CS++: Compressed Sensing & Beyond 
Tuesday 21 April 2009 
Room 313BC 
16:0018:00 
Moderators: 
Pablo Irarrazaval and Krishna S. Nayak 



16:00 
377. 
Accelerating SENSE Using
Distributed Compressed Sensing 


Dong Liang^{1},
Kevin f. King^{2}, Bo Liu^{3},
Leslie Ying^{1
1}Dept. of Electrical Engineering and Computer
Science, Univ. of WisconsinMilwaukee, Milwaukee,
WI, USA; ^{2}Global Applied Science Lab, GE
Healthcare, Waukesha, WI, USA; ^{3}MR
Engineering, GE Healthcare, Waukesha, WI, USA 


Most existing methods
apply compressed sensing (CS) to parallel MRI as a
regularized SENSE reconstruction, where the
regularization function is the L1 norm of the sparse
representation. However, the CS conditions such as
incoherence are not necessarily satisfied. To
address the issue, a method is proposed which first
reconstructs a set of aliased images from all
channels simultaneously using distributed CS (DCS),
and then the final image using Cartesian SENSE. The
results on a set of eightchannel data show that the
proposed method is able to achieve a higher
reduction factor than the existing methods. 



16:12 
378. 
Distributed Compressed Sensing
for Accelerated MRI 


Ricardo Otazo^{1},
Daniel K. Sodickson^{1
1}Center for Biomedical Imaging, NYU School of
Medicine, New York, NY, USA 


A framework for
combining parallel imaging with compressed sensing
is presented using the theory of distributed
compressed sensing which extends compressed sensing
to multiple sensors using the principle of joint
sparsity. We present a greedy reconstruction
algorithm named JOMP (Joint Orthogonal Matching
Pursuit) that uses intra and intercoil
correlations to jointly sparsify the multicoil
image instead of sparsifying the individual images.
We show that for a sufficient number of coils, the
number of measurements required by JOMPPMRI to
reconstruct a truly sparse image is very close to
the image sparsity level. The performance of
JOMPPMRI with compressible images is assessed with
a simulated brain image to show feasibility of
higher accelerations with increasing number of
coils. 



16:24 
379. 
L_{1} SPIRIT:
Autocalibrating Parallel Imaging Compressed Sensing 


Michael Lustig^{1},
Marcus Alley^{2}, Shreyas Vasanawala^{2},
David L. Donoho^{3}, John Mark Pauly^{1
1}Electrical Engineering, Stanford University,
Stanford, CA, USA; ^{2}Radiology, Stanford
University; ^{3}Statistics, Stanford
University 


A detailed approach of
combining autocalibrating parallel imaging (acPI)
with compressed sensing (CS) is presented. The
acquisition and the reconstruction are carefully
optimized to meet the requirements of both methods
in order to achieve highly accelerated robust
reconstructions. Poissondisc sampling distribution
is used to achieve the required incoherency for CS
and uniform density for acPI. A novel L1wavelet
penalized, iterative reconstruction (L1 SPIRiT) is
used to enforce consistency with the calibration and
data acquisition, and in addition, joint sparsity of
the reconstructed coil images. High quality in
vivo, 5fold accelerated reconstruction using
only 4 coils is demonstrated. 



16:36 
380. 
L1Norm Regularization of Coil
Sensitivities in NonLinear Parallel Imaging
Reconstruction 


Carlos
FernándezGranda^{1,2}, Julien Sénégas^{3
1}École des Mines, Paris, France; ^{2}Universidad
Politécnica de Madrid, Spain; ^{3}Philips
Research Europe, Hamburg, Germany 


Joint estimation of the
coil sensitivities and the image in parallel imaging
can suppress aliasing more effectively than methods
based on lowresolution sensitivity estimates. We
propose a joint estimation approach related to
Compressed Sensing that exploits the sparsity of the
coil sensitivities in kspace and in a base of
Chebyshev polynomials within a greedy scheme to
solve the illposed reconstruction problem. In
vivo data reconstructions are presented and
compared to results obtained with Generalized SENSE
and Joint SENSE. 



16:48 
381. 
SPArse Reconstruction Using a
ColLEction of Bases (SPARCLE) 


Ali Bilgin^{1,2},
Onur Guleryuz^{3}, Theodore P. Trouard^{2,4},
Maria I. Altbach^{2
1}Electrical and Computer Engineering,
University of Arizona, Tucson, AZ, USA; ^{2}Dept.
of Radiology, University of Arizona, Tucson, AZ,
USA; ^{3}Dept. of Electrical Engineering,
Polytechnic Institute of NYU, Brooklyn, NY, USA;
^{4}Biomedical Engineering, University of
Arizona, Tucson, AZ, USA 


We introduce a new
sparse reconstruction framework where sparsity is
enforced in a collection of bases rather than a
single one. Results indicate that this new framework
yields significantly improved reconstruction
quality. 



