Objectives: To understand;
1
How various images may be classified.
2
Basic DSA apparatus
3
DSA image processing modes
4
Formation of parametric images
5
Energy subtraction modes including SNR issues
6
Spatial frequency filtering-noise power spectrum
7
Basic ideas of image compensation
As time goes on, more and more radiological imaging techniques have
become implemented in digital format. Some techniques such as
computed tomography have been digital from their beginnings.
Following some general considerations regarding image classification,
this chapter will specifically deal with digital implementations of the
more traditional radiographic and fluoroscopic techniques.
There are several advantages to digital acquisition, processing and
storage of image information. Direct digitization of incoming data
eliminates the noise associated with intermediate analog storage.
Having the data in digital format permits quantitative processing and
generation of several derived images, formed from combinations of
single images, which may more specifically display some clinically
relevant subset of the available image information.
Examples include display of temporal, geometric or energy
dependence.
Digital storage is convenient for the purpose of rapid retrieval and
transmission of image information and may eventually lead to
replacement of a significant fraction of film use.
Image subtraction was introduced in the thesis of Ziedses des
Plantes in Holland circa 1930. The application involved the
elimination of confusing bone shadows which obscured vascular
information in cerebral blood vessel imaging (angiography). Film
images were obtained before and after the introduction of iodinated
contrast material into the cerebral arteries. A negative version of
one of the images was superimposed upon the other and a third
film was exposed yielding an image in which, presuming adequate
image registration, everything would cancel except the iodine. This
procedure, which is an example of simple first order time
subtraction, is illustrated in Figure 1.
Film Subtraction
Angiography
Ziedses des Plantes 1934
Negative of Pre Contrast Film
Post - Contrast
Positive Film
Subtraction Film
This illustrates how a priori knowledge about something of interest
in the image can allow for a more specific imaging procedure to
select the relevant information.
In a paper widely read by my mother and years of captive graduate
students, this concept of information selection through subtraction
was generalized to image variables other than time.
The image classification scheme which evolved from this approach
was called Generalized Subtraction Imaging and suggested several
new kinds of images which were subsequently implemented by our
group and others.
The basic idea is to consider the radiographic transmission image to be
a function of the variables x,y,z, time and energy. Consider the
relationship between images at two nearby points in the
multidimensional image space. This can be expressed as a Taylor
series as
By using pairs of images I and I’ with all but one variable held
fixed, images associated with all of the first order derivative terms
can be formed.
First order time subtraction, illustrated in Figure 1, is just one
example of this.
Dual energy imaging, to be discussed later, is another example.
In practice, the variable differences involved are larger than those
consistent with any quantitative use of the Taylor expansion
formula.
Its purpose is simply to display the possible image combinations
which may be formed. Its use has been primarily in categorizing
existing and new image processing and data acquisition schemes.
In addition, however, it stimulated the investigation of some of the
new images displayed in the expansion. We will discuss several
image processing schemes, pointing out the relevant terms in the
Taylor expansion as we go along.
Historical Background Digital angiography has been one of the
most successful applications of digital techniques to applications
formerly done in conventional radiographic or fluoroscopic
geometry. The events leading up to this development are of some
historical interest.
As shown in Figure 2, vascular disease was well known to the
ancients as illustrated by the varicose vein in the leg of a Greek god.
In those days, when there was the ever present desire to cut health
care costs, the gods just mailed in the parts needing repair in order to
avoid in-patient charges.
VARICOSE
VEIN IN THE
LEG OF A GOD
Amynos et al.
Circa 400 BC
VARICOSE
VEIN IN A GOD
Vascular HMO
More specialized images, generally involving more pieces of
required a priori knowledge may also be isolated.
For example a d2I/ dEdt image can be isolated using four images
having coordinates (E1,t1), (E2,t1),(E1,t2), and (E2,t2).
This kind of image is called a hybrid time-energy subtraction image
and was investigated as a means for eliminating soft tissue
swallowing artifacts in digital subtraction angiography of the
carotid arteries in the neck following intravenous contrast injection.
Early Examination of The
Cardiovascular System
EARLY
CARDIOVASCULAR EXAM
Franz von Mieris the Elder 1657
Wilhelm Conrad Roentgen
FIRST FILM ANGIOGRAM
Hascheck and Lindenthal 1896
Contrast
chalk
Patient Preparation
amputation
Exposure time
57 minutes
( Reimbursement Rejected
by Medicare )
FIRST ANGIOGRAM
First Angiogram in A Living Patient
Moniz , June 28, 1927
Film Subtraction
Angiography
Ziedses des Plantes 1934
Negative of Pre Contrast Film
Post - Contrast
Positive Film
Subtraction Film
EARLY IV ANGIOGRAPHY
EARLY IV ANGIO
AFRAID TO LOOK
Robb and
Steinberg
1939
Robb and
Steinberg
1939
Pont Neuf Toulouse
Intravenous Film Subtraction Angiography
Ducos de Lahitte
University of Toulouse
~ 1979
Intravenous Angiography
Analog acquisition - Off-line Computer Processing
Brennecke et al.
