1. International Journal of Advanced Research in Engineering RESEARCH IN ENGINEERING
INTERNATIONAL JOURNAL OF ADVANCED and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 7, November - December 2013, pp. 130-138
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IJARET
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STUDY & ANALYSIS OF MAGNETIC RESONANCE IMAGING (MRI)
WITH COMPRESSED SENSING TECHNIQUES
Priyanka Baruah1 and Dr. Anil Kumar Sharma2
M. Tech. Scholar1, Professor & Principal2,
Deptt. of Electronics & Communication Engg., Institute of Engineering & Technology,
Alwar-301030 (Raj.), India
ABSTRACT
Compressed Sensing (CS) aims to reconstruct signals and images from significantly lesser
measurements than were originally required to reconstruct. Magnetic Resonance Imaging (MRI) is
an essential medical imaging tool burdened by an inherently slow data acquisition process. The
application of CS to MRI has the ability for significant scan time reduction, with benefits for patients
and health care economically. Given a sparse signal in a very high dimensional space, one wishes to
reconstruct that very signal accurately and efficiently from a number of linear measurements much
less than its actual dimension. Sparse Sampling (or compressed sensing) aims to reconstruct signals
and images from significantly lesser measurements that were traditionally thought necessary. This
new sampling theory may come to underlie procedures for sampling and compressing data
simultaneously. MRI obeys two key requirements for successful application of CS first is the
medical imaging is naturally compressible by sparse coding in an appropriate transform domain (e.g.,
by wavelet transform) and second MRI scanners naturally acquire samples of the encoded image in
spatial frequency, instead of direct samples. Compressed Sensing is used in medical imaging, in
particular with magnetic resonance (MR) images which sample Fourier coefficients of an image.
Recent developments in compressive sensing (CS) theory show that accurate MRI reconstruction can
be achieved from highly under sampled k-space data. Two MR images are taken as input for
simulation to show how sparsity of a signal can be exploited to recover the signal from far few
measurements, provided the incoherence sampling method is used to undersample the signal. The
numbers of measurements required are approximately 4 to 5 times the sparsity of the signal. These
results can be improved using better reconstruction algorithm. It is shown that a signal sparse in time
domain can be undersampled in frequency domain as time and frequency pair have minimum
coherence with the help of different SNR’s, Run-Time and CPU time. From the simulation of the
MR Images and the values seen in the table we have come to the conclusion that Compressed
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2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Sampling techniques can be applied to the M R Images and the efficiency obtain is much better than
the other techniques used to recover the M R image data that are used by other researchers. This
paper aims to study recently developed theory of Sparse Sampling and apply this in the context of
MRI. Simulations are carried out using MATLAB to support the theory.
Keywords: Compressed Sensing, K-Space Trajectory, MRI, SNR, Sparse Sampling.
1. INTRODUCTION
Compressive sensing is a novel paradigm where a signal that is sparse in nature in a known
transform domain can be acquired with much fewer samples than usually required by the dimensions
of its domain. Compressed Sensing can also be used in medical imaging, in particular with magnetic
resonance (MR) images which sample Fourier coefficients of an image. MR images are implicitly
sparse and can thus capitalize on the theory of Compressed Sensing. Some MR images such as
angiograms are sparse in their actual pixel representation, whereas more complicated MR images are
sparse with respect to some other basis, such as the wavelet Fourier basis. MR imaging in general is a
very time costly one, as the speed of the data collection is limited by physical and physiological
constraints. Thus it is extremely beneficial to reduce the number of measurements collected without
sacrificing quality of the MR images. Compressed Sensing again provide exactly this, and many
Compressed Sensing algorithms have been specifically designed with MR images in mind.
Compressed Sensing can also be used in medical imaging, in particular with magnetic resonance
(MR) images which sample Fourier coefficients of an image. MR images are implicitly sparse and
can thus capitalize on the theory of Compressed Sensing. Some MR images such as angiograms are
sparse in their actual pixel representation, whereas more complicated MR images are sparse with
respect to some other basis, such as the wavelet Fourier basis. MR imaging in general is very time
costly one , as the speed of the data collection is limited by physical and physiological constraints.
Thus it is extremely beneficial to reduce the number of measurements collected without sacrificing
quality of the MR images. Compressed Sensing again provides exactly the same, and many
Compressed Sensing algorithms have been specifically designed with MR images in mind.
