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Description  |
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FIELD OF THE INVENTION
This invention relates to tomography and more particularly to continuous
wave fan beam tomography systems which measure a continuous radiation beam
at a plurality of radiation detectors, wherein the source and the
detectors move continuously and circumferentially about the subject
examined.
BACKGROUND OF THE INVENTION
Computer aided tomography systems derive images by placing the subject
between a source and one or more radiation sensors, wherein a source of
radiation and radiation sensors move together in one or more rotational or
lateral axes. The computer aided tomography systems produce the image by
indirect means. Specifically, a multiplicity of x-ray readings are taken
of the subject which in themselves do not directly characterize the
elements within the subject as known and readable to the human observer.
The computer then interprets the multiplicity of x-ray readings taken
together in a particular manner in which a readable image is created to
define the subject of interest. A subgroup of tomography systems of
present interest is known as continuous wave fan beam tomography systems.
The term "continuous wave fan beam" specifies the radiation source to be
continually emitting radiation in a beam pattern resembling a sector of a
circle. As part of this type of system, there are typically several
hundred radiation sensors in the path of the fan beam on the opposite side
of the subject to receive the x-ray radiation as attenuated along defined
path lines through the subject. The sensors form an arcuate segment of
sufficient length to intercept the entire radiation beam transmitted along
a path through and absorbed by the subject from the radiation source and
generate individual output signals. In prior fan beam tomography systems
simultaneous acquisition of all x-ray readings for each gantry position
are believed to be the most preferred manner in which to provide the
necessary mathematical basis for tomographic image (re)construction. The
individual radiation sensor output signals are therefore (in prior
systems) each initially processed by individual resettable integrators,
known collectively as the "integrate-and-dump" technique, which are then
sampled and stored by subsequent system elements. According to the
continuous wave fan beam tomography systems and included techniques of the
prior art, it is believed that the best estimate of the radiation
attenuation along each defined path can be derived from the individual
outputs of integrate-and-dump circuits which are designed to collect as
much detector output signals, and therefore x-ray radiation signals, as
possible.
Another aspect of prior art, relating to computer-aided continuous wave fan
beam tomography systems has been the great expense of the required
associated auxiliary circuitry, in addition to the several hundred
precision resettable integrators. In general, auxiliary transfer circuitry
has been required for each input channel to rapidly receive, upon a
transfer command, the accumulated integration values, allowing the
aforesaid input integrators to be rapidly reset at the end of an
integration period and be allowed to continue to integrate during the next
integration time interval.
A universal goal in tomography systems is to reduce the radiation dosage.
The dosage requirements are generally defined by the detector sensitivity
to x-ray radiation, the radiation detector geometry and the subsequent
signal processing apparatus. In the prior art, it is assumed that
collecting as much radiation signal as possible (with a resettable
integrator for each radiation detector) was the best way of minimizing the
radiation dosage. However, in spite of system improvements according to
prior art teachings, the dosage required still remains relatively high,
thus limiting the number of examinations any one subject may undergo.
SUMMARY OF THE INVENTION
The present invention filters the detector output signals from moving x-ray
detectors in a continuous wave fan beam tomography system by known
filters, described by determined parameters, having output signals sampled
at a sampling rate. The tomographic image is accurately formed from
radiation values derived, at discrete points in time from the filter
output signals, thus eliminating the need to simultaneously sample all
detector outputs at the discrete points in time, as in prior art systems.
The gantry position moves continuously wherein specific gantry positions
are related to the discrete points in time. The filter output signals are
sequentially sampled at a sampling rate which typically differs from the
discrete points in time. The derived radiation values are each a
best-estimate value at specific gantry positions according to the
sequentially sampled filter output signals. The accuracy of the
best-estimated radiation value is enhanced by removing error signals from
the filter output signals according to the filter design. The filters are
optimized according to parameters which include filter bandwidth, filter
transient response, filter phase response, system geometry limitations,
subsequent computer reconstruction method and system cost. In so doing,
the filters minimize error signals included in the detector output signals
which, in turn, improves the estimate of the x-ray absorption at the
discrete points in time. For instance, the inventive concept recognizes
that the maximum frequency of the signal derived by the continuous wave
tomography systems is fundamentally limited by the source of the
radiation, the size of the target to be detected, the cross-sectional area
of the radiation detector and the geometry and motion of these components
relative to each other. Furthermore, it is recognized that photon
randomness can be expressed as noise having a noise bandwidth far in
excess of the remaining tomography system bandwidth. The present invention
improves the signal quality significantly by processing the detector
signals with a temporally continuous filter to limit the noise, whose
output is sufficiently sampled prior to conversion for subsequent
processing.