Kiel Kinderklinic
1976
University of Arizona
(When Mistretta was a post doc)
Intravenous Angiography
Digital Acquisition - Off-line Computer Processing
Ovitt et al
The University of
Arizona ~ 1977
Real Time Digital Video Image Processor --1976
Memory -- 0.25 megabytes
Intravenous Angiogram of
Human Carotids
1st Exam on UW
Real-time DSA
System
Dr. William Zwiebel, 1977
Real Time Digital Subtraction Angiography
Pre-Injection
Mask
Post-Injection
Image
IV DSA Image
University of Wisconsin circa 1979
Move to New Hospital -1979
View From DVIP Console
In New Hospital Site
EARLY PHOTO
SHOWING
THE NUMBER OF
PHYSICISTS REQUIRED
FOR FIRST IV-DSA
EXAM
Number of
Companies
Selling DSA
Equipment
FOUR
ZERO
1979
Philips
Technicare
CGR
ADAC
1980
~ THIRTY
•
•
•
Picker
Siemens
GE
Diasonics
American
Edwards
Omni
•
•
1981
After the Bird RSNA
Aaaaa! There gooes another batch of eggs Frank!
No wonder this nest was such a deal.
INTRA-VENOUS DSA
INTRA-ARTERIAL DSA
Arteriographic Complications in the
DSA Era
In 939 patients, IA DSA stroke rate
was 0.3%compared to 1.0 - 2.4%
using film angiography
JR Waugh and N Sacharias,
Radiology 1992; 182:243-246
Intravenous techniques are still occasionally used in connection with
patients who have obstructions which prevent arterial placement of the
catheter.
The disadvantages of the intravenous techniques are many. Large
amounts of contrast material, which is potentially toxic to the kidneys,
are required. Because the arterial section of interest might be
inadequately viewed in the chosen projection, repeat injections are
often required. This shortcoming of intravenous DSA has been
reduced in intravenous CT angiography which permits reformatting of
the data to provide alternate view angles.
Another difficulty, which will be illustrated later, is the possibility of
motion in the time, on the order of ten seconds, required for passage of
the contrast material from the artrial to the venous side. Often
misregistration occurs leading to obscuration of the arterial anatomy.
Typical apparatus for implementation of DSA is shown in Figure 8.
EFFECT OF INTERMEDIATE
ANALOG STORAGE
Direct Digital
Acquisition
KRUGER AND RIEDERER
p. 102-103
Digitization from
Analog Disc
DSA and its variations provide several examples of image processing
in the time domain.
This is basically the digital implementation of the old film subtraction
technique with a few key variations which ensure optimal image
quality. These include:
-Integration of adequate quantum information
-Logarithmic processing prior to image subtraction
-Subtraction of images prior to intermediate analog
storage of images
-Real time digital subtraction and enhancement of
images prior to display.
The logarithmic processing is required so that the iodine signal
isolated by the subtraction process is linearly related to the iodine
thickness tI rather than being modulated by the local image brightness.
In connection with this process it is necessary to make a first order
correction for scatter as illustrated in Figure 2 and the subsequent
equations.
For the pre-contrast case the output intensity is given by
(1)
Assuming that the iodine present in the post-contrast image is not
sufficient to significantly alter the scatter distribution we obtain
(2)
The scatter subtraction is accomplished by making the approximation
that the scatter field is uniform and adjusting the black level, the point
in the signal where the zeroth digital level is assigned. Applying this
subtraction, dividing by the input intensity, and taking the logarithms
results in
(3)
=
This image is usually called the mask M. Performing the same
operations on the post contrast image results in
(4)
=
Subtracting we obtain
CMμ t
I
I
(5)
which is a signal proportional to the iodine thickness. This signal may
be displayed as white or black and is typically enhanced digitally by
a factor of 8-16 prior to D/A conversion.
ILLUSTRATION OF
LOG PROCESSING
PRIOR TO
SUBTRACTION
KRUGER AND RIEDERER P.163
The mask mode operation is shown schematically in Figure 3.
Intravenous Angiogram of
Human Carotids
1st Exam on UW
Real-time DSA
System
Dr. William Zwiebel, 1977
The primary limitation to mask mode is misregistration of images due
to patient motion. Typically, a single mask is subtracted from all
subsequent contrast images.
If motion occurs, it is possible to reprocess the image sequence by
choosing alternate masks which were acquired after the motion.
If it is not possible to find such a mask which is relatively free of
iodine signal early in the sequence, one can often find a late mask
obtained after the iodine has begun to clear from the vessels of
interest.
Figure 4 illustrates this idea.
