Generalized Autocalibrating Partially Parallel
Acquisitions (GRAPPA)
Mark A. Griswold,
1
*
Peter M. Jakob,
1
Robin M. Heidemann,
1
Mathias Nittka,
2
Vladimir Jellus,
2
Jianmin Wang,
2
Berthold Kiefer,
2
and Axel Haase
1
In this study, a novel partially parallel acquisition (PPA) method
is presented which can be used to accelerate image acquisition
using an RF coil array for spatial encoding. This technique,
GeneRalized Autocalibrating Partially Parallel Acquisitions
(GRAPPA) is an extension of both the PILS and VD-AUTO-
SMASH reconstruction techniques. As in those previous meth-
ods, a detailed, highly accurate RF field map is not needed prior
to reconstruction in GRAPPA. This information is obtained from
several k-space lines which are acquired in addition to the
normal image acquisition. As in PILS, the GRAPPA reconstruc-
tion algorithm provides unaliased images from each compo-
nent coil prior to image combination. This results in even higher
SNR and better image quality since the steps of image recon-
struction and image combination are performed in separate
steps. After introducing the GRAPPA technique, primary focus
is given to issues related to the practical implementation of
GRAPPA, including the reconstruction algorithm as well as anal-
ysis of SNR in the resulting images. Finally, in vivo GRAPPA im-
ages are shown which demonstrate the utility of the technique.
Magn Reson Med 47:1202–1210, 2002. © 2002 Wiley-Liss, Inc.
Key words: parallel imaging; rapid MRI; RF coil arrays; SMASH;
SENSE; PILS
Since the development of the NMR phased array (1) in the
late 1980s, multicoil arrays have been designed to image
almost every part of the human anatomy. These multicoil
arrays are primarily used for their increased signal-to-noise
ratio (SNR) compared to volume coils or large surface coils.
Recently, several partially parallel acquisition (PPA)
strategies have been proposed (2–19) which have the po-
tential to revolutionize the field of fast MR imaging. These
techniques use spatial information contained in the com-
ponent coils of an array to partially replace spatial encod-
ing which would normally be performed using gradients,
thereby reducing imaging time. In a typical PPA acquisi-
tion, only a fraction of the phase encoding lines are ac-
quired compared to the conventional acquisition. A spe-
cialized reconstruction is then applied to the data to re-
construct the missing information, resulting in the full
FOV image in a fraction of the time.
The primary limiting factor of the majority of PPA tech-
niques is their requirement of accurate knowledge of the
complex sensitivities of component coils. In practice, the
actual coil sensitivity information is difficult to determine
experimentally due to contamination by, for example,
noise. Additionally, subject or coil motion between the
time of coil calibration and image acquisition can be prob-
lematic if this information is not taken into account during
the reconstruction.
Last year, we presented the parallel imaging with local-
ized sensitivities (PILS) technique (14) and demonstrated
several advantages. In PILS it is assumed that each com-
ponent coil has a localized sensitivity profile. Whenever
this is true, uncombined coil images can be formed for
each component coil using only knowledge of the position
of the coil in the FOV, which can be obtained trivially
using a number of methods (14). Besides providing an
efficient reconstruction process (14,20), PILS was shown
to provide optimal SNR for all accelerations tested, since
the uncombined coil images can be combined using a sum
of squares or other optimal array reconstruction method.
The PILS technique represents a departure in recon-
struction philosophy compared to other previous PPA
methods. In all previous methods the steps of image re-
construction (unaliasing) and SNR optimization (image
combination) occur in one step. Therefore, both processes
had to be simultaneously optimized for a good reconstruc-
tion. On the other hand, the process of unaliasing and SNR
optimization are completely decoupled in PILS, so that
both can potentially be optimized separately. We believe
that this general philosophy could lead to more robust and
optimized PPA reconstructions. However, in order to de-
couple these processes uncombined images need to be
formed by the PPA reconstruction technique. To date, no
such method other than PILS exists.