More specifically, according to the present invention, a substantial
amplitude of error signal arising from the radiation source is removed by
filtering the detector signals with a low-pass filter having a cutoff at a
frequency below the sampling rate. The mechanical system, including the
detectors, produces a signal which is essentially a convolution of the
target with the detector cross-section. The resulting time varying signal
has its associated frequency components which have a related bandwidth.
One embodiment of the invention provides a low-pass filter which extends
only to the maximum useable frequency of the above-mentioned bandwidth.
The sampling rate is determined according to the maximum useable
frequency. The maximum useable frequency is selected according to an
objective or a subjective analysis of a Fourier transform of the time
varying signal in view of the above-mentioned criteria. The present
invention thereby provides increased signal-to-noise and resolution of the
signals which are used to compute tomographic images. The improvement is
sufficient to allow an image to be reconstructed from the data obtained
with a reduced source radiation level. This, in turn, provides a lower
subject dosage and increased availability of the tomographic aided
diagnosis to the public.
Additionally, the system according to the present invention includes
continuous filtering before sampling and eliminates the need for
individual storage elements (for each sensor) in tomography systems, which
significantly decreases overall system cost.
Briefly, the continuous wave fan beam tomography system according to the
present invention includes a continuous wave radiation source and a
plurality of radiation detectors positioned in opposition to the source
about the subject to be examined. A gantry retains and moves the radiation
source and the radiation detectors about a center of rotation located
within said subject. The radiation source provides a fan beam (generally
known within the art as uniform radiation in a fan shape in a first plane
and having a small width and substantially no divergence in a second
plane, and a fan angle at the first plane of sufficient magnitude to
illuminate the entire subject cross-section). The detectors are located
behind the subject to form an arcuate segment sufficiently long to fully
intercept the radiation transmitted through the subject. Each detector
provides a detector output signal relating the radiation received. The
detector output signal is then filtered by a plurality of detector filters
having an input to receive the detector output signals optimized to
produce a continuous filter output signal relative to each detector output
signal which provides a determinable best-estimate of the total x-ray
radiation absorption along a determined path through the subject when the
filter output signal is sampled at a sampling rate by subsequent elements
of a continuous wave fan beam tomography system including a processing
computer. An image is reconstructed according to a best-estimated x-ray
value at discrete points in time which, in view of the sequential nature
of the filter output sampling, are skewed in time from the sampling rate,
or have a different periodicity.
The sampling periods occur at a sampling rate, which also determines a
practical limit to the bandwidth of the detector filters. The sampling
rate is limited to a frequency corresponding to a maximum useable
frequency of the detector output signal. The maximum useable frequency of
the detector output signals is determined according to the largest and
smallest object or target to be resolved, the size and location of each
detector and the mechanical system movement relative to the subject. The
source of radiation, the objects to be resolved and detector cross-section
are convolved in time to produce a time varying signal, the Fourier
transform of which describe a group of frequency domain signals having an
uppermost frequency domain signal. The maximum useable frequency is
related according to a subjective or a determined known objective analysis
of the uppermost frequency domain signal. It is according to the present
invention that signals outside of the above-specified bandwidth are, in
general, error signals, noise or other unwanted signals and are to be
minimized. The resulting signal may be processed in a processing computer
to form best-estimate signals derived from the sampled filter output
signals. The best-estimate signals are formed for discrete point in time
(which typically differ from the sampling rate), where the discrete points
in time relate to specific gantry positions. The processing computer forms
a tomographic image in a variety of known manners; the image is then
subsequently displayed by appropriate display means.
BRIEF DESCRIPTION OF THE DRAWING
These and other features of the present invention are more fully described
in the following detailed description and in the accompanying drawing in
which:
FIG. 1 is a schematic representation of the mechanical geometry of a
typical continuous wave fan beam tomography system;
FIG. 2 is a block diagram of a generalized sampling and reconstruction
subsystem of the present invention;
FIG. 2A is the transfer characteristic of one element of the subsystem of
FIG. 2;
FIG. 2B is the time response of a prior art integrate-and-dump circuit in
the context of the subsystem of FIG. 2;
FIG. 3 is a graph of the signals of interest in the frequency domain;
FIG. 4 is a block diagram of a single channel of the continuous filter
according to one embodiment of the present invention;
FIG. 5 is a schematic diagram of one embodiment of the continuous filter
according to the present invention; and
FIG. 6 is a typical filter output signal of the circuit of FIG. 4.
