1
p
2⇡
e
1
2 (
ri )2
where ri determines the distance between th
point and the center grid point, and n is the t
scattered points in the 3⇥3⇥3 neighborhood.
called the standard deviation and determines th
bell-shaped Gaussian function. Larger values f
weights to the points far from the center gird
a smoother reconstructed base image. For the
this paper, we set = 0.5.
Three orthogonal image planes from an a
who deliberately moved during the scan are s
and compared to the reconstructed ˜B0 image (
stationary gold standard image in which the v
asked to be still (Fig. 3c). In this scan 6 out
were b=0, i.e. Nb=0 = 6 and the subject delib
including making head rotations up to 30 . Ther
slice motion in 3 out of 6 b=0 volumes on
shown in Fig. 3a. It should be noted that intr
corrupted slices was automatically detected and
reconstruction of the ˜B0 image. Normalized roo
errors (NRMSE) between the gold standard
reconstructed ˜B0 image was, 0.0357, 0.0306, a
the first, second and the third iteration show
improvement in terms of NRMSE after the sec
2) Registration of diffusion sensitized imag
image: The reconstructed ˜B0 image was e
reference image to bring all diffusion sensitized
the same coordinate by registering all slices to B
the motion estimation algorithm explained in
Similar to the motion estimation in b=0 ima
motion-corrupted slices were automatically ide
parameters corresponding to the time step o
corrupted slice were considered equal to those
time step. Estimated motion parameters for e
stored for the reconstruction of diffusion tens
steps.
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. , NO., OCT 2015
Then, similar to (6), given n 6 diffusion-sensitized poi
with noncollinear gradient directions, diffusion tensors
computed by minimizing the following objective function
f( ) =
1
2
nX
i=1
w2
i ↵2
i
0
@ln
Bi,irregular
˜B0,irregular
! 6X
j=1
Mi,j j
1
A
2
where ↵i = Bi,irregular, Bi,irregular is the observ
diffusion-sensitized signal (gray-scale value) at any moti
corrected point location, and ˜B0,irregular is the correspond
non-diffusion weighted signal, which is interpolated from
˜B0 image at that irregular point location. Finally, wi i
weighting factor that is computed as
wi =
1
p
2⇡
e
1
2 (
ri )2
(
where ri is the distance between the ith point and the cen
of the grid point, is the standard deviation of a bell-shap
Gaussian function, and n is the total number of points in
neighborhood. The weights (wis) balance the contribution
multiple observed points based on their distance to the locat
where the tensor is computed.
III. ALGORITHM DESIGN AND IMPLEMENTATION
The slice-level registration-based motion tracking explain
in the previous section is a generic motion correction meth
which can be used for processing any set of sequentially
quired 2D MR images (structural, functional or diffusion M
from a dynamically moving subject. Our focus in this stu
has been on DW brain MRI, which involves relatively lo
duration scans with varying contrast that makes it particula
challenging for such an image registration-based approach
The flowchart of our motion-robust DW brain MRI rec
struction technique is shown in Fig. 1. Given a set of D
brain MRI volumes, first, slices corrupted by through-pl
motion were automatically detected using image featur
These motion-corrupted slices were excluded from mot
estimation and DTI reconstruction. Then, an isotropic
image was reconstructed from multiple b=0 images. T
proposed filtering-based motion estimation method was u
to correct for the slice-level motion in all b=0 images and
reconstruct a 3D base image (i.e., ˜B0) which is a weigh
average of all b=0 images. In the next step, temporal h
motion was estimated using the approach proposed in Sect
II-A through registering all diffusion-sensitized image sli
to the reconstructed ˜B0 image. Finally, diffusion tensors w
computed in the ˜B0 coordinates using image information fr
all gradient directions. In the following subsections these st
are explained in detail.