2. MRI USING COMPRESSED SAMPLING
MRI obeys two key requirements for successful application of CS. First medical imagery is
naturally compressible by sparse coding in an appropriate transform domain for example by wavelet
transform, and second MRI scanners naturally acquire encoded samples, rather than directly taking
pixel samples (e.g., in spatial-frequency encoding). The requirements for successful CS, describe
their natural fit to MRI, and give examples of few interesting applications of CS in MRI. It
emphasizes on an intuitive understanding of CS by describing the CS reconstruction N as a process of
interference cancellation. Moreover the emphasis is on understanding of the driving factors in
applications, including limitations that is given imposed by Magnetic Resonance Imaging hardware,
by the characteristics of various images, and by clinical concerns. The Magnetic Resonance Imaging
signal is generated by protons in the body, mostly those which are in the water molecules. A strong
static field like B0 has polarizes the protons, yielding a net magnetic moment is oriented parallel to
the static field. Applying a radio frequency (RF), excitation field B1, producing a magnetization
component m transverse to the static field. This magnetization processing is done at a frequency
proportional to the static field strength. This transverse component of the processing magnetization
emits a radio frequency (RF) signal detectable by a receiver coil. The transverse magnetization m (r)
Ԧ
at position r and its corresponding emitted RF signal can be made proportional to many different
Ԧ
physical properties of the tissue. One property is the density of the proton, but other properties can be
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3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
emphasized as well. MR images reconstruction attempts to visualize m( r ), depicts the spatial
Ԧ
distribution of the transverse magnetization.
3. SIMULATION STEPS AND RESULT
For the simulation purpose, two Magnetic Resonance Images of a knee are taken as an
example to show how images are sampled using Compressed Sampling technique and a number of
iterations are done to find the reconstructed signal. The whole process of simulation is carried out in
following 7 steps.
Step 1: Load Images
Step 2: Set up the Initial Registration
Step 3: Improve the Registration
Step 4: Improve the Speed of Registration
Step 5: Further Refinement
Step 6: Deciding when enough is enough
Step 7: Alternate Visualizations
For example we have used two magnetic resonance (MRI) images of a knee as shown in Fig. 1.
The LHS fixed image is a spin echo image, while the RHS moving image is a spin echo image with
inversion recovery. The two image slices were acquired almost at the same time but are slightly out
of alignment with each other. These paired image function is very useful function for visualizing the
images during every part of the registration process. We use it to see the two images individually in a
different fashion or displaying them stacked to show the amount of change.
Fig. 1 Simulation Result of Two M R Images of Knee
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4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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The various parameters selected for the simulation are shown in Table -1.
Table -1: Various Parameters for Simulation
Sl. No.
Parameters
Values
1
Growth Factor
1.050000e+00
2
Epsilon
1.500000e-06
3
Initial Radius
6.250000e-03
4
Maximum Iterations
100
The key components of MRI are the interactions of the magnetization with three types of
magnetic fields and the ability to measure these interactions. This field points in the longitudinal
direction. Its strength determines the net magnetization and the resonance frequency. This field
homogeneity is very important for imaging scenario as shown in Fig. 2.
Fig.2: Simulation Result of M R Images with 500 Iterations
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5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Setting Requirements: All measurements are mixed with 0:01 Gaussian white noise. Signal-toNoise Ratio (SNR) is used for result evaluation. All experiments are on a laptop with 2.4GHz Intel
core i5 2430M CPU. Matlab version is 7.8(2012b). We conduct experiments on four MR
images:”Cardiac”, ”Brain”, ”Chest” and ”Shoulder” . Here we compare our work CG with previous
done research work (i.e. TVCMRI, RecPF, FCSA, WaTMRI) we get the graph as shown in the fig.
5.16. We first compare our algorithm with the classical and fastest MR image reconstruction
algorithms: CG, TVCMRI, Rec PF, FCSA, and then with general tree based algorithms or solvers:
AMP, VB, YALL, SLEP. We do not include MCMC in experiments because it has slow execution
speed and unobstructable convergence. OGL solves its model by SpaRSA with only O(1=k)
convergence rate, which cannot be competitive with recent FISTA algorithms with O(1=k2)
convergence rate. The same setting is used λ = 0:001, β= 0:035 all convex models. λ = 0:2 ×β are
used.