DETAILED DESCRIPTION OF THE INVENTION
Turning now to the drawing and in particular FIG. 1, a generalized
schematic view of the geometry of a continuous wave fan beam tomography
system is shown in a mechanical configuration generally known as a gantry
10 containing an x-ray source 12 which emits a continuous broad x-ray beam
for the transmission through the subject 14 to an array of x-ray detectors
16, each having a detector cross-sectional area. The emitted radiation fan
beam 18 diverges from source 12 as the emission travels towards the
plurality of detectors 16, (diverging over a fan angle in a sector pattern
through the subject 14 in a first plane perpendicular to the subject,
where the sector pattern has a relatively narrow width substantially
without divergence in a second plane extending perpendicular to the first
plane along the axis of the subject). Of interest is the detection and
imaging of particular targets within the subject 14, those targets being
exemplified by a single target 20. The source 12 and the detector array 16
move together about the subject 14 through a rotation angle and direction
labeled 22; the desired information is typically produced by a rotation
through an angle 22 of 360.degree. , while the source 12 emits a
continuous fan beam of radiation 18. The plurality of detectors each
provide a continuous signal relating the reception of x-ray photons from
the source 12 through the subject 14 as the assembly is continuously moved
through the rotation angle 22. The signals from the detector array are
each directly related to the volume of photons received, and therefore it
is inversely proportional to the absorption of the subject 14 through each
line 15 traveled by the x-rays from the source 12.
The signals produced by the detectors are conditioned by a data acquisition
system 24. The data acquisition system 24 contains a plurality of
channels, one for each detector output signal and provides an output
signal for additional data acquisition logic such as signal multiplexers
and digitizers, not shown. Thereafter, the signal is processed by a
general purpose or a specialized processing computer system 28 in a
predetermined manner to provide a reconstructed image of a transaxial
view. A complete fan beam tomography system, described in greater detail
in U.S. Pat. No. 4,135,247, is hereby incorporated by reference. The
above-mentioned subsequent signal processing may be provided according to
the above-mentioned patent or by other ways currently known.
According to FIG. 1, it can be seen that the presence of a target 20 is
detected by a shadow which it casts by absorbing the energy of the beam 18
as seen by one of the detectors 16. The position of the target and its
shape is deduced from its level of absorption according to the line
integral over each path 15 as well as its motion relative to the source 12
and the detectors 16. The reconstruction of the target 20 may be provided
according to known techniques.
The method and apparatus according to the present invention concerns the
formation of a best-estimate of the absorption for each path 15 through
the subject 14 at discrete points in time for a given set of values for
the rotation angle 22 of the source 12 and detector array 16. The
best-estimates at the discrete points in time are interpolated,
synthesized, or otherwise derived from sequentially sampled detector
signals in an image processor, which reconstructs a tomographic image. It
is therefore essential that the sampled detector signals allow such
best-estimated absorption values to be derived accurately.
The system pre-processing functions can be generalized as shown in FIG. 2,
wherein each detector 16 produces a output signal x(t) received by a
functional block 23 with a generalized transfer function H(f) or time
domain response h(t). The block 23 produces an output y(t) which is
periodically and instantaneously sampled by sampling block 25 according to
sampling signal s(t) to produce a sampled signal z(t). More specifically,
the sampling signal s(t) is defined in a generally known form:
##EQU1##
where U.sub.o is an impulse function, .alpha. is a statistical phase
constant (see FIG. 6) and f.sub.o is the sampling frequency. The samples
of y(t) form z(t) as
##EQU2##
where the set of values {y(Kt+.alpha.)} are the sample values. The
reconstructed output x(t) is given by
##EQU3##
where functional block 26 has the transfer characteristic shown by FIG.
2A, or that of an ideal low pass filter.
An error .epsilon.(t) can be defined in the sampling and reconstruction
process. The detector 16 output x(t) is assumed to have a spectral density
S.sub.x (f) and an .alpha. uniformly distributed over the time interval
[0,T], allowing the definitions:
##EQU4##
The statistical average means-square error .epsilon..sup.2 (t) function:
##EQU5##
which, when reduced, provides the least sampling and reconstruction error,
is minimized when:
##EQU6##
to produce an error which is:
##EQU7##
which includes all signal power of x(t) outside of the reconstruction
region, earlier defined as being between [-f.sub.o /2, f.sub.o /2].