A. Identification of Motion-Corrupted Slices
In routine slice image acquisitions, diffusion-weighted sli
are obtained in an interleaved order to avoid slice cross-t
and spin history artifacts. In an interleaved acquisition adjac
slices are obtained at different time points and patient’s h
motion results in corruption of image slices independently.
this scheme, artifacts caused by motion can be easily identifi
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. , NO., OCT 2015
Then, similar to (6), given n 6 diffusion-sensitized points
with noncollinear gradient directions, diffusion tensors are
computed by minimizing the following objective function
f( ) =
1
2
nX
i=1
w2
i ↵2
i
0
@ln
Bi,irregular
˜B0,irregular
! 6X
j=1
Mi,j j
1
A
2
(9)
where ↵i = Bi,irregular, Bi,irregular is the observed
diffusion-sensitized signal (gray-scale value) at any motion-
corrected point location, and ˜B0,irregular is the corresponding
non-diffusion weighted signal, which is interpolated from the
˜B0 image at that irregular point location. Finally, wi is a
weighting factor that is computed as
wi =
1
p
2⇡
e
1
2 (
ri )2
(10)
where ri is the distance between the ith point and the center
of the grid point, is the standard deviation of a bell-shaped
Gaussian function, and n is the total number of points in the
neighborhood. The weights (wis) balance the contribution of
multiple observed points based on their distance to the location
where the tensor is computed.
III. ALGORITHM DESIGN AND IMPLEMENTATION
The slice-level registration-based motion tracking explained
in the previous section is a generic motion correction method,
which can be used for processing any set of sequentially ac-
quired 2D MR images (structural, functional or diffusion MRI)
from a dynamically moving subject. Our focus in this study
has been on DW brain MRI, which involves relatively long
duration scans with varying contrast that makes it particularly
challenging for such an image registration-based approach.
The flowchart of our motion-robust DW brain MRI recon-
struction technique is shown in Fig. 1. Given a set of DW
brain MRI volumes, first, slices corrupted by through-plane
motion were automatically detected using image features.
These motion-corrupted slices were excluded from motion
estimation and DTI reconstruction. Then, an isotropic 3D
image was reconstructed from multiple b=0 images. The
proposed filtering-based motion estimation method was used
to correct for the slice-level motion in all b=0 images and to
reconstruct a 3D base image (i.e., ˜B0) which is a weighted
average of all b=0 images. In the next step, temporal head
motion was estimated using the approach proposed in Section
II-A through registering all diffusion-sensitized image slices
to the reconstructed ˜B0 image. Finally, diffusion tensors were
computed in the ˜B0 coordinates using image information from
all gradient directions. In the following subsections these steps
are explained in detail.
A. Identification of Motion-Corrupted Slices
In routine slice image acquisitions, diffusion-weighted slices
are obtained in an interleaved order to avoid slice cross-talk
and spin history artifacts. In an interleaved acquisition adjacent
slices are obtained at different time points and patient’s head
motion results in corruption of image slices independently. In
this scheme, artifacts caused by motion can be easily identified
Input: I3D, yk, ˆxk 1
Output: ˆxk
1: slice-to-volume registration:
2: zk max
p
f (I2D(p), yk); p0 = ˆxk 1
3: predict states:
4: ˆxk ˆxk 1 , ˆxk ˆxk
5: Pk Pk 1 + Q , Pk Pk
6: repeat
7: update noise:
8: = zk ˆxk
9: ⇤k = (sR + T + Pk)/(s + 1)
10: update states:
11: Kk = (Pk + ⇤k) 1Pk
12: ˆxk = ˆxk + KT
k (zk ˆxk )
13: Pk = KT
k ⇤kKk + (I Kk)T Pk (I Kk)
14: until converged
15: return ˆxk
B. Image Reconstruction
Estimated motion parameters for each diffusion-sensitized
image slice allow us to bring all DWI data to the same coor-
dinates and perform further analysis. Although more complex
models of the diffusion signal could be considered to benefit
from motion correction, for the sake of simplicity and to focus
on the effect of motion correction, we consider reconstruction
of the diffusion tensor matrix based on the Stejskal-Tanner
(ST) equation. Having a base ˜B0 image and Nb6=0 diffusion-
sensitized volumes, a diffusion tensor can be estimated at any
point of the regular grid in ˜B0 by solving ST equation as
Bi,regular = ˜B0,regulare bgT
i Dgi
1  i  Nb6=0 (5)
where ˜B0,regular is the intensity at the regular grid location
in ˜B0 and Bi,regular is the corresponding intensity at the ith
diffusion-sensitized image; gi = [gix, giy, giz] represents the
ith diffusion gradient direction in the ˜B0 coordinates and b is
an imaging sequence dependent constant, which specifies the
diffusion sensitivity. Furthermore, D is a 3⇥3 symmetric pos-
itive definite matrix representing a diffusion tensor expressed
in ˜B0 coordinates with elements that are then rearranged in a
parameter vector = [Dxx, Dxy, Dxz, Dyy, Dyz, Dzz].