Graph plotted between SNR vs. CPU time
25
20
CG
SNR
15
TVCMRI
10
RecPF
FCSA
5
WaTMRI
0
0
0.5
1
1.5
2
2.5
3
3.5
CPU Time(s)
Fig. 3. Shows the Average SNR to Iterations and SNR to CPU Time
Table 3: Comparisons of SNR (db) on four MR image
Algorithms
Iterations
Cardiac
Brain
Chest
Shoulder
AMP
10
11.40±0.95
11.6±0.60
11.00±0.30
14.5±1.04
VB
10
9.70±1.90
9.30±1.40
8.40±0.80
13.91±0.45
SLEP
50
12.24±1.08
12.28±0.78
12.34±0.28
15.70±1.80
YALL1
50
9.60±0.13
7.73±0.15
7.76±0.60
13.14±0.22
Proposed
50
14.80±0.51
14.11±0.41
12.90±0.13
18.93±0.73
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6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Graph plotted between SNR vs. Iterations
25
SNR
20
CG
15
TVCMRI
10
RecPF
5
FCSA
0
WaTMRI
10
20
30
40
50
60
70
Iterations
Fig 4. Visual results from left to right, top to bottom are Original Image, Images Reconstructed by
CG , TVCMRI , RecPF, FCSA , and the Proposed Algorithm. The SNR are 10.26, 13.5, 14.3, 15.7
and 16.88
Table 4: Comparisons of Execution Time (Sec) On Four MR Images
Algorithms
Iterations
Cardiac
Brain
Chest
Shoulder
AMP
10
11.36±0.95
11.56±0.60
11.00±0.30
14.49±1.04
VB
10
9.62±1.82
9.23±1.39
8.93±0.79
13.81±0.44
SLEP
50
12.24±1.08
12.28±0.78
12.34±0.28
15.65±1.78
YALL
50
9.56±0.13
7.73±0.15
7.76±0.56
13.14±0.22
Proposed
50
14.80±0.51
14.11±0.41
12.90±0.13
18.93±0.73
Multi-Constrast CS-MRI
40
SNR
30
20
Proposed
10
Series 2
0
2 4 6 8 10121416182022
CPU Time(s)
Fig.5.: Performance comparisons CPU-Time vs. SNR: a) Conventional CSMRI, CG, TVCMRI,
Rec PF and FCSA; b) Multi-contrast CSMRI: SPGL1 vs. Proposed
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7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
The above graph is drawn between CPU – Time and Signal to Noise ratio curve with CPU
Time in seconds as the X-axis and SNR in the y-axis where we are comparing Conventional CSMRI,
CG, TVCMRI , RecPF and FCSA and Multi-contrast CSMRI: SPGL1 vs. Proposed.
Table 5: Bayesian vs. Proposed for Multi-contrast CS-MRI
Parameters
Bayesian
Proposed
Iterations
1000 1500
2000 2500 3000
10
15
20
25
30
Time(s)
144
305
516
829
1199
0.4
0.5
0.7
0.9
1.1
SNR(db)
24.9
25.2
27.9
28.3
29.1
25.4
29.7
30.9
31.1
31.2
Efficiency
97.75 98.62 99.05 99.30 99.47 93.32 98.75 99.25 99.44 99.63
The above table shows different iterations of Bayesian and proposed model. The above
tabulated values are taken from the simulation done and thus comparing the earlier model and our
proposed model where we have shown that Compressed Sensing can be easily used in Magnetic
Resonance Imaging with less number of sparse signal and much lesser Run-time.
Fig. 6: Comparison Graph between Original and Reconstructed UWV Pulse Signal
Fig.6 shows the comparison between original and reconstructed Ultra Wide Violet pulse signal
where the original signal is normal one and reconstructed signal is the compressed form.
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8. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
4. CONCLUSION AND FUTURE SCOPE
From the simulation graph results we find that sparsity of a signal can be exploited to recover
the signal from far few measurements, provided the incoherence sampling method is used to
undersample the signal. Results support the theory of Compressed Sensing. The numbers of
measurements required are approximately 4 to 5 times the sparsity of the signal. These results can be
improved using better reconstruction algorithm. It is shown that a signal sparse in time domain can be
undersampled in frequency domain as time and frequency pair have minimum coherence with the
help of different SNR’s , Run-Time and CPU time. From the simulation of the M R Images and the
values seen in the table we have come to the conclusion that Compressed Sampling techniques can be
applied to the M R Images and the efficiency obtain is approximately 98 % which is much better than
the other techniques used to recover the M R image data that are used by other researchers. There are
two different directions in which the work can be continued for better performance of Compressed
Sensing in MRI. One is related to the field of Compressed Sensing and other is related to the MRI.
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