Thus, according to one embodiment of the invention incorporating linear
filtering for all discrete points in time (.alpha. not limited to a
particular value), the best reconstruction of x(t) resides within the
bandwidth [-f.sub.o /2, f.sub.o /2] for a given sample rate f.sub.o =1/T.
The best linear estimator x(t) is therefore obtained with H(f) of 23
comprising that of an ideal low pass filter, shown in FIG. 3 at 40, which
passes all signals at a frequency equal to or below the filter cutoff
frequency, and rejects all signals at a frequency greater than the cutoff
frequency, and an error given by the high-frequency power of x(t) as
defined by equation (9). However, if x(t) has no high-frequency power,
S.sub.H (f)=0, then .epsilon..sup.2 (t)=0 for optimum H(f).
When h(t) is h.sub.2 (t) as shown in FIG. 2B for a typical prior art
integrate-and-dump response over time period T, the function block 22
transfer response is
H.sub.2 (f)=Sin .pi.fT/.pi.fT (10)
shown as curve 42 in FIG. 3, and can be compared in FIG. 3 as wave 42 with
the optimum filter response 40 to reveal error signals indicated by shaded
areas 50 which exist whenever S.sub.H .noteq.0. Therefore, to minimize
extraneous signal energy, such as photon noise power discussed below, the
optimum filter is an idealized low-pass filter. In other words, any
signals passed by G(f), shown by FIG. 2A, and H(f) above the sampling
frequency (above S.sub.L) will result in the addition of unrecoverable
error. The sampling rate f.sub.o is selected to be at least two times
greater than the highest useful frequency component in x(t) from the
sensor 16 according to the Nyquist criteria. The highest useful frequency
component may be objectively or subjectively selected (considering the
above-mentioned system parameters) according to the overall shape of the
frequency domain characteristics of the detector or target signals.
The overall shape of the frequency domain characteristics of target signals
is described according to the Fourier transform of the respective time
varying signal, which is the convolution of the cross-section with the
target cross-section as the two are moved respective to each other during
the rotational scan period of the source and the detectors relative to the
patient. A typical frequency domain representation of the signals present
in the tomography system of interest is shown in FIG. 3. For illustration,
hypothetical broadband signal derived from a long target with sharp
irregularities in the time domain is shown in the frequency domain by
curve 48 on FIG. 3. Most generally, the low frequency limit is defined by
the maximum duration of the absorption or shadow cast by the object during
the rotation, e.g., a cross-section of the skull at a nearly tangential
detection sight wil show a continuous absorption during the revolution of
the gantry, resulting in a DC component, thereby defining the low
frequency requirement. The upper frequency requirement is the limit
imposed by sharpness or the rapidity of the variations of the time varying
convolution signal.
The major source of error in the reconstructed signals arise from the
inherent uncertainty of the source emissions; that is, the regularity with
which the x-rays are produced by a source of radiation and that the
electronic system noise is generally relatively minor. Although the photon
noise is broadband, the signals derived by the mechanical system appearing
at the detector outputs have a limited bandwidth in relation to the target
to be imaged within the subject. The present invention improves the
usefulness or accuracy of reconstructed signals by restricting the
bandwidth of those electrical signals passed according to the maximum
bandwidth as defined by the target and the mechanical geometry of the
tomography system as described above and sacrifices the remaining signal
from the detector outputs as unwanted noise.
It is shown in FIG. 3, according to the present invention, that the
performance may be enhanced significantly by providing a filter circuit
adjusted to pass primarily the convolution signal 48 produced at the
detector output, and minimize the contribution of the photon noise 44
beyond the maximum useful frequency of the convolution signal. A typical
filter of that description is shown by curve 46, having the characteristic
of a three-pole Butterworth filter with a 3 dB point of approximately 380
hertz when the sample period is one millisecond.
An embodiment of one channel of the data acquisition system, according to
the filter of the present invention includes a detector amplifier in the
amplifier-filter 70, shown in FIG. 4. The remaining calibration 54 and
protection 34 circuitry of each channel may be retained as in the prior
art or other circuitry modifications may be made according to known
methods and apparatus. The specification of the filter 3 dB point, as well
as its other characteristics, e.g. Butterworth, Tchebycheff, Elliptical or
other filter types, are made at the designer's discretion in a known
manner according to the desired phase, frequency and time characteristics
of the data acquisition system, the mechanical system, subsequent
processing of the image signals into a completed tomographic picture and
total system cost. The careful design and selection of the filter
characteristics in relation to the desired criteria, mentioned above, will
result in a signal of improved signal-to-noise ratio.