Given n 6 diffusion-sensitized images with noncollinear
gradient directions and a constant b-value, diffusion tensors
can be estimated by minimizing an objective function as [22]
f( ) =
1
2
nX
i=1
↵2
i
0
@ln
Bi,regular
˜B0,regular
! 6X
j=1
Mi,j j
1
A
2
(6)
where n = Nb6=0, and
M = b
2
6
4
g2
1x 2g1xg1y 2g1xg1z g2
1y 2g1yg1z g2
1z
...
...
...
...
...
...
g2
nx 2gnxgny 2gnxgnz g2
ny 2bgnygnz g2
nz
3
7
5 (7)
is an n⇥6 design matrix. Moreover, ↵is are weights for
different gradient directions in the objective function. Koay et
method. Sim
of the desig
guaranteed
typical solu
D = UT
U
zero diagon
In order
intensities o
locations id
case, howe
image inte
points in
approach t
corrected D
to reconstr
common re
these imag
This app
and motion
be available
grid points
or larger) is
locations. H
out the reco
of the final
window in
image poin
artifacts in
approach d
motion on
To mitig
interpolatio
and directly
using data
this end, w
locations an
a local neig
characteriz
value, b va
Gradient
are in the sc
directions i
of the acqu
has to be c
slice with
estimation
the rotation
and Rm is
the slice-to
the diffusi
coordinates
where g0i i
in the scan
3.2. Diffusion Tensor Model
Each scattered point is associated with a
gradient direction, motion parameters, b0 and
bi intensities
3.1. Constructing an
isotropic 3D base image
with desired resolution
from multiple b0 images
of the grid point, is the standard deviation of a bell-shaped
Gaussian function, and n is the total number of points in the
neighborhood. The weights (wis) balance the contribution of
multiple observed points based on their distance to the location
where the tensor is computed.
III. ALGORITHM DESIGN AND IMPLEMENTATION
The slice-level registration-based motion tracking explained
in the previous section is a generic motion correction method,
which can be used for processing any set of sequentially ac-
quired 2D MR images (structural, functional or diffusion MRI)
from a dynamically moving subject. Our focus in this study
has been on DW brain MRI, which involves relatively long
duration scans with varying contrast that makes it particularly
challenging for such an image registration-based approach.
The flowchart of our motion-robust DW brain MRI recon-
struction technique is shown in Fig. 1. Given a set of DW
brain MRI volumes, first, slices corrupted by through-plane
motion were automatically detected using image features.
These motion-corrupted slices were excluded from motion
estimation and DTI reconstruction. Then, an isotropic 3D
image was reconstructed from multiple b=0 images. The
proposed filtering-based motion estimation method was used
to correct for the slice-level motion in all b=0 images and to
reconstruct a 3D base image (i.e., ˜B0) which is a weighted
average of all b=0 images. In the next step, temporal head
motion was estimated using the approach proposed in Section
II-A through registering all diffusion-sensitized image slices
to the reconstructed ˜B0 image. Finally, diffusion tensors were
computed in the ˜B0 coordinates using image information from
all gradient directions. In the following subsections these steps
are explained in detail.
A. Identification of Motion-Corrupted Slices
In routine slice image acquisitions, diffusion-weighted slices
are obtained in an interleaved order to avoid slice cross-talk
and spin history artifacts. In an interleaved acquisition adjacent
slices are obtained at different time points and patient’s head
motion results in corruption of image slices independently. In
this scheme, artifacts caused by motion can be easily identified
intensity in the difference image. Volumes with more than
15% corrupted slices were excluded from the analysis.