In this study, we describe the first extension of this basic
philosophy which is applicable to coils which are not
necessarily spatially localized. In this technique, Gene-
Ralized Autocalibrating Partially Parallel Acquisitions
(GRAPPA), a more generalized view of the variable density
AUTO-SMASH (VD-AUTO-SMASH) technique (15), is
used to generate uncombined coil images from each coil in
the array. It is shown that this reconstruction process
results in images in higher SNR and better overall image
quality compared to previous VD-AUTO-SMASH imple-
mentations. After introduction of the reconstruction
method, computer simulations will be presented which
highlight the benefits of the GRAPPA reconstruction. Fi-
nally, the first in vivo results using an eight-channel re-
ceiver system and the GRAPPA reconstruction are shown.
THEORY
Review of AUTO-SMASH and VD-AUTO-SMASH
In order to understand the GRAPPA process, it is instruc-
tive to review the basics of both the AUTO-SMASH (11)
1
Julius-Maximilians Universita¨t Wu¨ rzburg, Physikalisches Institut, Wu¨ rzburg,
Germany.
2
Siemens Medical Solutions, Erlangen, Germany.
*Correspondence to: Mark Griswold, Department of Physics, University of
Wu¨ rzburg, Am Hubland, 97074 Wu¨ rzburg, Germany. E-mail: mark@physik.
uni-wuerzburg.de
Received 7 September 2001; revised 14 January 2002; accepted 13 February
2002.
DOI 10.1002/mrm.10171
Published online in Wiley InterScience (www.interscience.wiley.com).
Magnetic Resonance in Medicine 47:1202–1210 (2002)
© 2002 Wiley-Liss, Inc. 1202
and VD-AUTO-SMASH (15) methods. In AUTO-SMASH,
an additional calibration line, or auto-calibration signal
(ACS), is collected along with the reduced data acquisi-
tion. To determine the weights used for reconstruction, a
line in the reduced dataset is fit to the ACS line. This
process can be represented by:
冘
l⫽1
L
S
l
ACS
共k
y
⫺ m⌬k
y
兲 ⫽
冘
l⫽1
L
n共l, m兲S
l
共k
y
兲 [1]
for a line offset by m⌬k
y
, where l counts through the coils
up to the total number of coils, L. This equation is equiv-
alent to eq. 7 in Ref. 11. The weights n(l,m) are then used
to reconstruct the missing lines as in the original SMASH
technique (2).
This process was later extended in the VD-AUTO-
SMASH approach. In this method, more than one ACS line
is acquired in the center of k-space, which allows for
multiple fits to be performed for each missing line, thereby
moderating the effects of both noise and coil profile im-
perfections (15). In addition to the improved fit provided
by the VD-AUTO-SMASH approach, the extra ACS lines
could be included in the final image, thereby further re-
ducing image artifacts.
It is important to note that in both AUTO-SMASH and
VD-AUTO-SMASH, as well as the original SMASH tech-
nique, the fitting process determines the weights which
transform a single line acquired in each of the individual
coils into a single shifted line in the composite k-space
matrix. This process is shown schematically in Fig. 1. The
data acquired in each coil (black circles) are fit to the ACS
line in a composite image (gray circle), which in most
cases is the simple sum of the ACS lines acquired in each
coil, although in some cases the lines are phased prior to
summation (13). This process is simply repeated with
multiple lines and combinations in VD-AUTO-SMASH.
This process leads to two major problems found in all
previous k-space-based reconstructions. First, the result-
ing SNR is that of a complex sum image (4), instead of the
better sum of squares image or an image combined using
optimal reconstruction weights (1). As shown previously,
this can lead to losses of
公
L
for L coils or worse at low
acceleration factors. This is particularly problematic when
one considers increasing the number of coils used in the
reconstruction.
