|
Medical Patent Abstract
A method for defining image quality characteristics of X-ray based
medical projection imaging devices is provided. A spatial frequency-dependent
signal-to-noise ratio function includes image quality parameters
of spatial resolution, object contrast and noise. The detectability
of an object embedded into a defined background, such as a cardiac
guide wire in a patient is determined. An X-ray system may be defined
and set up for obtaining an optimized image quality to determine
the best object detectability for a given patient dose.
Medical Patent Claims
What is claimed is:
1. A method for quantifying image quality of an x-ray based medical
projection imaging system, comprising the steps of: directing a
beam of x-ray energy to a detector to produce an image; performing
a deterministic calculation to determine an average probability
for x-ray quanta being absorbed by an active layer of the detector;
blurring the image in a frequency domain to produce a blurred image;
performing a Fourier transform of the blurred image to produce a
transformed blurred image; performing a stochastic simulation based
on Monte Carlo track structure calculations for emitted x-ray quanta
to determine energy deposition distribution during imaging; performing
an analytical calculation as a linear cascaded model to determine
influence of physical processes in the detector; calculating the
spatial frequency dependent signal to noise ratio using output of
said Fourier transform and said stochastic simulation and said analytical
calculation according to the following: .function..function..function..times.
##EQU00016## using a result of said calculating step to optimize
an X-ray imaging system.
2. A method as claimed in claim 1, wherein said step of performing
said Fourier transform includes a step of: scaling the blurred image.
3. A method as claimed in claim 1, wherein said step of performing
said stochastic simulation includes: determining absorption probability;
determining a ratio of scatter to primary energy deposition; determining
a mean energy deposition per quantum; and determining a variance
of absorbed x-ray spectrum.
4. A method as claimed in claim 1, wherein said steps of performing
said stochastic simulation and said step of performing said analytical
calculation provides a determination of an absolute signal of a
background of the image.
5. A method as claimed in claim 1, wherein said step of performing
said analytical calculation includes: converting x-ray quanta to
optical quanta; scattering optical quanta in a scintillator; selecting
light quanta; spatially integrating interacting light quanta; and
outputting discrete detector elements.
6. A method as claimed in claim 5, wherein said step of converting
x-ray quanta to optical quanta includes: distributing energy of
the x-ray quanta via secondary particles; and generating optical
quanta by optical transitions of the secondary particles in a scintillator.
7. A method for optimizing image quality during setup of a medical
projection x-ray device, comprising the steps of: directing a beam
of x-ray energy to a detector to produce an image; performing a
deterministic calculation to determine an average probability for
x-ray quanta as registered in the detector; blurring the image in
a frequency domain to produce a blurred image; performing a Fourier
transform of the blurred image to produce a transformed blurred
image; performing a stochastic simulation for emitted x-ray quanta
to determine energy deposition distribution during imaging; performing
an analytical calculation to determine influence of physical processes
in the detector; calculating the spatial frequency dependent signal
to noise ratio using output of said Fourier transform and said stochastic
simulation and said analytical calculation according to the following
function: .function..function..function..times. ##EQU00017## adjusting
the medical projection x-ray device to maximize a value of SNR(u,
v) at a given frequency pair u, v.
8. A method as claimed in claim 7, further comprising the step
of: varying spatial frequency depending on characteristics of an
object to be detected to optimize object detection in an image by
the x-ray imaging system.
9. A method as claimed in claim 8, wherein said object characteristics
include object size and object movement rate.
10. A method for quantifying image quality of an x-ray based medical
projection imaging system, directing a beam of x-ray energy to a
detector to produce an image; performing a deterministic calculation
to determine an average probability for x-ray quanta registered
in the detector; blurring the image in a frequency domain to produce
a blurred image; performing a Fourier transform of the blurred image
to produce a transformed blurred image; performing a stochastic
simulation for emitted x-ray quanta to determine energy deposition
distribution during imaging; performing an analytical calculation
to determine influence of physical processes in the detector; calculating
the spatial frequency dependent signal to noise ratio using output
of said Fourier transform and said stochastic simulation and said
analytical calculation according to the following function: .function..function..function..times.