B. Constructing an Isotropic 3D b=0 Image
Multiple b=0 images are often acquired along with
diffusion-sensitized images. We reconstructed a base image
namely ˜B0 in an isotropic regular 3D grid from multiple
b=0 images through an iterative process. We chose the first
b=0 volume or a b=0 with least amount of motion as the
reference image at the beginning and registered this image to
slices in all other b=0 image volumes. Then, an isotropic 3D
image was reconstructed in the coordinates of the selected b=0
image using image information of all b=0 images. Iterations of
motion correction and reconstruction were performed similar
to the previous works [16], [17]; The reconstructed ˜B0 image
at each iteration, was used as the reference image in the next
iteration to reconstruct a final ˜B0 image. Our experiments
on various image data showed that the algorithm converged
after 2-3 iterations. The image intensity at the center of the
regular grid points of the ˜B0 image, was computed based on
all (n) irregular points around the center grid in a 3⇥3⇥3
neighborhood using
˜B0,regular =
Pn
i=1 wiB0,irregular
Pn
i=1 wi
(11)
where wi is a distance weight based on a Gaussian kernel
centered at the regular grid point, computed using (10), where
ri determines the distance between the ith point and the center
grid point. For the experiments in this study, we set = 0.5.
C. Motion Estimation and Reconstruction
The reconstructed ˜B0 image was then used as a reference
volume to bring all diffusion-sensitized images b6=0 to the
same coordinates and calculate diffusion tensors. This was
achieved through the techniques explained in Section II. For
all practical purposes slice-to-volume registration (SVR) was
performed through registering the reference volume to the slice
and inverting the transformation. Estimated motion parameters
for each slice were stored for the reconstruction of diffusion
tensors in the next step. Similar to the motion estimation
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. , NO., OCT 2015
Then, similar to (6), given n 6 diffusion-sensitized points
with noncollinear gradient directions, diffusion tensors are
computed by minimizing the following objective function
f( ) =
1
2
nX
i=1
w2
i ↵2
i
0
@ln
Bi,irregular
˜B0,irregular
! 6X
j=1
Mi,j j
1
A
2
(9)
where ↵i = Bi,irregular, Bi,irregular is the observed
diffusion-sensitized signal (gray-scale value) at any motion-
corrected point location, and ˜B0,irregular is the corresponding
non-diffusion weighted signal, which is interpolated from the
˜B0 image at that irregular point location. Finally, wi is a
weighting factor that is computed as
wi =
1
p
2⇡
e
1
2 (
ri )2
(10)
where ri is the distance between the ith point and the center
of the grid point, is the standard deviation of a bell-shaped
Gaussian function, and n is the total number of points in the
neighborhood. The weights (wis) balance the contribution of
multiple observed points based on their distance to the location
where the tensor is computed.
III. ALGORITHM DESIGN AND IMPLEMENTATION
The slice-level registration-based motion tracking explained
in the previous section is a generic motion correction method,
which can be used for processing any set of sequentially ac-
quired 2D MR images (structural, functional or diffusion MRI)
from a dynamically moving subject. Our focus in this study
has been on DW brain MRI, which involves relatively long
duration scans with varying contrast that makes it particularly
challenging for such an image registration-based approach.
The flowchart of our motion-robust DW brain MRI recon-
struction technique is shown in Fig. 1. Given a set of DW
brain MRI volumes, first, slices corrupted by through-plane
motion were automatically detected using image features.
These motion-corrupted slices were excluded from motion
estimation and DTI reconstruction. Then, an isotropic 3D
image was reconstructed from multiple b=0 images. The
proposed filtering-based motion estimation method was used
to correct for the slice-level motion in all b=0 images and to
reconstruct a 3D base image (i.e., ˜B0) which is a weighted
average of all b=0 images. In the next step, temporal head
motion was estimated using the approach proposed in Section
II-A through registering all diffusion-sensitized image slices
to the reconstructed ˜B0 image. Finally, diffusion tensors were
computed in the ˜B0 coordinates using image information from
all gradient directions. In the following subsections these steps
are explained in detail.