Because the alternate masks may contain some iodine, this will
subtract from the iodine signal leaving a result which is no longer
proportional to iodine thickness. However the resulting image is still
often adequate for diagnosis.
An example of remasking is shown in Figure 5. In this case, the carotid
arteries in the neck were obscured by patient motion during an
intravenous injection. By choosing a mask following the motion it was
possible to obtain an adequately registered subtraction image.
In general, the subtraction image I obtained from a series of images
obtained during the passage of contrast material can be written as
(6)
Assuming that the non-iodinated background anatomy signals are
constant during the contrast passage,
 α  0cancellation of the background
signal requires that
i
i
(7)
Noise reduction may be achieved when a series of images are obtained
by adding several images together to form a combined mask and a
combined contrast image as illustrated in Figure 6.
The noise per image reduces approximately as N1/2 where N is the
number of images integrated (assuming equal noise per frame). Note
that there can be unequal numbers of mask and contrast images
summed, as long as the sum of the weighting coefficients is zero as
stated in equation 7.
A potential problem with multi-frame integration is that resolution loss
may occur because of anatomical motion. The blood vessels may blur
out, or background anatomy may become misregistered as in Figure
5A.
In this mode the weighting coefficients are chosen to be the difference
between the current value of the iodine contrast curve C(t) at a chosen
point in the image, and its average value at that point as shown in
Figure 7.
Kruger has shown that this combination of weighting coefficients
optimizes signal to noise ratio. This mode produces somewhat
improved signal to noise ratio relative to integrated mask mode but
suffers from the same potential blurring problems.
When arterial and venous structures are simultaneously present in a
field of view as they are in intravenous examinations, modified
matched filters may be chosen to, for example, completely suppress
the venous signal, although usually with some degradation of the
arterial signal. Windham and coworkers have done extensive work in
this area.
This mode is an approximation to a true time derivative image and
shows short term changes in iodine contrast. It has been applied with
some success to heart wall motion studies. The mode and an integrated
version are shown in Figures 8A and 8B.
Figure 8A
Figure 8B
A
C
B
D
A convenient way of achieving a mode similar to the integrated TID
mode was developed by Kruger. In this mode all images in the past are
summed with weights which decrease for times more and more remote
from the present. Two such integrated images with different temporal
weightings are combined to produce an integrated time derivative
image.
The integration scheme for a single image is shown in Figure 10.
Current
image
Add
memory
Multiply
by a
Output
image
The first input image is stored in memory and proceeds out to the
display. This image is then multiplied by a weighting factor aand
added to the next input image. The sum is stored in memory,
displayed, and fed back once again to be weighted and added to the
third incoming image. For a series of input images Ii the output images
Oi are given by
O1 = I1
O2 = I2 +aI1
O3 = I3 + a(I2 +aI1)
O4 = I4 + aI3 + a(I2 +aI1)
aI3a I2a I1
For approximately constant image amplitude I = Ii the series can be
summed to obtain
(8)
The contribution of an early image at time t’ to the sum at time t is
exponentially decreasing with time t-t’ as shown in Figure 11.
The sum at time t may be described as the sum of the tails of the
earlier images and is given by a convolution integral
I(t)  I(t' )e -  t dt'  I  e βt
t

o
where the factor e- bt is called the impulse response function and
b = - lna /t where t is the time between images. The impulse
response function in the time domain is analogous to the line spread
function in the spatial domain.
This can also be thought of in terms of the weighting factors W(t-t’)
applied at time t to images from earlier times t’. This is shown in
Figure 12.
The recursively filtered image is relatively noiseless because of the
high degree of image integration. However the image has
considerable lag in the sense that moving objects can leave trails of
intensity behind them, much like the signals from early vidicon
cameras. The amount of increases as a approaches unity.
A mode similar to integrated TID can be implemented if two recursive
filters with different amounts of lag are subtracted. This is shown in
Figure 13.
Figure 13A shows the two recursive filters while Figure 13B shows a
weighted subtraction of the two which produces a current contrast
image associated with time t and a trailing mask separated by a time
which depends on the difference of the decay constants in each filter.
The temporal frequency response of such a dual recursive filter goes
to zero at temporal frequency  = 0, insuring that static background
anatomy will cancel out.
Depending on the amount of integration in the low lag image, very
high frequency information is also filtered out. Thus the a values may
be chosen to provide a filter which produces a frequency bandpass of
the desired width.
This is a process by which a two dimensional image is made, usually
from a series of images, to represent some quantity other than the
basic x-ray transmission. A simple example can be taken from time
domain DSA.
Consider the iodine contrast pass curve C(t) shown in Figure 14.
Two simple parametric images which can be easily formed are
Cmax(x,y) and tmax(x,y) showing images of the maximum achieved
contrast in each pixel and the distribution of times at which Cmax
occurred.