##EQU00018## using a result of said calculating step to optimize
an X-ray imaging system.
11. A method as claimed in claim 10, further comprising the step
of: comparing a value produced by said function for said imaging
system to a value of said function of another x-ray imaging system.
Medical Patent Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to medical X-ray imaging
and in particular to a method for determining spatial resolution
and noise level in medical projection X-ray imaging.
2. Description of the Related Art
Projection X-ray imaging is used in a medical setting to image
structures within the body of a patient. The medical projection
X-ray imaging device must be set up to provide a compromise between
spatial resolution and noise level. For example, a large focal spot
size guarantees a high quantum flux and thus a reduced noise level.
On the other hand, image resolutions suffers from a poorly conditioned
source. Duration of the exposure also determines image quality since
motion of an object during the exposure results in blurring of the
object image if the exposure time is too long. On the other hand,
short pulses or exposure times reduce the motion blurring effect
but lead to high noise levels.
Issues of spatial resolution, contrast, and noise are addressed
by the following methods.
In CNR (contrast to noise ratio) or SDNR (signal difference to
noise ratio) techniques, the two noted parameters combine contrast
and noise.
In MTF (modulation transfer function) techniques, the function
describes the loss of modulation amplitude for every spatial frequency,
which is caused by the imaging system.
In DQE (detective quantum efficiency) techniques, the function
describes the detected performance of a detector compared to an
ideal detector, which is in reference to spatial resolution, contrast
and noise.
In NPS (noise power spectrum) techniques, the frequency-dependent
noise level is considered.
The exposure parameters on an X-ray system are usually chosen in
such a way as to ensure a constant detector dose by an automatic
exposure control system (AEC). The properties of the object being
imaged, such as the speed of an object in motion, are not taken
into account.
SUMMARY OF THE INVENTION
The present invention provides a method for determining exposure
parameters in an X-ray imaging device.
The objective quality of medical X-ray images is basically determined
by three parameters: spatial resolution, contrast and noise. These
three parameters are integrated into a single function according
to the present invention, the function being the frequency-dependent
signal-to-noise ratio SNR=SNR (u,v). This function describes the
ratio between the signal and the noise detected in the X-ray image
which is dependent on the two-dimensional spatial frequencies u
and v.
Let H(u,v) be the Fourier transform of the deterministic signal
h(x,y) and NPS(u,v) be the corresponding noise power spectrum, the
frequency-dependent signal-to-noise ratio SNR(u,v) can be calculated
by:
.function..function..function. ##EQU00001##
As a fundamental aspect of the present invention, a set of exposure
parameters are determined in such a way that the value of SNR(u,v)
will achieve its maximum value.
In particular, the equation SNR(u,v) includes spatial resolution
and noise information. The contrast in the image, in terms of the
signal difference, is incorporated into the spatial-frequency-dependent
signal. A high contrast image results in a strong signal amplitude
in the corresponding frequency band. A linearity between the contrast
(the signal difference) and the value of SNR(u,v) is a consequence
of the following mathematical relations: signal modulus of the Fourier
transform h(x,y) |H(u,v)| ah(x,y)+b |aH(u,v)+b.delta.(u).delta.(v)|.
(2)
For u or v unequal to zero, the modulus of H(u,v) is proportional
to any signal scaling.
The value of SNR(u,v) is invariant to linear deterministic image-processing
algorithms. Neither a variation of image brightness or contrast,
nor the application of spectral filters (high-pass filter, low-pass
filter, harmonization, etc.) have any influence on the frequency-dependent
value SNR(u,v).
