Transcript Undersampling

Fast imaging using an NMR device with a weak and non-homogeneous magnetic field
Miri Belgart, Dr. Uri Nevo
Dept. of Biomedical Engineering, Tel-Aviv University
Introduction
Method #2
Magnetic resonance is an imaging modality that does not involve patient irradiation or significant
side effects, while maintaining a high spatial resolution. However, the need for a strong and
homogeneous magnetic field causes limitations of size, cost and availability, so that the benefits of
MRI are not used to their full potential.
Open-coil systems such as the NMR-MOUSE (Fig. 1) were developed as a means of non-destructive
testing. Imaging with these systems is limited due to strong magnetic field inhomogeneity and low
field strength, which result in very long acquisition times.
Reconstruction
The objective of this project is to reduce the MOUSE’s acquisition time by at
least 50% without compromising image quality, using partial sampling of the
k-space and non-linear reconstruction of the image.
• The missing k-space data is not filled.
Instead, the image is changed until an optimal solution is reached:
The NMR-MOUSE
• Lustig et al. offered performing the CS image reconstruction using a nonlinear conjugate gradient method.
This requires solving the following optimization problem:
ψ –
m –
Fu –
y –
the sparsifying transform operator (wavelet, DCT…),
the reconstructed image,
the undersampled Fourier operator,
the measured k-space data
s.t. ||Fum – y||2 < ε
Promote image
sparsity
Maintain data
consistency
mk+1 = mk + tΔm (t = step size)
Results
Matlab simulation
30% undersampling
Method #1
minimize ||ψm||1
CS reconstruction at
various undersampling
rates
Compressed Sensing (CS)
• Natural images have a well-documented susceptibility to compression with little or no visual loss
of information (JPEG, MPEG…).
15%
30%
50%
• According to the CS approach, it is possible to acquire the compressed information directly from a
small number of samples
‘Undersampling’
The probability density function (pdf)
• Undersampling violates the Nyquist criterion  aliasing
• To avoid aliasing Lustig et al. (2007) proposed random undersampling
 incoherent artifacts that behave much like additive random noise.
Full sampling
Incoherent artifacts after
random k-space undersampling
• Random undersampling is performed by:
1. Building a probability density function:
1
pdf = (1 – r)p
RMS:
15.5
9.6
4.6
Random
Random
Non-random undersampling undersampling
Low resolution undersampling
+ 2D IFFT + CS reconstruction
Matlab simulation
30% undersampling
s.t. pdf (center) = 1
2. Generating a sampling pattern using the logical expression:
random[0,1] < pdf (m,n)
The pdf
The sampling pattern
Future work involves applying a sampling scheme that exploits the fact that samples in every scan are
averaged. The general concept is to fully sample the k-space in the first few scans, and then use these scans
to determine the significant spatial frequencies of the image and thus optimize undersampling.