Combination Compress Sensing and Digital Wireless Transmission for the MRI signal Tan Due Tran , Tuyen Ta Due, and Tung Thanh Bui IMEMS and Microsystems Department, UET-VNU Hanoi, VIETN
Trang 1Combination Compress Sensing and Digital Wireless Transmission for the MRI
signal
Tan Due Tran , Tuyen Ta Due, and Tung Thanh Bui
IMEMS and Microsystems Department, UET-VNU Hanoi, VIETNAM 2Research Organization for Science and Engineering, Ritsumeikan University, JAPAN
XuanThuy Street, Hanoi, +844
Vietnam
Abstract:
Rapid image acquisition in magnetic resonance imaging
(MRI) offers a number of potential benefits, such as
avoiding physiological effects or scanning time on
patients, overcoming physical constraints inherent
within the MRI scanner, or meeting timing requirements
when imaging dynamic structures and processes In this
paper, the combination of compressed sensing and
parallel magnetic resonance imaging techniques was
proposed in order to increase the data acquisition speed
of MRI However, each coil arrangement is connected to
the reception circuit via a coaxial cable which leads to
several limitations To reduce this disadvantage, we also
propose a design of digital wireless transmission system
based on 802.11b standard for MRI application
1 INTRODUCTION
Magnetic resonance imaging (MRI), an imaging technique,
is widely used in medical diagnosis in order to acquire
images of the inside of the human body Previously,
techniques for rapid imaging include parallel MRI (PMRl) in
which the simultaneous use of multiple coils is deployed
Two typical parallel imaging techniques are simultaneous
acquisition of spatial harmonics (SMASH) and sensitivity
encoding (SENSE) [1, 2] In pMRI, a coaxial cable is need
for connecting each coil to the corresponding received
circuit The number of the cables and so on the required
connectors is need as high as possible but limited due to
constraint space and cross-talk among these coils Wireless
transmission can be a good candidate to replace cable
connections of the coil arrays to reduce these disadvantages
Recently, compressed sensing (CS) is a breakthrough
research field, which finds ways to sample signals at much
lower rate than the Nyquist one The condition is that the
sensing signal is sparse in some domain of representation
(Fourier transforms, for example) However, most of
developments in CS are based on the use of a single
channel/coil
In this paper, we combined compress sensing and digital
wireless transmission for the rapid MRI The organization of
this paper is as follows Section II describes operation
principle of our proposed wireless multi-channel compressed
sensing for MRI based on two conventional methods:
compressed sensing, parallel imaging, and digital wireless
transmission Section III presents our simulation results
Conclusions are drawn in the last section
2 OPERATION PRINCIPLES 2.1 Compressed sensing
Compressed sensing (CS) is a type of random under-sampling which allows for rapid acquisition of spare
or compressible signals, at a frequency significantly lower than the usual Nyquist frequency [3] To consider a I x N discrete time signal x and assume that x is a k-space in the N-dimensional space:
where 'P is N x N sparsitying matrix, s is the N x I transform vector containing K non-zero coefficients, K «
N When used in MRI, 'P is a Fourier matrix
In CS, x is linearly acquired by under-determined system which is represented by a measurement matrix <1>
y= <1>x (2) where y is M - dimensional measurement vector obtained incomplete measurements (M<N)
The reconstruction can be done using various spare approximation techniques such as II-optimization based Basic Pursuit or Orthogonal Matching Pursuit (aMP) [4] The condition of aMP is that the matrix <1> is coherence with 'P This condition is met by having <1> as a random matrix with Gaussian i.i.d elements
Fig I illustrates a MRI acquisition with a single coil in which Cartesian sampling is applied in k-space Note that the reconstruction can be easy performed by utilizing the inverse fast Fourier transform (IFFT)
ky
I
kx
Figure I Cartesian trajectory (a) and MRI undersampling in k-space [5] 2.2 Parallel Imaging
To receiver the MRI data, several array coils are used concurrently (Fig 2) Consequently, each coil would have
Trang 2individual values of image's intensity The k-space signal
obtained from the l-th coil:
xY
Where:
p(x,y) is the image function to be recover
Clx,y) is the sensitivity function for the l-th coil
(x,y) are spatial domain coordinate
(kx, ky) are samples in k-space
Figure 2 Illustration of using multi-coils for pMRl [5)
It's certain that Equ (3) is the Fourier transform of the
sensitivity-weighed images: C](x,y) p(x,y) The sensitivity
functions Clx,y) are often not known and the l-th image S]
could be expressed as the ideal image modulated by
sensitivity functions as:
In pMRI, only a smaller of data is acquired to reduce the
acquisition time The number of excitations, consequently,