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1a is a side view of a geometrical model and FIG. 1b is a
top view of the geometrical model used for the calculation of the
formula according to the present invention;
FIG. 2 is a flow chart illustrating the calculation procedure for
the present method;
FIG. 3 is a graph showing an influence of exposure time on the
present method for a given spatial frequency, velocity of object
and magnification factor;
FIG. 4 is a schematic representation of an optimum exposure time
for a guide wire moving perpendicular to its axis;
FIG. 5 is a graph illustrating velocities of a cardiac cycle for
different regions of a heart at 72 beats per minute;
FIGS. 6a, 6b, 6c, 6d, 6e and 6f are images of a moving guide wire
obtained with different exposure times; and
FIG. 7 is a graph of power spectra of a typical anatomical image
and a single guide wire.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A method for optimizing a medical projection X-ray imaging device
provides a single function, namely the frequency-dependent signal-to-noise
ratio SNR which incorporates spatial resolution, contrast and noise.
The frequency-dependent signal-to-noise ratio SNR describes the
ratio between the signal and noise detected in the X-ray image dependent
on two-dimensional spatial frequencies u and v so that SNR=SNR(u,v).
The calculation of SNR(u,v) utilizes the Fourier transform of the
deterministic signal h(x,y) as the value H(u,v) and the noise power
spectrum signal NPS(u,v) according to the following formula:
.function..function..function. ##EQU00002##
The noise power spectrum is only defined if the underlying signal
is spatially invariant. An object of interest which is being imaged
by the X-ray, however, absorbs either more or less radiation than
the background. As such, the noise power spectrum is different at
the location of the object of interest. Assuming that the object
of interest is small and that the signal difference between the
object signal and the signal of the background is also small, the
noise power spectrum can be determined at a position of a sufficiently
large, homogeneous background area.
The formula for the frequency-dependent signal-to-noise ratio SNR(u,v)
includes spatial resolution information and noise information. The
contrast in the image signal in terms of the signal difference is
incorporated in the spatial frequency-dependent signal. A high contrast
image results in a strong signal amplitude in the corresponding
frequency band. The linearity between the contrast (or signal difference)
and the formula SNR(u,v) is a consequence of the following mathematical
relations: signal modulus of the Fourier transform h(x,y) |H(u,v)|
ah(x,y)+b |aH(u,v)+b.delta.(u).delta.(v)|. (2)
For values of u or v which are not equal to zero, the modulus of
H(u,v) is proportional to any signal scaling.
The formula SNR(u,v) is invariant to linear deterministic image-processing
algorithms. Neither a variation of image brightness or contrast,
nor the application of spectral filters (such as a high pass filter,
low pass filter, harmonization, etc.) have any influence on the
frequency-dependent formula SNR(u,v).
The formula for the frequency-dependent signal-to-noise ratio is
related to the detective quantum efficiency DQE(u,v). The detective
quantum efficiency DQE(u,v) describes the performance properties
of a detector, while the signal-to-noise ratio SNR(u,v) is focused
on the complete X-ray imaging system and setup, measuring its ability
to detect a certain object. This can be expressed mathematically
wherein SNR(u,v) is the signal-to-noise ratio at the output of the
detector while the detective quantum efficiency DQE(u,v) is the
ratio between the squared SNR(u,v) values at the output and at the
input of the detector, as follows:
.function..function..times..times..function. ##EQU00003##
The signal-to-noise ratio (u,v) like the detective quantum efficiency
DQE(u,v) is not a single number but a function. Here, the spatial
frequencies u and v that are used in the function SNR(u,v) refer
to the detector plane. To be able to use this parameter in a real
scoring system for an X-ray system and setup, it must be determined
which spatial resolution, in other words which spatial frequency
region, is most important for the actual detection problem. If thin
guide wires have to be observed, the function SNR(u,v) should be
analyzed for higher spatial frequencies. Images of soft tissue,
on the other hand, require large SNR(u,v) values in the low frequency
domain. Furthermore, when imaging an object, it is important to
know whether the object itself or whether the details of that object
are to be imaged. For example, it may be desired to image a possible
stenosis in the vascular system.