17:00 
382. 
UltraHigh Resolution 3D Upper
Airway MRI with Compressed Sensing and Parallel
Imaging 


YoonChul Kim^{1},
Shrikanth S. Narayanan^{1}, Krishna S. Nayak^{1
1}Ming Hsieh Department of Electrical
Engineering, University of Southern California, Los
Angeles, CA, USA 


Ultrahigh resolution 3D
imaging of the vocal tract can provide insight into
the shaping that occurs during complex speech
articulation. The combined use of compressed sensing
(CS) and parallel imaging is investigated to
maximize spatial resolution while maintaining
scantime appropriate for a single sound production
task (~7 seconds). Compared to conventional
reconstructions, boundary depiction was improved by
using highresolution phase constraints, sensitivity
encoding, and regularization based on total
variation and the l1norm of the wavelet transform.
Eightfold acceleration was achieved leading to
1.33x1.33x1.33 mm^{3} resolution and
7second scan time. 



17:12 
383. 
HighlyAccelerated FirstPass
Cardiac Perfusion MRI Using Compressed Sensing and
Parallel Imaging 


Ricardo Otazo^{1},
Daniel Kim^{1}, Daniel K. Sodickson^{1
1}Center for Biomedical Imaging, NYU School of
Medicine, New York, NY, USA 


Compressed sensing and
parallel imaging are combined into a single joint
reconstruction paradigm named kt ParallelSparse
for highly accelerated first pass cardiac perfusion
imaging. The method exploits the joint sparsity in
the sensitivityencoded images to achieve higher
accelerations than for coilbycoil sparsity alone,
and it does not require dynamic training data. We
demonstrate the feasibility of high in vivo
acceleration factors of 8 and 12 and assess the
effect of respiratory motion. 



17:24 
384. 
Motion Estimated and
Compensated Compressive Sensing Dynamic MRI Under
Field Inhomogeneity 


Hong Jung^{1},
Jaeseok Park^{2}, Jong Chul Ye^{3
1}KAIST, Daejon, Korea; ^{2}Yonsei
Univ. medical center, Korea; ^{3}KAIST,
Korea 


Recently, we proposed a
compressed sensing dynamic MR technique called kt
FOCUSS that extends the conventional kt BLAST/SNESE
by exploiting the sparsity of xf signal.
Especially, we found that when a fully sampled
reference frame is available more sophisticated
prediction methods such as RIGR and motion
estimation and compensation (ME/MC) can
significantly sparsify the residual and improve the
overall reconstruction quality. Among these, ME/MC
is especially useful since it can be used for
arbitrary trajectories such as radial and spiral.
However, our extensive experiments with noncartesian
trajectory have demonstrated that there exist
technical issues in applying the ME/MC to noncartesian
trajectory due to the field inhomogeneities. This
paper showed that if the ME/MC is done in magnitude
image domain and the lost phase is compensated from
the current frame estimate, the field inhomogeneity
problem can be significantly alleviated.
Furthermore, we showed that the introduction of
halfpel ME/MC and intra block mode within the
estimation loop can improve the overall
reconstruction quality of compressed sensing dynamic
MRI. 



17:36 
385. 
Fast Relaxation Parameter
Mapping from Undersampled Data 


Mariya Doneva^{1},
Christian Stehning^{2}, Peter Börnert^{2},
Holger Eggers^{2}, Alfred Mertins^{1
}University of Luebeck, Luebeck, Germany; ^{
2}Philips Research Europe, Hamburg, Germany 


The quantitative
assessment of MR parameters like T1, T2, ADC, etc.
requires the acquisition of multiple images of the
same anatomy, which results in long scan times.
However, these data can be described by a model with
only a few parameters and in that sense they are
highly compressible. Thus, Compressed Sensing (CS)
could be applied to accelerate the data acquisition.
In this work we introduce a modelbased
reconstruction from undersampled data, which
performs simultaneous image reconstruction and
parameter mapping and demonstrate it for the example
of T1 mapping. 



17:48 
386. 
Quality Index for Detecting Reconstruction Errors
Without Knowing the Signal in L_{0}Norm
Compressed Sensing 


Carlos A. SingLong^{1,2},
Cristian A. Tejos^{1,2}, Pablo Irarrazaval^{1,2
1}Departamento de Ingenieria Electrica,
Pontificia Universidad Catolica de Chile, Santiago,
R.M., Chile; ^{2}Biomedical Imaging Center,
Pontificia Universidad Catolica de Chile, Santiago,
R.M., Chile 


Compressed Sensing
allows reconstructing signals, if they are sparse in
some representation, from some of its Fourier
coefficients. The reconstruction conditions are
stated in terms of the support size of the signal.
Since it is generally unknown, it is impossible to
determine if there are reconstruction errors due to
high undersampling rates. Our work introduces a
modified fixedpoint solver for a continuous
approximation of the l_{0}norm and an index
which shows high correlation with the reconstruction
error. This index does not need any a priori
information and may be used to determine if the
undersampling rate needs to be reduced. 