In addition to these SNR issues, previous k-space-based
methods suffered from severe phase cancellation in cases
where the phases of the different coils were not exactly
aligned or cases where slight phase differences existed
between residual aliased signal and the unaliased normal
signal. In these cases, signal losses or even complete can-
cellation could be observed using VD-AUTO-SMASH, for
example. The only way to measure this phase without
collecting a complete coil map (which would defeat the
advantage of any auto-calibrating approach) is to make a
separate measurement of the noise correlation between the
coils. However, this method can fail to provide adequate
definition of the coil phases in many instances, resulting
in suboptimal image quality and/or severe phase cancel-
lation artifacts. For this reason, in previous AUTO-
SMASH studies (e.g. Ref. 3), great care was taken to ensure
that the phases of the coils were phase-aligned prior to
reconstruction.
An additional problem of these previous approaches is
the potential of a poor fit of the measured lines to the ACS
lines, due to the nonoptimal coil sensitivities that are
encountered in practice. When this occurs, image artifacts
can result for particular coil-slice orientations. While in-
corporating the ACS lines into the final image, as in VD-
AUTO-SMASH, improves the situation, residual artifact
can still be a problem with certain coil geometries.
GeneRalized Autocalibrating Partially Parallel Acquisitions
(GRAPPA)
GRAPPA can be seen at its most basic level as a more
generalized implementation of the VD-AUTO-SMASH ap-
proach (12,15,17–19). In GRAPPA, uncombined images
are generated for each coil in the array by applying multi-
ple blockwise reconstructions to generate the missing lines
for each coil. This process is shown in Fig. 2. Again, data
acquired in each coil of the array (black circles) are fitto
the ACS line (gray circles). However, as can be seen, data
from multiple lines from all coils are used to fitanACS
line in a single coil, in this case an ACS line from coil
4. This fit gives the weights which can then be used to
generate the missing lines from that coil. Once all of the
lines are reconstructed for a particular coil, a Fourier trans-
form can be used to generate the uncombined image for
that coil. Once this process is repeated for each coil of the
array, the full set of uncombined images can be obtained,
which can then be combined using a normal sum of
squares reconstruction.
In general, the process of reconstructing data in coil j at
a line (k
y
⫺ m⌬k
y
) offset from the normally acquired data
using a blockwise reconstruction can be represented by:
FIG. 1. The basic reconstruction although for both AUTO-SMASH
and VD-AUTO-SMASH. Each circle represents a line of acquired
data in a single coil. The read-out direction is left to right. In both
methods a single line of data acquired in each coil in the array is fit
to an ACS line in the composite image. In VD-AUTO-SMASH this
process is repeated several times and the results averaged together
to form the final reconstruction weights.
GRAPPA 1203
S
j
共k
y
⫺ m⌬k
y
兲 ⫽
冘
l⫽1
L
冘
b⫽0
N
b
⫺1
n共j, b, l, m兲S
l
共k
y
⫺ bA⌬k
y
兲 [2]
where A represents the acceleration factor. N
b
is the num
-
ber of blocks used in the reconstruction, where a block is
defined as a single acquired line and A ⫺ 1 missing lines
(see Fig. 2, right side). In this case, n(j,b,l,m) represents the
weights used in this now expanded linear combination. In
this linear combination, the index l counts through the
individual coils, while the index b counts through the
individual reconstruction blocks. This process is repeated
for each coil in the array, resulting in L uncombined single
coil images which can then be combined using a conven-
tional sum of squares reconstruction (1) or any other opti-
mal array combination (21).
The use of more than one block in Eq. [2] extends the
types of coil arrays and imaging planes which can be used
with GRAPPA compared to previous reconstructions. The
underlying assumption in AUTO-SMASH-type (and
SMASH-type) reconstructions was that a perfect spatial
harmonic could be generated using only the pure spatial
sensitivity profiles of the coils. While this is achievable
using special array geometries (22), it is not true in general,
resulting in lower-quality reconstructions. By using more
blocks of data to fit each missing line, GRAPPA incorpo-
rates more information into each reconstructed line, re-
sulting in a substantially improved fit.