Parameters involved in the formulation of SNR(u,v) using a pulsed
source X-ray imaging system include: the object (whether the object
to be imaged are guide wires, stents, contrast-media-filled vessels
with iodine or CO.sub.2, etc.), the source-to-image distance (SID),
the geometrical magnification factor of the object, the size of
the detector, the patient thickness, the tube voltage U, the material
and thickness of the pre-filter, the tube current I, and the exposure
time t.
Of the foregoing important parameters, the first five, namely the
object, source to image distance, geometrical magnification factor
of the object, size of the detector, and patient thickness, are
more or less defined by the attending physicist using the task parameters.
The last four variables, namely the tube voltage, pre-filter material
and thickness, tube current, and exposure time, can either be selected
manually or chosen by an automatic exposure control of the X-ray
imaging device. These are referred to as optimization parameters.
Turning now to FIGS. 1a and 1b, a geometrical model is utilized
for the calculation of the function SNR(u,v). In the model, a tube
focus 10 emits an X-ray signal toward a pre-filter 12 so that the
X-ray passes through a background 14 in an effort to image an object
16 imbedded in the background 14. X-ray signals which have passed
through the background 14 and object 16 are captured by an anti-scattering
grid 18 and detected by an active detective layer 20.
In the geometrical model, the background 14 is represented by a
cube that is of pure water, Lucite, or a mixture of soft tissue
and bones. These are materials which have absorption properties
that are close to those of the human body. The thickness of the
cube defines the patient thickness. An appropriate simplified shape
for the objects of interest 16 such as guide wires or vessels is
provided as a cylinder whose axis is perpendicular to the beam direction.
The object of interest 16 is situated in the center of the cube
14 representing the background.
The calculation procedures will now be described. Because of the
limited calculation power of present-day computers, it is not possible
to simulate a complete X-ray image by a pure Monte Carlo track structure
calculation technique for the determination of the function SNR(u,v).
The problem is solved by a combination of three different strategies.
First, deterministic calculations are performed, second, stochastic
simulations (which are equivalent to a Monte Carlo track structure)
are performed, and thirdly, analytical calculations (a cascaded
model) are performed. The whole process of the calculation of the
function SNR(u,v) is illustrated in FIG. 2, wherein deterministic
calculations 22 are performed to provide a sharp noiseless image
24. A blurring function 26 is performed to generate a blurred noiseless
image 28 which is then provided to a Fourier transform of the absolute,
blurred noiseless image 30 that is then provided to the signal-to-noise
ratio SNR(u,v) 32. Further stochastic simulations 34 are performed
to generate absorption probability, the ratio of scatter-to-primary
edge deposition, the mean energy deposition per quantum, and the
variance of the absorbed x ray spectrum 36. This results in an absolute
signal of the background NPS(u, v) 38 which is then provided to
both the Fourier transform 30 and the signal-to-noise ratio 32.
Further, analytical calculations 40 are provided as a cascaded model.
The output of the calculations is the absolute signal of the background
when combined with the information 36 which are then provided to
the Fourier transform 30 and the signal-to-noise ratio 32.
In particular, deterministic calculations are provided as follows:
A pencil-shaped X-ray beam from the focal spot to the center of
the detector pixel is considered for every detector pixel. With
the information on the material composition, the density, and the
thickness of the beam, it is possible to calculate the average probability
of primary X-ray quanta with an energy spectrum defined by the tube
setup (including the anode material, the anode angle, and the tube
voltage) being registered in the active layer of the detector. The
absolute signal height cannot be determined by the deterministic
calculations since the scatter radiation information is missing.