Images of tmax or the time to reach 1/2 Cmax are often taken to
represent contrast arrival time images. Delayed arrival times in the
heart muscle are associated with narrowing in the coronary arteries.
Images of Cmax and tmax can be obtained in real time using the
arithmetic logic unit (ALU) shown in Figure 15.
Greater of
A and B
Video
A/D
A
ALU
B
Tmax
memory
Updated Cmax
memory
In Figure 15 the incoming contrast is compared to the previously
stored contrast and the larger of the two is stored in the Cmax memory.
Whenever the Cmax memory is updated, the time of this new maximum
is stored in the tmax memory. These images may also be formed using
post processing of the digitally stored images.
One clinical application of parametric images of this type is in the
determination of blood flow, or usually ratios of blood flows at rest
and during stress. Stress is usually induced by exercise or a
pharmacological vasodilator designed to increase blood flow.
In a normal heart, the ratio of flows in these two states, called flow
reserve, is usually on the order of 4-5. When coronary narrowings
occur, they cause the downstream microvasculature to dilate. In that
case, the administration of some form of stress will no longer be able
to cause a significant increase in vasodilation and the flow ratio is
significantly smaller if not unity.
Examinations of this type are designed to add information to that
obtained by simple inspection of coronary angiograms which have
been shown to have a very large inter-observer variability with
regard to establishing the physiological significance of the observed
vessel narrowings.
Flow is usually modeled as shown in Figure16.
t
The equation shown is sometimes called the Central Volume
Theorem. The volume is taken to be proportional to the iodine
contrast in a region of interest in the myocardium.
The time is obtained from the tmax image or an image of the time to
1/2 Cmax.
Flow reserve images may be obtained from ratios of flow parameter
images formed from the equation in Figure 16.
Figure 17 shows an example of flow reserve images obtained before
and after occlusion of the circumflex coronary artery in a dog. This
artery feeds the section of the myocardium in the lower portion of the
image. The flow reserve value was essentially unity following
occlusion. Although the individual flow parameter images are not
quantitative because of unknown normalization factors, the flow
reserve images have been shown to correlate well with animal
experiments involving direct measurement of the coronary flow
reserve using electromagnetic flow meters placed on the arteries.
This is a technique designed to image specific materials by exploiting
knowledge of the energy dependence of the attenuation coefficient.
There are two major methods, k-edge subtraction and non k-edge
subtraction. Each of these has been implemented in a number of ways
for purposes such as iodine imaging, generation of tissue free or bone
free chest images and determination of bone mineral.
This was first implemented by Jacobson in Sweden in the 1960’s
using a point by point x-ray scanning technique designed to measure
endogenous iodine in the thyroid gland. In the early 1970’s Kelcz
sped up the technique by several orders of magnitude using filtered
quasi-monoenergetic beams and an image intensifier detector. In the
k-edge technique the primary objective is to image materials like
iodine which have k-edge attenuation coefficient discontinuities in
the diagnostic x-ray energy range.
The attenuation coefficients are qualitatively sketched in Figure 18.
Synchrotron Dual Energy DSA
RCA
WR Dix
DESY HASYLAB
By filtering the x-ray beam with materials such as iodine ( 33 keV Kedge ) and cerium (40 keV K-edge) it is possible, at the expense of an
order of magnitude loss in available beam intensity, to form fairly
narrow x-ray beams, also qualitatively sketched in Figure 19.
The iodine filter produces a low energy beam EL with most of the
radiation above the iodine k-edge removed and produces images with
very low iodine contrast.
The cerium filtered beam EH contains radiation predominantly between
the iodine k-edge and the cerium k-edge where iodine contrast is
optimal.
Consider passing these beams through serial thicknesses of iodine (tI),
bone(tb), and tissue (t) as shown in Figure 20.
Io
tI
t
tb
IH
IL
For each beam the output and input intensities are related by
I  I 0 e
(I t I  b t b  t t)
(10)
Defining the logarithms of the low and high energy beams as L and H
we obtain
(11)
(12)
In order to form a tissue cancelled image we form the image
combination which produces a zero effective tissue coefficient. This is
obtained by multiplying the high energy image by the ratio of the low
energy and high energy tissue coefficients, giving
The first term in brackets is zero. The second two terms represent the
effective attenuation coefficients for bone and iodine respectively.
Notice that although the bone contrast is reduced, it is not possible to
simultaneously cancel bone and tissue using a two beam approach.
Basically we have two equations but three unknowns.
An exception to this is the use of monochromatic synchrotron
radiation where beam energies very closely straddling the k-edge can
be formed. Such beams have been investigated with moderate success
for various applications including intravenous coronary angiography.
The two beam energy subtraction image is basically the dI/dE term in
the previously mentioned Taylor series.
Some research has been done using a third beam far above the k-edge
as shown qualitatively in Figure 21.