Using all acquired blocks for the reconstruction would
result in an exact, SENSE-like reconstruction of a single
coil data matrix in the absence of noise (12,17–19). How-
ever, in most cases the combination in Eq. [2] can be
significantly truncated to only a few blocks of lines since,
in general, only lines close to each missing line contribute
significant information, resulting in a small number of
significant terms in Eq. [2]. For example, Sodickson (12)
showed reasonable results using around seven blocks in an
extended SMASH-like reconstruction.
In our experience, we have found that reconstructions
using various numbers of blocks from four to eight result
in essentially the same reconstruction quality. This trun-
cation of the number of terms results in a more stable
reconstruction in the presence of noise compared to an
exact reconstruction using all acquired blocks in each
reconstruction. Additionally, a truncated linear combina-
tion offers a more computationally efficient, yet still high
quality, reconstruction, as shown below.
In order to perform the reconstruction in Eq. [2], one
needs to determine the weights used in the reconstruction.
As in VD-AUTO-SMASH, a block of extra ACS lines is
acquired in the center of k-space and used to determine
these complex weights n(j,b,l,m) by using several fits of the
form of Eq. [2]. As in VD-AUTO-SMASH, these extra ac-
quired lines can be included in the final image reconstruc-
tion to further improve image quality (15).
The blockwise reconstruction given above has been im-
plemented using a sliding block approach. This uses the
fact that each unacquired line can be reconstructed in
several different ways in a blockwise reconstruction, in-
stead of the only one combination possible in a strictly
VD-AUTO-SMASH acquisition. For example, when using
four blocks for the reconstruction (i.e., four acquired lines
used to reconstruct each missing line), there are four pos-
sible reconstructions for each unacquired line, two of
which are shown in Fig. 3. In GRAPPA, each possible
reconstruction is performed for each unacquired line, re-
sulting in multiple possible reconstructions for each line.
These lines are then combined in a weighted average to
form the final reconstructed line, providing a robust recon-
FIG. 2. The basic GRAPPA algorithm is shown schematically. In
GRAPPA, more than one line acquired in each of the coils in the
array are fit to an ACS line acquired in a single coil of the array. In
this case, four acquired lines are used to fit a single ACS line in coil
#4. In GRAPPA, a block is defined as a single acquired line plus the
missing lines adjacent to that line, as shown on the right for an
acceleration factor of two.
FIG. 3. In a sliding block reconstruction,
more than one reconstruction is possible
for each missing line. Two of the four pos-
sible reconstructions for this missing line
are shown.
1204 Griswold et al.
struction of each missing line. For perspective, it should
be noted that this sliding block reconstruction is essen-
tially reduced to the VD-AUTO-SMASH approach when-
ever the number of blocks is reduced to one.
The sliding block approach introduces the problem of
how to combine or optimally choose from the different
reconstructions. In the images shown throughout this ar-
ticle, a weighted average is used to obtain the final recon-
struction. Several different possibilities for performing
this weighted average of the different sliding block recon-
structions were tested, including the goodness of fit for a
particular reconstructed line and the SNR resulting from
the reconstruction of the line, given by the normalization
of the weights used for each particular reconstruction (4).
While both of these criteria work in practice, the latter is
preferred and used throughout this study, since in most
cases where the SNR is poor for a given line the fit is also
typically poor. Therefore, this method of weighting gives a
reconstruction which attempts to produce both high SNR
and low artifacts and has been shown to provide good
results.
As demonstrated in the rest of this study, this process
essentially removes the previous limitations on k-space-
based techniques, namely the low SNR, phase cancellation
problems, and poor reconstruction quality. Since the final
image combination in GRAPPA is performed using a mag-
nitude reconstruction, any phase-related issues are essen-
tially eliminated. No phasing information is required.