To avoid sampling effects due to a finite pixel size at that stage,
the real pixel length is reduced. To summarize, the result of this
deterministic calculation 22 is an extremely sharp, noiseless X-ray
image 24, given in relative intensities. In a preferred embodiment,
the deterministic calculations 22 are performed utilizing a program
named DRASIM, which is an internal program of Siemens AG. Primary
X-ray spectra can be taken from the publications by Boone et al.,
"An accurate method for computer generated tungsten anode x-ray
spectra from 30 to 140 kV", Med Phy 24, 1661-1670, 1997 and
Aichinger et al., "Radiation Exposure and Image Quality in
X-ray Diagnostic Radiology", Springer-Verlag, Berlin 2004
Subsequently, the perfect images are analytically blurred, at 26.
The blurring is done in the frequency domain. The images 28 are
Fourier transformed at 30 and scaled with the corresponding MTF(u,v)
functions where (u,v) are the spatial frequencies in the x and y
directions, respectively. For the determination of the MTF(u,v)
function, the following Fourier transform of a rectangular input
function with a base length a is helpful.
.times..function..times.<.gtoreq..times..times..function..times..times.-
.function..pi..times..times..pi..times..times..times..times. ##EQU00004##
Four blurring sources are considered: the focal spot, motion blurring,
the scattering of quanta in the detector, and detector pre-sampling.
Let f.sub.x and f.sub.y be the sizes of a rectangular focal spot
and .gamma. the magnification factor of the object of interest (.gamma.=1
object is directly on the surface of the detector; (.gamma.=2 object
is exactly half way between focal spot and the detector) such that
the corresponding MTF is: MTF.sub.foc(u,v)=sinc (f.sub.x(.gamma.-1)u)
sinc (f.sub.y)(.gamma.-1)v) (5)
Let m.sub.x and m.sub.y be the velocity of the object of interest
rectangular to the X-ray beam direction, t the exposure time, and
.gamma. the above defined magnification factor such that the corresponding
MTF is: MTF.sub.mot(u,v)=sinc (m.sub.xt.gamma.u)sinc (m.sub.y, t.gamma.v)
(6)
X-ray quanta and optical quanta in the case of an indirect-detection
detector cause blurring. A real corresponding MTF.sub.sci(u,v) function
is difficult to calculate due to the lack of a precise description
of the optical properties of the scintillator. Instead of doing
so, it should be measured. If scattering of X-ray quanta in the
active layer and variable interaction depths in the scintillator
are neglected, a single MTF function for all quanta with different
energies and absorption depths can be defined.
Let a.sub.x and a.sub.y be the sizes of the active regions of a
detector pixel such that the corresponding MTF is: MTF.sub.pix(u,v)=sinc
(a.sub.xu)sinc (a.sub.yv) (7)
In FIG. 2, the stochastic simulations 34 of the preferred embodiment
are based on Monte Carlo track structure calculations. The direction
and energy and the emitted X-ray quanta are randomly chosen from
a given angle and with know energy distributions. The complete history
of the primary particles and all possible secondary particles is
tracked. For example, all photon interactions with the pre-filter,
the background object, the anti-scatter grid, and finally the active
layer of the detector are simulated to determine the energy deposition
distribution. These photon interactions include the photoelectric
effect, coherent scattering, incoherent scattering, and K fluorescence.
The object of interest can be omitted in these simulations since
its total influence is assumed to be negligibly small. The statistics,
obtained by tracking approximately 10.sup.8 quantum histories, are
good enough to find out the following system properties, assuming
the scatter radiation is homogeneously distributed over the whole
detector area: the number of absorbed quanta N (including the primary
and secondary quanta) in the active layer of the detector per emitted
primary quantum, ratio S/P between the secondary energy deposition
and the primary energy deposition in the active layer of the detector,
mean deposited energy <E> per absorbed quantum, and the variance
of energy .sigma..sub.E.sup.2 of absorbed quanta. The stochastic
simulations 34 are performed, in a preferred embodiment, by a program
named MOCASSIM, which is an internal program of Siemens AG.