The third beam provides low iodine contrast and provides another
equation which permits bone as well as tissue to be canceled out. It
is of some historical significance that it was this type of image for
which the first real time digital video image processor, eventually
modified to perform DSA, was built.
The solution for the iodine image can be written as a linear
combination of two other energy subtraction images, one with tissue
canceled and one with bone canceled. This second order subtraction
corresponds to the d2I/dE2 term in the previously mentioned Taylor
series.
Most energy subtraction techniques presently employ a 2 beam non
k-edge approach which requires less filtration and provides increased
available beam intensity. In this case the beams used correspond to
energies E2 and E3 in Figure 21, although they are typically formed
without k-edge filtration. The lower energy beam is typically formed
at 60kVp, while the high energy beam is formed at 120 kVp with an
additional 3 mm of copper filtration to increase the average beam
energy and to render the transmitted fluence approximately equal for
both energies.
For these beams, typical parameters are,
For these values, the effective attenuation coefficients for the tissue
cancellation condition are, from equation 13,
Tissue is canceled completely except for any misregistration between
exposures and local variations in the energy dependent attenuation
coefficients due to beam hardening. Bone is somewhat suppressed by
about a factor of two relative to iodine.
Dual energy DSA is useful for cardiac imaging where motion makes
it difficult to maintain registration between contrast and mask images,
even when separate masks are used for each point in the cardiac cycle
(the so-called phase-matched mask mode). Registration is impossible
when the patient is consciously undergoing exercise which is a
common element of a left ventricular wall motion examination.
Figure 22 shows a comparison of a subject undergoing vigorous leg
exercise without suspension of respiration using time subtraction ( c
and d) and using dual energy imaging a and b.
Dual Energy
Time Subtraction
The time subtraction images suffer from extreme tissue
misregistration, primarily from the motion of the diaphragm. Notice
that in spite of the fact that this is a two beam technique, the ribs do
not present a serious distraction, although their signal must be taken
into account if quantitative analysis of the signals is undertaken.
The signal to noise ratio in an energy subtraction image used for
angiography is less than that for standard DSA time subtraction. This is
the price which must be paid for attempting to remove temporal
misregistration artifacts.
For time subtraction the difference image t is given in terms of the
60 kVp low energy image L by
(15)
The noise variance is then given by
     . 2 (60)
2
T
2
1
2
2
2
(16)
and the signal to noise ratio is given by
(17)
For energy subtraction, the image E is given by,
(18)
The noise variance is
(19)
For an image intensifier detector the high energy beam produces the
same signal size with fewer x-rays than the low energy beam.
Therefore the high energy image is noisier. Experimentally it is found
that
2E (120) . 1. 7 2 (60)
(20)
Therefore,
So
(22)
Since I(60) = 22 cm2/gm and the effective dual energy coefficient is
given by equation 14 as 14 cm2/gm, the effective dual energy
coefficient may be expressed as
14
  I (60) C
22
So,
14
I (60) C
S
22
S
%
. 0. 45
n E
n
2(60)
(23)
T
(24)
This indicates that the dual energy signal to noise ratio is less than
half of that for time subtraction. For some applications it is possible
to improve the dual energy signal to noise ratio.
One method employs blurring the high energy image. Since the high
energy image contains little iodine signal the iodine contrast is
affected little and the noise contribution from the high energy image
is reduced.
This is done at the expense of introducing some uncancelled high
spatial frequency artifacts into the dual energy subtraction image.
Another approach when processing a series of closely spaced dual
energy images is to average the two high energy images on either
side of the low energy image in order to reduce the noise in the
high energy image by the square root of 2.
A more powerful technique for dual energy noise reduction will be
discussed after we have introduced the concept of spatial frequency
filtering.
Original
Dual
Energy
For some time there was research and commercial interest in a mode involving
four images arranged to utilize the combined advantages of time and energy
subtraction. Some time around 1980 I was lying on the beach in Waikiki thinking
about which of the Taylor series terms might be advantageous to implement. I
considered the d2I/dEdt term as a possible improvement on DSA for the purpose
of removing m misregistration artifacts. Incorrectly, I reasoned that if there were
no motion, the time subtraction would cancel everything and that if there were
motion the dual energy tissue cancellation would still leave bone misregistration
artifacts. Based on this reasoning it was decided not to implement this mode.
Shortly thereafter Dr. William Brody and co-workers at Stanford
realized that in applications like carotid artery imaging and
abdominal imaging soft tissue motion is often unaccompanied by
bone motion. This occurs when the patient swallows following the
arrival of contrast material in the neck. It also occurs when the
bowels move.
The basic idea of hybrid imaging is to form a temporal subtraction of
dual energy images formed at two different times.
The dual energy images would remove potential tissue misregistration
while, in the absence of bone motion, the temporal subtraction would
remove the bone left uncancelled by the energy subtraction.