A. Identification of Motion-Corrupted Slices
In routine slice image acquisitions, diffusion-weighted slices
are obtained in an interleaved order to avoid slice cross-talk
and spin history artifacts. In an interleaved acquisition adjacent
slices are obtained at different time points and patient’s head
motion results in corruption of image slices independently. In
this scheme, artifacts caused by motion can be easily identified
i
c
t
t
s
c
a
i
i
i
A
i
m
i
a
t
i
1
B
d
n
b
b
r
s
i
i
m
t
a
i
o
a
r
a
n
w
c
r
g
C
v
s
a
a
p
a
f
t
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. , NO., OCT 2015
Then, similar to (6), given n 6 diffusion-sensitized points
with noncollinear gradient directions, diffusion tensors are
computed by minimizing the following objective function
f( ) =
1
2
nX
i=1
w2
i ↵2
i
0
@ln
Bi,irregular
˜B0,irregular
! 6X
j=1
Mi,j j
1
A
2
(9)
where ↵i = Bi,irregular, Bi,irregular is the observed
diffusion-sensitized signal (gray-scale value) at any motion-
corrected point location, and ˜B0,irregular is the corresponding
non-diffusion weighted signal, which is interpolated from the
˜B0 image at that irregular point location. Finally, wi is a
weighting factor that is computed as
wi =
1
p
2⇡
e
1
2 (
ri )2
(10)
where ri is the distance between the ith point and the center
of the grid point, is the standard deviation of a bell-shaped
Gaussian function, and n is the total number of points in the
neighborhood. The weights (wis) balance the contribution of
multiple observed points based on their distance to the location
where the tensor is computed.
III. ALGORITHM DESIGN AND IMPLEMENTATION
The slice-level registration-based motion tracking explained
in the previous section is a generic motion correction method,
which can be used for processing any set of sequentially ac-
quired 2D MR images (structural, functional or diffusion MRI)
from a dynamically moving subject. Our focus in this study
has been on DW brain MRI, which involves relatively long
duration scans with varying contrast that makes it particularly
challenging for such an image registration-based approach.
The flowchart of our motion-robust DW brain MRI recon-
struction technique is shown in Fig. 1. Given a set of DW
brain MRI volumes, first, slices corrupted by through-plane
motion were automatically detected using image features.
These motion-corrupted slices were excluded from motion
estimation and DTI reconstruction. Then, an isotropic 3D
image was reconstructed from multiple b=0 images. The
proposed filtering-based motion estimation method was used
to correct for the slice-level motion in all b=0 images and to
reconstruct a 3D base image (i.e., ˜B0) which is a weighted
average of all b=0 images. In the next step, temporal head
motion was estimated using the approach proposed in Section
II-A through registering all diffusion-sensitized image slices
to the reconstructed ˜B0 image. Finally, diffusion tensors were
computed in the ˜B0 coordinates using image information from
all gradient directions. In the following subsections these steps
are explained in detail.
A. Identification of Motion-Corrupted Slices
In routine slice image acquisitions, diffusion-weighted slices
are obtained in an interleaved order to avoid slice cross-talk
and spin history artifacts. In an interleaved acquisition adjacent
slices are obtained at different time points and patient’s head
motion results in corruption of image slices independently. In
this scheme, artifacts caused by motion can be easily identified
in
co
th
th
sit
cl
af
im
im
i.e
A
in
m
im
al
to
in
15
B.
di
na
b=
b=
re
sli
im
im
m
to
at
ite
on
af
re
al
ne
w
ce
ri
gr
C.
vo
sa
ac
al
pe
an
fo
te
fj 2 [0, 1] sum-of-unity fractions of occupancy
Materials and Methods
Results
Results
Fig. 3: DTI in adult volunteers
Orig VVR SVR MT-SMR GS
Orig: original images with motion
VVR: volume-to-volume registration
SVR: slice-to-volume registration
MT-SMR: motion tracking based on
simultaneous multi-slice registration
GS: gold standard, images with no motion
Materials and Methods
is computed in the image domain
considering slice profile.