In FIG. 2, the analytical calculations 40 are provided as a cascaded
model. The influence of the physical processes in the flat panel
detector on the uniform image (which is the image without an object
of interest) can be described with the help of a linear cascaded
model. The process is divided into five steps, for example, the
conversion of the X-ray quanta to optical quanta in the scintillator,
the scattering of optical quanta in the scintillator, the selection
of light quanta, the spatial integration of interacting light quanta,
and the output of the discrete detector elements.
In every step of the analytical calculations 40, the quantum flux
q (which is the mean number of particles per unit area) and the
corresponding noise power spectrum NPS(u, v) are updated. The input
parameters q.sub.0 and NPS.sub.0(u,v) can be calculated with the
help of the number of absorbed quanta N, the SID (source-to-image
distance), the X-ray tube gain Q for a certain tube voltage (which
is in 1/mAs/sr), the tube current I, and the exposure time t:
.times..times..times..times..times..times..times. ##EQU00005##
The conversion of the X-ray quanta into optical quanta can be split
into two gain processes: the first process provides that the energy
of the quantum is distributed via secondary particles (which are
mainly electrons). The second process provides that the optical
transitions, caused by the electrons in the scintillator, generate
optical quanta.
The energy deposition has a gain factor which is equivalent to
the mean deposited energy <E> per primary X-ray quantum, and
the variance .sigma..sub.E.sup.2 of this process is dependent on
the width of the absorbed spectrum. Both values are determined during
the statistical simulations.
A mean gain factor <G> for the generation of optical quanta
is dependent on the scintillator material; the gain factor is given
in optical quanta per absorbed energy. In the case of CsI, the mean
gain factor <G> is approximately 55/keV.sup.10. Under the
assumption of Poisson statistics, the variance of this distribution
is .sigma..sub.G.sup.2=<G>.
It is important to note that both of these gain processes always
have to be combined. The energy deposition is not a real gain process,
since energy units and particles are not produced. It is only justified
by immediate application of a second gain process. The resulting
quantum flux q.sub.1 and NPS.sub.1 are q.sub.1=<E><G>q.sub.0NPS.sub.1(u,v)=<E>.sup.2<G>.-
sup.2NPS.sub.0(u,v)+<G>.sup.2.sigma..sub.E.sup.2q.sub.0+.sigma..sub.-
G.sup.2<E>q.sub.0 (9)
Assuming a unique MTF.sub.sci(u,v) for all optical quanta inside
the scintillator, the resulting quantum flux q.sub.3 and NPS.sub.3
are: q.sub.2=q.sub.1NPS.sub.2(u,v)=(NPS.sub.1(u,v)-q.sub.1)MTF.sub.sci.sup.2(u-
,v)+q.sub.1 (10)
The probability .beta. for the detection of the optical quanta
includes the coupling efficiency of light from the scintillator
as well as the quantum efficiency of the detector array. This gain
process results in the following flux q3 and NPS.sub.3: q.sub.3=.beta.q.sub.2NPS.sub.3(u,v)=.beta..sup.2(NPS.sub.2(u,v)-q.sub.2)+-
.beta.q.sub.2 (11)
The detector pre-sampling signal corresponds to the spatial integral
over the active region of a detector pixel with a width of a.sub.x
and a.sub.y, respectively. The new flux q.sub.4 and the NPS.sub.4
equals: q.sub.4a.sub.xa.sub.yq.sub.3NPS.sub.4(u,v)=a.sub.x.sup.2a.sub.y.sup.2NPS.-
sub.3(u,v)sin c.sup.2(a.sub.xu)sin c.sup.2(a.sub.yv) (12)
Finally, the discrete detector signal is recorded. Let x.sub.0
and y.sub.0, respectively, be the distances between the center of
two neighboring pixels such that the expected digital signal value
q.sub.5 of a pixel and the digital NPS.sub.5 are:
.times..times..function..function..infin..times..infin..times..function..+-
-..+-. ##EQU00006##
The final calculation of the function SNR(u,v), at element 32 in
FIG. 2, is performed with the help of the scatter-to-primary ratio
S/P and q.sub.5, the intensities of the noiseless, blurred image
can be scaled. Assuming that the object of interest is small and
that the scatter radiation is homogeneously distributed over the
whole image area, a constant amount of scatter, which is the product
of the actual background intensity and the S/P, is added to all
pixels of the image. Then the image is scaled to achieve a background
intensity of q.sub.5, where the artificially reduced pixel length
of the deterministic calculation 22 has to be considered. The Fourier
transform H(u,v) can now be determined from the resulting scaled
image. Finally, the function SNR(u,v) can be calculated according
to the following:
.function..function..function. ##EQU00007##
For every point in the exposure parameter space, the function SNR(u,v)
can thus be obtained. The results can be used to find the optimum
parameter setup for the X-ray imaging device.