E-T
Subtraction
An example of a hybrid image is compared to a conventional DSA
image in Figure 23. (From Kruger and Riederer, Basic Concepts of
DSA). Note the tradeoff between improved artifact reduction but lower
SNR in the hybrid image.
Conventional DSA
Hybrid Time/Energy
The disadvantage of the hybrid technique, which eventually
relegated it to limited use is the fact that the signal to noise ratio is
down by another square root of two relative to dual energy imaging
because of the extra subtraction involved. This puts it at about one
third the signal to noise of the conventional DSA exam.
Recall that for equal image quality, in the absence of motion, an
increase in exposure by a factor of nine would be required to make
up for this SNR loss. This was too high a price to pay for occasional
improvement in motion artifacts, especially with the reasonable rate
of success of conventional DSA remasking.
Suppose that we have a digital image with a certain spatial frequency
content and noise per pixel. It is often useful to reduce the noise by
spatial averaging, provided that a decrease in resolution is acceptable,
for example if the image matrix allows for higher spatial frequencies
than are actually contained in the object Fourier transform. This can
be accomplished by a Low Pass Filter
This can be implemented by convolving the image with a two
dimensional function (kernel) which, for purposes of illustration we
will take to be a square. In this operation the intensity at all points
(x’,y’) is spread over a square of width a and the intensity at an
arbitrary point (x.y) receives contributions from all points (x’,y’) that
are within a distance determined by the kernel size as shown in Figure
24.
(x’,y’)1
y’
(x,y)
(x’,y’)2
x’
This amounts to the intensity at (x,y) being an average of the
intensities within an area equal to the kernel size centered at (x,y).
The convolved image IB(x,y) is related to the original image I(x’,y’)
by
I B(x, y)  I I(x', y') x (x' x)y (y' y)dx'dy'
(25)
wherex and y are one dimensional rectangle functions which in
general could have different dimensions.
We can write IB(x.y) as,
where IBy is an image blurred in only the y direction.
By the convolution theorem,
(27)
But since
This says that in frequency space the spatial frequency spectrum
is rolled off by the Fourier transforms of the kernel size
in each dimension. We know, for example, from our previous
calculations that the Fourier transform of a rectangle of width a is
given by
(31)
which may be regarded as the system MTF in the x direction for the
particular rectangular LSF chosen.
Therefore, for a kernel of width a,
What does the blurring do to the noise?
The noise
has a Fourier transform
Following blurring, we get
.
Since the noise at various frequencies adds in quadrature, the noise
variance is given by,
The quantity
is called the two dimensional Wiener noise power spectrum.
For x-ray noise prior to the detector W is constant over frequency
(white noise). Following the detector the noise variance at each
frequency is multiplied by the square of the detector MTF in each
direction.
When will a low pass filter improve signal to noise ratio? Consider a
single dimension for simplicity. Suppose the object spectrum and the
one dimensional Wiener noise spectrum look like those in Figure 25.
w
I
Kmax/2
kx
kx
kmax
If we apply a blurring kernel which has a sinc function which cuts off
just beyond kmax/2 we get the situation displayed in Figure 26.
w
IB
kmax/2
kmax
kmax/2
kmax
Since the filter affects W more than the object spectrum, the SNR is
improved following the filter.
Suppose we were looking for a small coronary artery passing over a
large contrast filled ventricle or over the top of the diaphragm. We
can use the fact that the spatial frequency spectrum of the artery
extends to larger frequencies than the larger objects in order to
preferentially visualize the artery. This can be done using a high-pass
filter which emphasizes high spatial frequencies.
This type of filter can be formed by subtracting a low passed version of
the original image from itself as shown in Figure 27.
I
k
Blur
Input image
I
-
I
k
k
Since the artery has a rather flat spectrum out to high spatial
frequencies, it will survive the filter, whereas larger structures will
be suppressed by the filter.
The effect if a high pass filter on a canine coronary angiogram is
shown in Figure 28.
Original
Dual Energy
High Passed
High Passed Dual Energy
Also shown for comparison is a dual energy version of the same
angiogram. In this case because much of the image dynamic range is
occupied by the diaphragm, which is canceled by the dual energy
process, the dual energy image provides even greater enhancement
than the high pass filter.
Suppose we have a pixel size of 0.25 mm and we wish to form a high
pass filter using a blurring kernel of 5 pixels for the low passed image.
The highest spatial frequency permitted by the Nyquist sampling
theorem is 1 line pair per two pixels or 2 line pairs / mm. The sine
function associated with the five pixel rectangle function will have the
form
with a equal to five pixels. This function has a zero at ka/2 =  or
f = 1/a = 1/1.25. The situation is summarized in Figure 29.