Algorithm 1 Pseudo-code of the ORKF-based motion estimation
slice.
Input: I3D, yk, ˆxk 1
Output: ˆxk
1: slice-to-volume registration:
2: zk max
p
f (I2D(p), yk); p0 = ˆxk 1
3: predict states:
4: ˆxk ˆxk 1 , ˆxk ˆxk
5: Pk Pk 1 + Q , Pk Pk
6: repeat
7: update noise:
8: = zk ˆxk
9: ⇤k = (sR + T + Pk)/(s + 1)
10: update states:
11: Kk = (Pk + ⇤k) 1Pk
12: ˆxk = ˆxk + KT
k (zk ˆxk )
13: Pk = KT
k ⇤kKk + (I Kk)T Pk (I Kk)
14: until converged
15: return ˆxk
B. Image Reconstruction
Estimated motion parameters for each diffusion-se
image slice allow us to bring all DWI data to the sam
dinates and perform further analysis. Although more c
models of the diffusion signal could be considered to
from motion correction, for the sake of simplicity and t
on the effect of motion correction, we consider recons
of the diffusion tensor matrix based on the Stejskal
(ST) equation. Having a base ˜B0 image and Nb6=0 dif
sensitized volumes, a diffusion tensor can be estimated
point of the regular grid in ˜B0 by solving ST equatio
Bi,regular = ˜B0,regulare bgT
i Dgi
1  i  Nb6=
where ˜B0,regular is the intensity at the regular grid l
in ˜B0 and Bi,regular is the corresponding intensity at
diffusion-sensitized image; gi = [gix, giy, giz] represe
ith diffusion gradient direction in the ˜B0 coordinates a
an imaging sequence dependent constant, which speci
diffusion sensitivity. Furthermore, D is a 3⇥3 symmet
itive definite matrix representing a diffusion tensor ex
in ˜B0 coordinates with elements that are then rearrang
parameter vector = [Dxx, Dxy, Dxz, Dyy, Dyz, Dzz]
Given n 6 diffusion-sensitized images with nonc
gradient directions and a constant b-value, diffusion
can be estimated by minimizing an objective function
f( ) =
1
2
nX
i=1
↵2
i
0
@ln
Bi,regular
˜B0,regular
! 6X
j=1
Mi,j j
1
A
where n = Nb6=0, and
M = b
2
6
4
g2
1x 2g1xg1y 2g1xg1z g2
1y 2g1yg1z g2
1z
...
...
...
...
...
...
g2
nx 2gnxgny 2gnxgnz g2
ny 2bgnygnz g2
nz
3
7
5
is an n⇥6 design matrix. Moreover, ↵is are weig
different gradient directions in the objective function. K
• DTI in 21 children (3 to 12 years old), multiple bi values and 90 directions
CC Cin LIC Pons
FA
0.3
0.4
0.5
0.6
0.7
0.8
Orig VVR SVR MT-SMR
Fig. 5: Boxplot analysis of FA values in regions of interest
degrees
-10
0
10
20 θx
θy
θz
mm
-10
0
10
tx
ty
tz
degrees
-10
0
10
20
mm
-10
0
10
slice number
1 157 313 469 625 781 937 1093 1249 1405
degrees
-10
0
10
20
slice number
1 157 313 469 625 781 937 1093 1249 1405
mm
-10
0
10
VVR
MT-SMR
SVR
Fig. 7: comparison of estimated motion parameters
corona radiata
CC
cingulum
Fig. 6: Whole brain tractography results
Fig. 8: Crossing fibers in the ball-and-stick model
Conclusions
Orig VVR SVR MT-SMR
Orig VVR SVR MT-SMR
amount of motion
4 6 8 10 12 14 16 18
∆FA
inCC
0.1
0.2
0.3
0.4
0.5
0.6
Orig VVR SVR MT-SMR
amount of motion
4 6 8 10 12 14 16 18
∆FA
incingulum
0.1
0.2
0.3
0.4
0.5
0.6
Orig VVR SVR MT-SMR
Fig. 4: Average FA value differences between the GS and each method in corpus callosum (CC) and cingulum
• DTI in adult volunteers 30 bi =1000 and 6 b0 images in14 motion cases
References
[1] B. Marami, B. Scherrer, O. Afacan, B. Erem, S. Warfield, A. Gholipour,
Motion-robust diffusion- weighted brain MRI reconstruction through slice-
level registration-based motion tracking, Med Imaging, IEEE T, 2016.