Since the GRAPPA reconstruction uses a sum of squares
reconstruction, the SNR efficiency of GRAPPA approaches
the SNR efficiency of a sum of squares reconstruction,
which can be up to
公
L
higher compared to previous
implementations.
Finally, as has been shown previously by others (12,17–
19), an approach using an extended blockwise reconstruc-
tion can lead to dramatic reductions in image artifact
power compared to previous implementations. An addi-
tional benefit of the autocalibrating process used in
GRAPPA is that, besides using the ACS lines to determine
the coil-weighting factors, these extra lines can be inte-
grated directly into the final image reconstructions to im-
prove image quality, as in VD-AUTO-SMASH. As sug-
gested by the previous studies on VD-AUTO-SMASH, it is
anticipated that the use of the maximum acceleration pos-
sible in the outer parts of k-space is the most beneficial,
since it results in the highest number of lines in the center
of k-space for the same number of acquired lines. It has
been shown that this strategy results in both a better de-
termination of the coil-weighting factors in the presence of
noise and a more robust reconstruction in the presence of
imperfect coil performance (15).
MATERIALS AND METHODS
The GRAPPA reconstruction algorithm as described in the
previous section was implemented in the Matlab program-
ming environment (MathWorks, Natick, MA). As imple-
mented, the user is free to decide the number of blocks to
use in each reconstruction. As mentioned above, in our
experience the numbers of blocks in the range of four to
eight showed similar good results. Therefore, four blocks
were used in each reconstruction for simplicity and to
minimize computational complexity of each reconstruc-
tion; however, as mentioned above, images with more
blocks showed essentially the same image quality.
Computer Simulations
Computer simulations were performed to establish the
SNR performance of GRAPPA at different acceleration fac-
tors for a typical imaging array. To this end, the four-
element linear array found in Ref. 22 was simulated using
an analytic integration of the Biot-Savart equation. These
coil sensitivities were then used with an image from a
standard resolution phantom to generate several datasets
with reduced encoding to determine the SNR performance
of the GRAPPA technique at various acceleration factors.
These calculations were performed for both the VD-AUTO-
SMASH reconstruction which results in a complex sum
reconstruction and a GRAPPA reconstruction using a sum
of squares reconstruction to demonstrate the benefits of the
uncombined-coil approach. SNR was estimated using mul-
tiple reconstructions of a phantom image each with differ-
ent additive noise. The SNR on a pixel-by-pixel basis can
then be calculated as the mean of the signal at each pixel
divided by the standard deviation at that pixel over the
various reconstructed images.
In Vivo Imaging
Several different imaging studies were performed on
healthy volunteers to assess the clinical application of the
GRAPPA technique. Informed consent was obtained be-
fore each study. Volunteers were scanned using a 1.5T
Siemens Quantum Symphony scanner (maximum gradient
strength: 30 mT/m, slew rate: 125 T/m/s) equipped with
eight receiver channels using either the standard four-
element body array or a prototype eight-element cardiac
array (Siemens Medical Systems, Erlangen, Germany).
This prototype array consists of eight rectangular coils
(200 ⫻ 120 mm) overlapped to null the mutual inductance
between neighboring elements, resulting in a total width
in the left–right direction of 444 mm. Four elements are
contained in a rigid frame which is placed on the scanner
bed, while the upper four elements are flexible and were
bent to fit each volunteer individually.
As an example of the improvement that can be obtained
using GRAPPA for conventional imaging, a 3D axial gra-
dient echo acquisition (FOV 300 ⫻ 400 mm, matrix 127 ⫻
256, TR 6.7 ms, TE 3.2 ms, flip angle 12°, 44 partitions each
4 mm thick) was used in combination with the standard
four-channel body array. For this acquisition, only a full
dataset was acquired and later decimated off-line by a
factor of two to simulate a reduced acquisition. This data-
set was then reconstructed using both the PILS reconstruc-
tion (14) and the GRAPPA reconstruction for comparison
of image quality. For the coil position information in PILS,
a reference line derived from a projection through the body
was used. For the GRAPPA reconstruction, 16 lines were
used to solve for the reconstruction parameters, although
none of these extra reference lines were used to simulate
variable density sampling in the final image.