I(f)
Hypothetical
Object
spectrum
IB(f)
fmax = 2
IHP
High pass
Filtered
spectrum
1/1.25
2
Blurred image
spectrum
1/1.25
2
Another example of a high pass filter operation, often called
unsharp masking, is shown in Figure 30 which shows an example
from chest radiography.
Shown are the original image (A), the blurred image (B) and two
different amounts of high pass filtering corresponding to different
linear combinations of the original image and the high pass filtered
image (C and D). ( S. Balter, Medicamundi, 38/2).
Original
Moderate High Pass
25 x 25 Blurring
Strong High Pass
It was noticed by Kalender, in the study of dual energy CT (The
d2I/dzdE term in the Taylor Expansion) that since the tissue image and
the bone image isolated by the dual energy process were both linear
combinations of the basic high and low energy images, the noise in
these material-selective images was correlated.
He proposed a noise reduction algorithm whereby a high passed
version of one of the material-selective images was weighted and
subtracted from the other material-selective image.
Thus he formed a noise reduced tissue image TNR and a noise reduced
bone image BNR as
The weighting factors pB and pT can be found by explicitly writing the
images in terms of their component images, grouping correlated noise
terms and minimizing the noise variance ( see homework problem).
Combining correlated terms we get,
pb )
pbRT – Rb )
Adding in quadrature we get
(1-pb)2
pbRT – Rb )2
The cross terms go away because L and H are uncorrelated.
Notice that pt can be chosen to cancel either the low energy or
high energy noise. The optimal value lies somewhere between
and can be found by differentiating the variance with respect to pb .
The result is (homework problem #1)
pb
The amount of noise reduction depends on the amount of the
frequency spectrum contained in the high passed image.
The greater the frequency content of the high passed image, the
greater will be the noise reduction.
However, for high degrees of noise reduction, high spatial frequency
artifacts from the high pass filtered image begin to appear as
uncancelled edges in the dual energy image.
This approach was investigated in detail by McCollough (U. Of
Wisconsin, PhD thesis). Figure 31 shows the effect of noise reduction
on a tissue selective phantom image containing 15 cm of Lucite and a
barium loaded strip.
Shown are a basic temporal subtraction image(D), a basic dual energy
tissue subtracted image(C) and two degrees of noise reduction (A and
B).
Although the noise reduction improves on the basic SNR of the dual
energy image in C, neither of the noise reduced images approaches the
SNR of the time subtraction image in D. Because of the absence of any
bone in this phantom, the introduction of bone edge artifacts is not
evident in A and B.
An equivalent, but somewhat more intuitive version of the dual energy
noise reduction process was introduced by Macovski and co-workers
who formed a noise reduced dual energy image by using a
combination of a low passed dual energy image and a high passed
version of the so-called optimal signal to noise ratio OSNR image
which is an unsubtracted image formed from the high and low energy
images.The OSNR image may be shown to be given by (homework
problem #2)
(36)
The noise reduction scheme is shown schematically in Figure 32 where
the combination of the dual energy image at low spatial frequencies
and the OSNR image at high spatial frequencies is shown.
I(k)
Low passed dual
energy image
High passed
OSNR image
kc
k
The noise in the dual energy image is reduced by the low pass filtering,
while the noise added by the OSNR image at high spatial frequencies is
small because an unsubtracted, noise optimized image is used.
The cutoff frequency kc, where the transition between the dual energy
and the OSNR image is made is selectable. In general as it is
decreased the amount of noise reduction is increased, but the edge
artifacts from the OSNR image are also increased.
The optimal weighting of the high and low energy images can be
found as follows. Assume the ratio of weightings is c, i.e.,
OSNR = L + cH
The tissue signal will be St Lt + cHt
the noise variance will be
The SNR is then given by
Differentiating this with respect to c and setting the derivative
equal to zero gives a solution for c
c = H2L2/ L2H2
which leads to (aside from an overall multiplier)
Presently the most convenient way to obtain digital radiographs of
moderately high resolution, suitable for example, for chest radiography
is by means of photostimulable phosphor plates. These plates which
physically look like conventional intensifying screens are usually made
of a material like Europium doped barium fluorobromide.
When x-rays interact with this screen, predominantly via the
photoelectric effect, long lifetime metastable states are created. These
states form a latent image which remains on the image plate until the
readout process.
Recording of information on the phosphor plate is linear over four
orders of magnitude. When these states are stimulated with red light,
by means of a scanning laser, light is emitted and, following filtration
of red light, is detected by a photomultiplier tube.
Because the coordinates of the scanning laser are known, the image
intensity at each coordinate may be recorded and stored as a digital
image. Following readout the plate can be prepared for further x-ray
exposure by flooding it with light to remove the latent image.
Once the digital image is obtained hard copy may be obtained by
means of a laser film printer. Depending on the application, various
information recognition algorithms can be use to decide which part
of the digital image should be transferred to the film. The net result is
that computed radiographs are immune to variations in exposure.