the number of phase-encoding steps determine for the total
acquisition time By skipping phase-encoding steps, the
sensed size of the imaged area is also reduced The spatial
resolution is not change but the aliasing artifact is appeared
The pMRI reconstruction algorithm has a role to estimate the
coil sensitivities C] then use these coil sensitivities to remove
the aliasing and reconstruct the ideal image The quality of
the reconstruction can be expressed as the absolute
difference between the reconstructed image and the ideal
image
There are two very basic methods for parallel MRI
reconstruction: Sensitivity encoding for fast MRI (SENSE)
[1] and Simultaneous acquisition of spatial harmonics
(SMASH) [2]
SENSE works in the image domain that using the un-aliasing
method to the reduce field of view (FOY) images In this
method, the inversion of the aliasing transformation for each pixel is calculated individually The important process is that estimation of the map of the coil sensitivities:
It can be seen that we have a calibration procedure with the reference images (without aliasing artifact and noise) In practice, we can smooth and extrapolate the coil sensitivities
to obtain a acceptable sensitivity map However, it is obvious that this map can only be estimated by using no-aliasing reference images
However, the SENSE can work only in a Cartesian grid but not in arbitrary sequence An effective method which is able
to overcome this problem is called conjugate gradient SENSE (CG-SENSE) [6] However, the CG-SENSE also requires the information of the sensitivity map In present, the SENSE method is modified in order to work in auto-calibration mode One of these versions is mSENSE [7] In CG-SENSE, MRI reconstruction from the k-space samples is performed by Nonlinear Conjugate Gradient (NCG) [8]
2.3 Digital Wireless Transmission
In this paper, the system schematic of digital wireless transmission for MRI signal is shown in Fig 3 The budget for transmission is calculated based on the MR image pixel size 128 x 128 x number of coils, accommodate framing, overhead, and checksum, etc Therefore, the 801.11 b standard is chosen due to its capable to provide the bit rate requirement at 11 Mbps
MRI signal
�
Channel
Figure 3 The system model of a single coil
For MRI application, high bit error rate (BER) performance
in communication is also required Fig 4 is the simulated result of BER performance versus signal to noise ratio (SNR)
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Figure 4 BER peformance of the 801.11b standard communication
2.4 Proposed System Descriptions
Our scheme can be summarized as following steps:
• Generate (kx, ky) that are Gaussian random sequences
The number of (kx, ky) based on pre-defined
compression ratio r = MIN For each channel, determine
coordinates in k-space based on (kx, ky) and store as a
mask
• For each channel, under-sample and acquire digital data
in k-space based on the mask and store them in a vector
y
• Synthesis and send the processed data to wireless
transmitter
• Receive the data at the computer
• Estimate sensitivity maps using polynomial fitting
• Perform SENSE reconstruction using conjugated
gradient method
3 RESULTS AND PERFORMANCE
The data source utilizing in this work is human MPRAGE
from [9] The BER condition of 10-9 is set in communication
setting The original image from 8 coils was shown in Fig 5
Figure 5 The original image from 8 channels
Fig 6 shows the k-space under-sampling points in this
scenario
Figure 6 The k-space sampling point (white points) for the compression
ratio r=0.2
Using the zero padding, the combined analysed images were displayed in Fig 7
Figure 7 The combined aliased image from 8 channels for the
compression ratio r=0.2
The image in Fig 8 was obtained by CG-SENSE reconstructing method The result can be also compared to the desired result (Fig 9) We can obtain this best reconstructed image by using the sampled ratio of 1.0
Figure 8 The SENSE reconstructed image for the compression ratio r=0.2
Trang 41.8
1.6
1.4
Figure 9 The reconstructed image with full-sampling, r=1.0
For each compression ratio, the error in the reconstructed
image as compared to the original image Suppose that I is a
NxM original image and] is the reconstructed image The
error between them can be defined by:
1 N M I � I
Fig 10 shows the reconstructed performance obtained by
Monte-Carlo method
0.12
0.1
w
(IJ 0.08
�
0.06
0 04
ratio
Figure 10 Reconstructed performance by random approach
4 CONCLUSION
We have successful in combining the random based
compressed sensing, parallel MRI, and digital wireless
transmission in order to improve the scanning time for MR
image acquisition The simulation on phantom image shows
that the system can be brought to practice economic system
ACKNOWLEDGMENT
This work is partly supported from the College of Technology, Vietnam National University, Hanoi
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