One embodiment of the continuous filter according to the present invention
is shown in detail in FIG. 5. The detector provides a current output, Is
to be received by input 60 through resistor R.sub.1 into the gate of a
differential J-FET pair Q.sub.1A, Q.sub.1B typically contained within a
common enclosure 62 to provide closer matched operations of the J-FET pair
over a temperature range. The protective circuit (34 of FIG. 1 and FIG. 5)
is implemented by CR.sub.1 containing back-to-back diodes D.sub.1A and
D.sub.1B across the Q.sub.1A gate to ground. The J-FET pair is biased from
-12 volts by R.sub.4 and R.sub.5 bypassed with C.sub.3 to ground. The
Q.sub.1B gate input is connected to ground establishing a zero volt
operating point of the circuit of FIG. 6. The drain load resistors of
Q.sub.1A and Q.sub.1B and R.sub.2 and R.sub.3, respectively, are connected
to +12 volts through a common resistor R.sub.7 bypassed by C.sub.9. The
drains of J-FET pair Q.sub. 1A and Q.sub.1B are received by the
non-inverting and inverting inputs of operational amplifier U.sub.1,
typically a TL062, commercially available. Resistor R.sub.6 and capacitor
C.sub.2 form a compensating network for U.sub.1 connected across the
inputs of U.sub.1. The J-FET pair function as a high impedance input stage
for U.sub.1 ; the J-FET pair Q.sub.1A and Q.sub.1B and operational
amplifier U.sub.1 operate in concert to form a high input impedance
operational amplifier. A filter network is formed comprising resistors
R.sub.8, R.sub.9, R.sub.10, R.sub.11 and R.sub.12, capacitors C.sub.4,
C.sub.5, C.sub.6 and C.sub.7, operational amplifier U.sub.2 (typically a
741, commercially available) and previously mentioned operational
amplifier U.sub.1 in conjunction with J-FET pair. The filter output Vo
appears at 64, which includes the operational amplifier U.sub.2 output as
filtered by network R.sub.13 in combination with C.sub.8 to work in
combination with preceding circuit components to effect a determined
overall filter response. The characteristics of the filter of FIG. 4 are
derived according to known engineering methods to provide a low-pass
Butterworth with a 3 dB point of 380 Hz and an overall gain below 380 Hz
of V.sub.o /I.sub.s =2.times.10.sup.7. A calibrate signal of predetermined
amplitude generated by calibration means 54 of FIG. 4 is provided at 66
into capacitor C.sub.1 ; when the calibrate signal is not provided, the
calibrate input 66 is grounded.
The present invention permits the filter output signal to be continuously
sampled at a rate desired, typically at the rate greater than that
specified by the Nyquist criteria according to the highest frequency
desired, e.g., if the highest frequency is about 380 hertz, a sampling
period of 1 millisecond will suffice. In addition, higher sample rates are
permissible as desired where the filter 70 output, after being processed
by analog-to-digital converter 32, is shown by signal 80 in FIG. 6, with
sampling points occurring at points 82, 84 and 86 between time intervals
t.sub.1 and t.sub.2.
Each of the filters as described above provide as an output, in response to
respective input signal from respective detectors in continuous wave fan
beam tomography systems, a continuous signal providing a best-estimate of
the radiation absorption along the path between said radiation source and
the respective detector at discrete points in time. The discrete points in
time are skewed in time, or have different periodicities, relative to said
sampling period for at least some of the filter signals.
The subsequent processing, digitization and display of the signal from each
channel of the data acquisition system is provided by means and according
to methods known in the art. Additional improvements in the image
reconstruction in the attached processing computer system 28 is
anticipated due to the increased information provided by the increased
sample rate beyond the minimum Nyquist rate, as well as the decreased
error signal from photon randomness in the filter output signal. These
enhancements may be made in a manner known in the art.
The construction of best-estimate reconstructed signals by continuous
filtering for detector signals having more complex spectral distributions
and in systems utilizing sampling rates at other than twice the highest
useable frequency are within the scope of this invention.
It is also within the scope of the present invention to sufficiently
over-sample the filter output signal so that a part of the above-described
filter or additional filter or correction processes and apparatus may be
included as part of and within the above-mentioned processing computer.
For instance, a filter may be formed within the processing computer
according to methods and apparatus known in digital filtering to add
several additional poles, or to provide phase correction characteristics
according to the characteristics of the discrete filter embodiment
described above.
These and other embodiments according to the present invention made by
those skilled in the art are within the scope of the invention, which is
not to be limited to what has been described except as defined by the
appended claims.
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