Electronic noise, which is independent of detector dose, has been
neglected in this derivation, which is justified only for sufficiently
high detector doses. Nevertheless, the method can easily be extended
to include these effects.
The following describes motion blurring verses high dose imaging.
An advantage of the image quality parameter SNR(u,v) defined here
is the ability to find the best compromise between image sharpness
and noise. In the following example, the optimum exposure time is
determined for the detection of moving guide wires, which are typically
used in cardiology. In the following example, the guide wires have
a substantially cylindrical shape have, a diameter of d, and we
moved at a velocity m which is perpendicular to the axis of the
wire, and the system has a magnification factor of .gamma.. The
tube voltage and the tube current are fixed in this example.
Since a constant motion can be fully described in one dimension,
it is sufficient here to determine the influence of the exposure
time t on the one-dimensional function SNR(u). Here, u is the corresponding
spatial frequency with respect to the direction of motion. The exposure
time t affects the function SNR(u) in two ways: First, a long exposure
time generates blurring of the image because the object is moving.
For a constant tube current during the X-ray pulse, the influence
on SNR(u) can be described by: SNR(u).varies.sin c(mu.gamma.t) (15)
Secondly, increasing exposure times raise the contrast and noise
levels. See equation (8). In total, according to equation (14),
the formula SNR(u) behaves like:
.function..varies. ##EQU00008##
Equations 15 and 16 can be combined to yield the following:
.function..varies..function..pi..times..times..times..times..gamma..times.-
.times..pi..times..times..times..times..gamma..times. ##EQU00009##
Referring now to FIG. 3, one can think of an optimal exposure time
for the X-ray image. The dependence of the formulation SNR(u) on
exposure time t is given in the figure wherein a fixed spatial frequency
u, a velocity m of the object, and a magnification factor .gamma.
are provided.
With increasing exposure time, the number of quanta arises. The
object dominates more and more over the background noise. A further
increase in the exposure time leads to enhanced motion blurring,
and a deterioration the image quality. Thus, there is an optimal
value t.sub.opt for the exposure time, which is given by:
.apprxeq..times..times..gamma..times..times. ##EQU00010##
The foregoing formula is a result of an analysis of a transcendental
equation, which leads to the coefficient of 0.37. This result for
the option time t.sub.opt shall be illustrated. A spatial frequency
or the center frequency band has to be found, which is, for example,
the importance for the detection of a guide wire. The frequency,
whose half wave length is equal to the size .gamma. d of the guide
wire in the detector plane is presumed to be a major contributing.
Hence, the formula
.times..times..times..gamma. ##EQU00011## which enables the Equation
(18) to be rewritten as:
.apprxeq..times. ##EQU00012##
In the foregoing formula, d/m is the time period which is necessary
for one edge of the guide wire to pass the original position of
the other edge. Here, an adequate exposure time for imaging moving
guide wires is given when there is an overlap of approximately 25%
between the guide wire at the beginning and at the end of the exposure,
which is independent of the magnification factor.
Turning now to FIG. 4, an illustration of the optimum exposure
time for a guide wire moving perpendicular to its axis is provided.