As a further example, a segmented TrueFISP sequence
was used for cardiac cine imaging on a healthy volunteer
in combination with the eight-element prototype array.
GRAPPA 1205
The sequence parameters were TR ⫽ 3.64 ms, TE ⫽
1.82 ms, 15 lines/segment, FOV ⫽ 276 ⫻ 340 mm, matrix
210 ⫻ 256, slice thickness ⫽ 6 mm, flip angle ⫽ 70°. Using
the GRAPPA approach with an acceleration factor of two,
18 phases could be acquired over nine heartbeats. In this
case, eight additional ACS lines were acquired during the
first phase of the cardiac cycle and the weights calculated
from these lines were used for all other phases. This se-
quence was repeated in another volunteer and was recon-
structed with both the AUTO-SMASH and VD-AUTO-
SMASH techniques to demonstrate the benefits of
GRAPPA over the previous techniques.
Besides traditional anatomical imaging, we investigated
the performance of GRAPPA in single-shot acquisitions.
Unlike multishot experiments, these techniques are af-
fected by spin relaxation and evolution over the entire
course of an acquisition. In these cases, PPA techniques
have previously been shown to improve image resolution
in all single-shot imaging sequences and to decrease image
distortions in EPI (23).
However, in single-shot imaging situations, a variable
density sampling approach cannot be used, since fully
sampling lines in the center of k-space would result in a
decrease in image quality. Therefore, in all single-shot
experiments, a separate acquisition of ACS lines was ap-
plied before the acquisition of the reduced encoded image
data. These lines were then only used for determination of
the coil-weighting factors and then discarded.
To study the benefits of combining GRAPPA with single-
shot imaging in the abdomen and chest, several sequences
were used. A multislice HASTE was used to image both
the liver and kidneys using the prototype cardiac array. An
inversion recovery HASTE was used to image the lung,
also with the cardiac array. The sequence parameters used
in each of these acquisitions is given in their respective
figures.
RESULTS
Computer Simulations
The results of the computer simulations are shown in Fig.
4 and Table 1. As can be seen, the GRAPPA reconstruction
using the sum of squares reconstruction results in higher
SNR than the VD-AUTO-SMASH complex sum approach
at all accelerations tested. For this particular coil arrange-
ment and slice orientation, the GRAPPA approach with
the sum of squares reconstruction achieves nearly perfect
SNR efficiency at the acceleration factors tested. It should
also be noted that in the limit where all lines are acquired,
GRAPPA approaches the sum of squares reconstruction, so
that nearly no loss in performance should be expected,
especially for low acceleration factors.
In Vivo Imaging
Figure 5 shows a comparison between the GRAPPA recon-
struction and the PILS reconstruction using the same basic
FIG. 4. SNR vs. acceleration factor
for GRAPPA with uncombined coil
reconstruction, VD-AUTO-SMASH
reconstruction, and a PILS recon-
struction. GRAPPA has substantially
higher SNR than the VD-AUTO-
SMASH reconstruction, in particular
at lower accelerations.
Table 1
SNR vs. Acceleration Factor for GRAPPA and VD-AUTO-SMASH
SNR 1X 2X 3X 4X
Relative SNR GRAPPA 1.000 0.706 0.522 0.443
Relative SNR/Time GRAPPA 1.000 0.999 0.905 0.887
Relative SNR—
VD-AUTO-SMASH 0.660 0.654 0.480 0.448
Relative SNR/Time—
VD-AUTO-SMASH 0.660 0.926 0.832 0.896
1206 Griswold et al.