This is illustrated in Figure 33 which compares film and computed
radiography images of the head obtained over a wide range of
exposures.
Clearly the computed radiographs are able to cope with the exposure
variations better than the film. Although films of wider latitude are
becoming available, it is unlikely that they will be able to match the
exposure latitude possible with phosphor plate system.
The exposure latitude of computed radiography has made it an
excellent choice for bedside radiography where exposure control is
difficult.
Computed radiography lends itself well to applications in which
quantitative computations are required. One example is dual energy
chest radiography where scatter and beam hardening corrections,
image combination and noise reduction computations must be done.
An example of such an application is shown schematically on the
next slide in Figure 34 where a cassette consisting of four phosphor
plates is used to acquire, in a single exposure, low and high energy
images from the front and back plates, respectively, with the two
intermediate plates acting as a filter to separate the energy spectra.
A gadolinium filter is used to provide some initial separation of the
incident spectrum into a low and high energy portions which are
further filtered by the phosphor plates.
Gadolinium
filter
Input
spectrum
Absorbed in
Front plate
Absorbed in
Rear plate
•
Phosphor
plates
Images obtained with this detector system are illustrated in Figure 35
(F. Zink, Ph. D Thesis, U. Of Wisconsin) which shows a low energy
image (A) and the tissue (B) and bone (C) images derived from the
front and back plate images following several processing steps
incorporating the corrections mentioned above.
Conventional
Tissue
Bone
A clinical study of lung nodule detection indicated that bone removal
produces a statistically significant increase in the detection rate for
lung nodules.
Many radiographic applications involve large variations in
transmitted intensity which are difficult for film to record. In
addition, SNR is highly non-uniform in the detected image.
One approach to overcoming this problem in chest radiography is
to use generic beam filters which attempt to filter the beam in the
lung, thus decreasing image dynamic range.
The problem with these filters is that they are not patient specific
and do not provide optimal compensation in many cases.
A scheme investigated by Hasegawa is shown in Figure 36. An
electronic detector was used to obtain a preliminary image of the
patient.
computer
Detector
patient
Cerium
Mask

printer
This was sent to a computer which drove a special printer equipped
with cerium ribbon which was deposited in multiple layers in a
spatially variable manner in order to form a patient specific
attenuation filter.
This device provided dramatic improvements in image quality in
poorly penetrated regions of the image as shown in Figure 37 which
shows a chest radiograph before and after compensation.
Unfortunately the printer, particularly the cerium ribbons proved to
be difficult to manufacture in a consistent manner.
Unprocessed image
Filter image
Compensated image
Another compensation scheme was developed by Plewes. This used
a scanning x-ray beam to expose the patient. Based on local
transmission information provided by an electronic detector,
feedback signals were supplied to the generator in order to adjust
the output.
The technique is illustrated in Figure 38.
X-ray tube
x and y
collimator
patient
film
detector
Aft
collimator
X-ray generator
computer
This scheme worked very well but suffered from poor utilization of
the x-ray tube. Following Plewes’ work, commercial systems using a
line-scanned instead of a point-scanned geometry were developed.
In at least one of the commercial versions, a series of computer
driven shutters along the scan line provide spatially variable patient
specific beam compensation.
Performance Characteristics of the
Scanning-Beam Digital X-ray (SBDX)
Cardiac Imaging System
Michael A. Speidel
November 13, 2002
Advisor: Michael S. Van Lysel
UW Department of Medical Physics
UW Cardiac Catheterization Research Laboratory
and Nexray Medical, Inc., Los Gatos, CA
SBDX System Overview
Detector
Array
Reconstructor
30 fps
Patient
X-ray pencil beam
Collimator
Scanning
Source
Target
Electron beam
© 2002 Michael A. Speidel
UW System
Multi-hole Collimator
(close-up)
© 2002 Michael A. Speidel
SBDX dose reduction strategy
Eliminate contrast-degrading x-ray scatter,
• scanning pencil beam, large airgap
without attenuating primary x-rays.
• non-ideal anti-scatter grid eliminated
High efficiency detector
• thick CdTe photon-counting array
Deliver x-rays over a larger patient area
• “reverse geometry” yields entrance dose reduction
© 2002 Michael A. Speidel
Wide-beam
vs.
Scatter fraction in region:
SF = S/(S+P)
Scanned-beam
Same P, minimal S
Cannot add
scatter to
neighboring
regions
© 2002 Michael A. Speidel
Cannot emit
scatter
SBDX
Fixed detector array
and source collimator.
EM-deflected focal spot.
150 cm
High frame rate scanning.
30,15,7.5 frames/sec
II/TV
“reverse geometry”
Mean temporallyintegrated intensity ~ 1/r2
from detector.
45 cm
Requires high speed
detector, reconstructor.
Tomographic effects.
© 2002 Michael A. Speidel