Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
1998-09-18
2001-03-27
Oda, Christine K. (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S307000
Reexamination Certificate
active
06208139
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates generally to magnetic resonance imaging (MRI), and more particularly to system and method of phase sensitive MRI reconstruction using partial k-space data to minimize data acquisition time (TE) while preserving phase information and reducing edge blurring in the reconstructed image.
In MR imaging, the scan time can be reduced by using a partial NEX, or alternatively, the echo time can be reduced by using a fractional echo. This moves the time to the echo peak closer to the start of the read-out gradient waveform than in a full echo. However, in all partial echo or half-Fourier reconstruction strategies, all phase information is lost. The present invention is a method and system for using the homodyne reconstruction algorithm to generate a complex-valued image from which phase information can be extracted.
In general, the synthesis of the missing k-space data assumes that the MR data is Hermitian for a real-valued image. That is:
F
(−
k
x
)=*(
k
x
) [1]
where the * denotes a complex conjugate. If the k-space is divided into 4 quadrants, the data for at least two of the four quadrants is needed in order to generate an image. Therefore, either a partial echo (partially filled k
x
) or partial NEX (partially filled k
y
) can be used, but not both.
The following background is a review of the prior art homodyne method. If ƒ(x) is the real-valued image and &phgr;(r) is the spatially varying phase in the image, the expression for the complex valued image can be written as:
I
(
x
)=ƒ(
x
)exp(
j
&phgr;(
x
))=ƒ
L
(
x
)exp(
j
&phgr;
L
(
x
))+ƒ
H
(
x
)exp(
j
&phgr;
H
(
x
)). [2]
This expression is a linear combination of the Fourier transforms of the low-pass and high-pass filtered k-space data, respectively. In homodyne reconstruction, the phase is assumed to be slowly varying and that &phgr;
L
(x)≈&phgr;
H
(x). Therefore, if only one-half of the high-pass filtered data is available, this is equivalent to multiplying the high-pass filtered data by a Heaviside function such that the resulting image is given by:
I
H
(
x
)
=
f
L
(
x
)
exp
(
j
φ
L
(
x
)
)
+
f
H
(
x
)
exp
(
j
φ
L
(
x
)
)
⊗
1
2
(
δ
(
x
)
+
1
j
π
x
)
,
[
3
]
where
denotes a convolution. Since the convolution term decays with 1/x and that the phase is slowly varying, Eqn. [3] can be rewritten as:
I
H
(
x
)
≈
(
f
L
(
x
)
+
1
2
f
H
(
x
)
-
j
2
f
H
(
x
)
⊗
1
π
x
)
exp
(
j
φ
L
(
x
)
)
.
[
4
]
If the available high frequency data is weighted by 2, Eqn. [4] can be written as:
I
H
(
x
)
=
(
f
L
(
x
)
+
f
H
(
x
)
-
j
f
H
(
x
)
⊗
1
π
x
)
exp
(
j
φ
L
(
x
)
)
.
[
5
]
If the spatially varying phase term is divided out, the image is then the real-valued part of I
H
(x)exp(−j&phgr;
L
(x)), i.e.:
ƒ
L
(
x
)+ƒ
H
(
x
)=ƒ(
x
)=
Re
(I
H
(
x
)exp(−
j
&phgr;
L
(
x
))), [6]
where the spatially varying phase is estimated from the phase of the Fourier transform of the low-pass filtered data. It is noted that in Eqn. [6], all phase information has now been lost. Note that Eqn. [6] could easily be written as ƒ(x)=Re(I
H
(x))e
−j&phgr;
L
(x)
where the phase in the image is the low spatial frequency phase. However, this phase is only an estimate and is of little use. Hence, this technique is not suitable for phase contrast reconstruction. Furthermore, the loss of phase information requires that the Fourier transform in the y direction be performed first, before the homodyne reconstruction is applied to the data in the x direction.
It would therefore be desirable to have a system and method capable of preserving magnitude and phase information in a partially acquired k-space data set that allows reduced data acquisition times and significantly improves edge blurring in the reconstructed MR image.
SUMMARY OF THE INVENTION
The present invention provides a system and method of phase sensitive FIRS reconstruction using partial k-space data that overcomes the aforementioned problems.
The present invention describes a technique by which a phase sensitive reconstruction can be performed on either half-echo or half-NEX MR data. This allows an image with higher spatial resolution (reduced edge blurring) to be acquired in a much shorter period of time and yet preserve the image phase information. This method builds on the prior art homodyne reconstruction process to estimate and correct for the edge blurring in partial echo or partial NEX data that is usually reconstructed using zero-filling to preserve phase information. Zero-filling alone results in some image degradation as the asymmetrical echo data is not corrected prior to image reconstruction, forcing a much higher partial echo or partial NEX fraction to be used in order to restore the loss in image fidelity.
In accordance with one aspect of the invention, a method of phase sensitive magnetic resonance image (MRI) reconstruction using partial k-space data is disclosed having the steps of acquiring a partial k-space data set having both imaginary and real components representative of both magnitude and phase information, filtering the partial k-space data set through high and low-pass filters, and Fourier transforming the filtered data set. The method next includes the step of estimating a blurring correction term representative of a convolution error factor from a portion of the filtered data set and applying the blurring correction factor to the filtered data set to remove the convolution term and reconstruct an MIR having both magnitude and phase information while minimizing edge blurring in the reconstructed MRI.
In accordance with another aspect of the invention, the above described steps are accomplished in a system to correct edge blurring in an image reconstructed with partial k-space data. The system includes a magnetic resonance imaging system having a number of gradient coils positioned about a bore of a magnet to impress a polarizing magnetic field and an RF receiver system and an RF modulator controlled by a pulse control module to transmit RF signals to an RF coil assembly to acquire MR images. The system includes a computer programmed to acquire only a partial k-space data set having both magnitude and phase information. The program also filters the partial k-space data set through high and low-pass filters and Fourier transforms the filtered data set. Next, a blurring correction factor is estimated from a portion of the filtered data set and applied to the filtered data set to remove a convolution error term and reconstruct an MRI having both magnitude and phase information thereby minimizing data acquisition time and edge blurring in the reconstructed MRI.
In accordance with another aspect of the invention, a system for minimizing edge blurring in a reconstructed MRI using partial k-space data is comprised of a means for acquiring partial k-space data containing both magnitude and phase components, a means for partially calculating a homodyne reconstructed MRI, and a means for retaining the phase components in the partially calculated homodyne reconstructed MRI. The system further includes a means for removing a blurring error term from the partially calculated homodyne reconstructed MRI having both the phase component and a magnitude component therein with reduced MRI edge blurring.
Various other features, objects and advantages of the present invention will be made apparent from the following detailed description and the drawings.
REFERENCES:
patent: 5243284 (1993-09-01), Noll
patent: 5602934 (1997-02-01), Li et al.
patent: 5729140 (1998-03-01), Kruger
Foo Thomas K. F.
Polzin Jason A.
Boyle Fredrickson
Cabou Christian G.
Fetzner Tiffany A.
General Electric Company
Oda Christine K.
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