The solid line represents the position of the guide wire at the
beginning of an exposure and the broken outline gives the position
of the guide wire at the end of the exposure. Assuming a typical
diameter d of 0.36 mm for a guide wire and a typical average velocity
m of 40 mm/s (see FIG. 5) in a cardiology application, the optimum
exposure time is approximately 6.7 ms, which is in good agreement
with published measurements. In particular, FIG. 5 is a graph illustrating
the velocity of a cardiac cycle for different regions of the heart
at 72 beats per minute. The designation LAD refers to the left anterior
descending coronary artery, LCX refers to the left circumflex, and
RCA to the right coronary artery. The velocity in millimeters per
second is provided on the vertical axis.
Turning now to FIG. 6, examples of exposures at different times
have been simulated example is simulated with the help of the DRASIM
program. The exposure time is varied from 0.5 ms to 18 ms. The object
in the simulation is a set of parallel orientated guide wires, moving
perpendicular to their axis. The detectability increases up to 6.3
ms, whereas motion blurring effects dominate beyond that. Finally,
at an exposure of 18 ms, individual guide wires are no more visible.
The use of a set of guide wires instead of a single guide wire
has prompted by the fact, that this periodical object is mainly
based on the spatial frequency around
.times..times..times..gamma. ##EQU00013## whereas a single guide
wire also includes low-frequency components. These components would
profit from long exposure times. Consequently, the detectability
of a single guide wire could rise even with increasing exposure
time, even if the guide wire becomes more and more blurred. A real
anatomical image, however, includes anatomical noise and structures,
typically with a high amplitude at lower spatial frequencies, as
shown. See FIG. 7 in this regard. Therefore, it is recommended to
focus the optimization on the intrinsic spatial frequencies for
a guide wire around
.times..times..times..gamma. ##EQU00014##
Referring to FIG. 7, a power spectra for a typical anatomical image
and a single guide wire are provided. An arrow has been indicated
in the graph to indicate the spatial frequency
.times..times..times..gamma. ##EQU00015##
Thus, a generalized objective image quality measure has been made
for X-ray based medical projection imaging. The spatial frequency-dependent
signal-to-noise ratio SNR=SNR(u,v) is disclosed. This function has
its origins in the DQE concept. It combines three main objective
image quality parameters, namely the spatial resolution, object
contrast, and noise. Besides the analytical definition, the present
function can be calculated for a test phantom at a typical flat-panel
detector by applying a combination of analytical calculations and
Monte Carlo simulations. In the example, the function SNR(u,v) is
used to optimize a pulsed X-ray imaging device. For a moving object,
the most suitable exposure time has been determined.
Thus, there is disclosed a method for providing a generalized objective
image quality measurement for an X-ray based medical projection
imaging apparatus. The spatial frequency-dependent signal-to-noise
ratio function is provided, which includes three main image quality
parameters, namely spatial resolution, object contract, and noise.
The DQE concept does not characterize the detector, but rather the
detectability of certain objects embedded in a defined background.
The effects of focus size and radiation scatter are quantified by
the present method. The signal-to-noise ratio is independent of
basic linear post-processing steps such as appropriate windowing
or spatial filtering.
By means of the signal-to-noise ratio, different X-ray systems
and setups can be compared with each other and with theoretical
calculations. X-ray systems, including the detector, beam quality,
geometry, anti-scatter grid, and basic linear post-processing steps
etc. can be optimized to deliver the best object detectability for
a given patient dose. The signal-to-noise ratio is defined using
analytical formulas. The foregoing demonstrates how the function
can be applied with a test phantom to a typical flat panel detector
system by a combination of analytical calculations and Monte Carlo
simulations. The foregoing demonstrates how the signal-to-noise
ratio function is used to optimize an X-ray imaging device.
Although other modifications and changes may be suggested by those
skilled in the art, it is the intention of the inventors to embody
within the patent warranted hereon all changes and modifications
as reasonably and properly come within the scope of their contribution
to the art.
|