MRI image quality improvement using matrix regularization

Details MRI image quality improvement using matrix regularization MRI image quality improvement using matrix regularization

2001-05-14

2002-11-26

Arana, Louis (Department: 2862)

Electricity: measuring and testing

Particle precession resonance

Using a nuclear resonance spectrometer system

C324S309000

Reexamination Certificate

active

06486671

ABSTRACT:

CROSS-REFERENCE TO RELATED APPLICATIONS
Not applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
BACKGROUND OF THE INVENTION
The field of the invention is nuclear magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to systems and methods for increasing the signal to noise ratio in MRI images where image data has to be unwrapped during data processing.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B
0
), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B
1
) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M
z
, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M
t
. A signal is emitted by the excited spins after the excitation signal B
1
is terminated, this signal may be received by receiver coils and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G
x
G
y
and G
z
) are employed to select locations within the tissue for excitation. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which gradients G
x
G
y
and G
z
vary according to the particular localization method being used. Herein it will be assumed that gradient G
y
is used to adjust the phase of signals along a phase encoding axis Y. The resulting set of received nuclear magnetic resonance (NMR) signals are digitized and stored in a k-space raster format. An exemplary k-space raster
10
is illustrated in FIG.
2
and includes a plurality of rows
12
of data. After all of the k-space data has been acquired, the data is typically subjected to a two-dimensional Fourier transform and the resulting data is then used to reconstruct an image using one of several different reconstruction techniques. An exemplary resulting image
14
is also illustrated in FIG.
2
.
Thus, the intensity of each pixel in an MR image is generally a function of two factors. First, pixel signal intensity is a function of the spin density m at a point in an object slice being imaged that corresponds to the particular pixel in the image. Second, pixel signal intensity is also a function of the operating characteristics of the receiving coil that receives the NMR signal and converts the signal to an analog signal and then to a digital signal for storage in k-space. Specifically, the coil operating characteristic that affects the end pixel intensity the most is referred to as coil sensitivity s. Thus, intensity i for a pixel y can be expressed by the following Equation:
i
(
y
)=
s
(
y
)
m
(
Y
)  Equation 1
There are several different factors that can be used to judge the value of any imaging system but two of the most important factors are the quality of the resulting images and the speed with which imaging data can be acquired. Higher quality images increase diagnostic value. Acquisition speed increases system throughput (i.e., the number of imaging sessions that can be performed in a given period) and can also increase image quality as patient movement is reduced when the acquisition period is chortened (i.e., patient movement is less likely during a shorter period than during a longer period. With MRI systems, throughput is extremely important as MRI systems are relatively expensive and the expense is in part justified by the amount of use a system receives.
One way to increase system throughput is to reduce the amount of data collected during an imaging session. For example, one way to reduce the amount of collected data is to increase the space between phase encoding lines in k-space. Referring to
FIG. 3
, an exemplary k-space raster
20
having half as many k-space lines as the raster
10
of
FIG. 2
is illustrated. The time required to collect the data in raster
20
would be approximately half the time required to collect the data in raster
10
.
By reducing the number of phase encoding lines employed during data acquisition, the field of view (FOV) along the phase encoding axis Y of the resulting image is also reduced. Referring again to
FIG. 3
, the FOV for the image
15
in
FIG. 3
is shown as being approximately ½ the FOV in the image of
FIG. 2
along the phase encoding axis Y. Where the object being imaged fits within the reduced FOV, the reduced FOV does not affect the resulting image. Because reducing the k-space phase encoded lines reduces the FOV, the factor by which the k space phase encoding lines are reduced is referred to as the reduction factor R.
Unfortunately, where the object being imaged extends outside the reduced FOV, the image sections that correspond to the out-of-FOV object sections “wrap around” on the image and are overlaid on other image sections. Thus, in
FIG. 3
, out-of-FOV image sections
22
and
24
wrap around and are overlaid on in-FOV image section
25
thereby generating wrapped sections
28
and
26
, respectively. Each wrapped section (e.g.,
22
) includes pixel intensities that are the sum of two intensities corresponding to two different pixels in a non-wrapped image (i.e., in an image like that of FIG.
2
). The two intensities that combine to produce each wrapped pixel intensity include one intensity corresponding to an in-FOV pixel and one intensity corresponding to an out-of-FOV pixel. For example, referring to
FIGS. 2 and 3
, the FOV of
FIG. 3
is also illustrated in
FIG. 2
by the space between lines
36
and
38
and thus when the FOV is reduced as in
FIG. 3
, pixel
30
is an in-FOV pixel and pixel
40
is an out-of-FOV pixel. Thus the pixel intensity of pixel
40
wraps as indicated by arrow
41
and is laid over pixel
30
intensity. Together the intensities of pixels
30
and
40
add to generate the intensity of pixel
42
upon wrapping.
Where the reduction factor R is greater than 2 additional image wrapping can occur thereby causing wrapped image pixels to include intensity corresponding to more than two (e.g., 3, 4, etc.) unwrapped pixels. This additional wrapping further reduces the diagnostic value of the resulting image.
The industry has devised ways to effectively “unwrap” wrapped images like the exemplary image in FIG.
3
. It has been recognized that by providing several NMR signal receiving coils where the sensitivities of each coil are known, a permutation of Equation 1 above can be used to separate the intensity of a wrapped pixel into the in-FOV intensity and the out-of-FOV intensity. To this end, along a phase encoding axis the intensity of a wrapped pixel y corresponding to first and second receiver coils can be expressed as:
i
1
(
y
)=
s
1
(
y
)
m
(
y
) +
s
1
(
y+D
)
m
(
y+D
)  Equation 2
i
2
(
y
)=
s
2
(
y
)
m
(
y
) +
s
2
(
y+D
)
m
(
y+D
)  Equation 3
respectively, where D is the phase encoding FOV (see FIG.
3
).
Referring still to Equations 2 and 3, assuming that the sensitivities s
1
and s
2
for each of the first and second coils are known, after intensity data has been acquired for each of the first and second coils, only m(y) and m(y+D) are unknown. Thus, Equations 2 and 3 can be solved for each of the unknowns to determine the spin densities m(y) and m(y+D) at pixels y and y+D, respectively. The spin densities at each pixel can then be converted to intensities to “unwrap” the image.
By increasing the reduction factor R, the amount of data acquired is reduced and therefore throughput is accelerated. The number of unknowns, however, that can be resolved in any system is equal to the number of separate receiver coils in the system. Thus, in any given system the maximum reduction factor R is equal to the number of receiver coils N. For example, in the exemplary system described above that includes four receiver coils the maximum reduction factor R

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