[2] T. Behrens, M. Woolrich, H. Johansen-Berg, R. Nunes, P. Matthews, J.
Brady, S. Smith, Characterization and propagation of uncertainty in diffusion-
weighted MR imaging, Magnet Reson Med 50 (2003) 1077–88
• Motion estimation through simultaneous
multi-slice-to-volume registration
outperformed slice-to-volume, and volume-
to-volume registration.
• MT-SMR leverages estimation power of
the outlier-robust Kalman filter and the 3D
coverage of the anatomy at multiple image
planes provided by SMS DWI.
•This technique can extend the use of SMS
DWI to populations that continuously move
during lengthy DWI scans by real-time
prospective motion tracking and correction.
Algorithm 1 Pseudo-code of the ORKF-based motion estimation for ea
slice.
Input: I3D, yk, ˆxk 1
Output: ˆxk
1: slice-to-volume registration:
2: zk max
p
f (I2D(p), yk); p0 = ˆxk 1
3: predict states:
4: ˆxk ˆxk 1 , ˆxk ˆxk
5: Pk Pk 1 + Q , Pk Pk
6: repeat
7: update noise:
8: = zk ˆxk
9: ⇤k = (sR + T + Pk)/(s + 1)
10: update states:
11: Kk = (Pk + ⇤k) 1Pk
12: ˆxk = ˆxk + KT
k (zk ˆxk )
13: Pk = KT
k ⇤kKk + (I Kk)T Pk (I Kk)
14: until converged
15: return ˆxk
B. Image Reconstruction
Estimated motion parameters for each diffusion-sensitiz
image slice allow us to bring all DWI data to the same coo
dinates and perform further analysis. Although more compl
models of the diffusion signal could be considered to bene
from motion correction, for the sake of simplicity and to foc
on the effect of motion correction, we consider reconstructi
of the diffusion tensor matrix based on the Stejskal-Tann
(ST) equation. Having a base ˜B0 image and Nb6=0 diffusio
sensitized volumes, a diffusion tensor can be estimated at a
point of the regular grid in ˜B0 by solving ST equation as
Bi,regular = ˜B0,regulare bgT
i Dgi
1  i  Nb6=0 (
where ˜B0,regular is the intensity at the regular grid locati
in ˜B0 and Bi,regular is the corresponding intensity at the i
diffusion-sensitized image; gi = [gix, giy, giz] represents t
ith diffusion gradient direction in the ˜B0 coordinates and b
an imaging sequence dependent constant, which specifies t
diffusion sensitivity. Furthermore, D is a 3⇥3 symmetric po
itive definite matrix representing a diffusion tensor express
in ˜B0 coordinates with elements that are then rearranged in
parameter vector = [Dxx, Dxy, Dxz, Dyy, Dyz, Dzz].
Given n 6 diffusion-sensitized images with noncolline
gradient directions and a constant b-value, diffusion tenso
can be estimated by minimizing an objective function as [2
f( ) =
1
2
nX
i=1
↵2
i
0
@ln
Bi,regular
˜B0,regular
! 6X
j=1
Mi,j j
1
A
2
(
where n = Nb6=0, and
M = b
2
6
4
g2
1x 2g1xg1y 2g1xg1z g2
1y 2g1yg1z g2
1z
...
...
...
...
...
...
g2
nx 2gnxgny 2gnxgnz g2
ny 2bgnygnz g2
nz
3
7
5 (
is an n⇥6 design matrix. Moreover, ↵is are weights f
different gradient directions in the objective function. Koay