Circulation. 1998;98:634-641
(Circulation. 1998;98:634-641.)
© 1998 American Heart Association, Inc.
Clinical Investigation and Reports |
Myocardial Tissue Characterization After Acute Myocardial Infarction With Wavelet Image Decomposition
A Novel Approach for the Detection of Myocardial Viability in the Early Postinfarction Period
Aleksandar N. Neskovi
, MD;
Aleksandra Mojsilovi, PhD;
Tomislav Jovanovi, MD, PhD;
Jovan Vasiljevi, MD, PhD;
Miodrag Popovi, PhD;
Jelena Marinkovi, PhD;
Milovan Boji, MD, PhD;
; Aleksandar D. Popovi, MD, PhD, FESC
From the Cardiovascular Research Center, Dedinje Cardiovascular
Institute, Belgrade University Medical School (A.N.N., J.M., M.B., A.D.P.);
Belgrade University Faculty of Electrical Engineering (A.M., M.P.); and the
Institutes of Physiology (T.J.) and Pathology (J.V.), Belgrade University
Medical School, Belgrade, Yugoslavia.
Correspondence to Aleksandar D. Popovi, MD, PhD, FESC, FACC, Cardiovascular Research Center, Dedinje Cardiovascular Institute, Milana Tepica 1, 11040 Belgrade, Yugoslavia. E-mail epopoval{at}ubbg.etf.bg.ac.yu
 |
Abstract
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Background—Only a few texture
measures can be used for texture characterization of infarcted
myocardium and detection of reperfused
myocardium early after infarction. This study was conducted
to establish the relationship between texture properties of infarcted
myocardium and infarct-related artery patency by
quantitative computer analysis of 2-dimensional
echocardiographic images with the wavelet-based method
for texture characterization, evaluate the relationship between texture
properties and myocardial viability, and correlate histopathologic
changes after experimental infarction with the texture
measures.
Methods and Results—We analyzed 2-dimensional
transthoracic echocardiographic images in
18 patients at different time points after infarction using the wavelet
transform method. Regional wall motion of infarcted segments was
analyzed on a follow-up echocardiographic study
obtained 6 months after infarction. To verify the accuracy of the
proposed texture measure and energy difference cutoff value, we
prospectively evaluated another group of 19 patients. In addition,
histopathologic changes in 9 dogs with experimental infarction were
correlated with the texture measures. Sensitivity, specificity, and
accuracy of the wavelet method for detection of reperfusion in the
study group were 73%, 86%, and 78%, respectively, on day 2; 91%,
86%, and 89%, at 1 week; and 100%, 100%, and 100% at 3 weeks.
Among 9 patients with improvement in regional wall motion on a
follow-up study, 7 on day 2, 8 at 1 week, and 9 at 3 weeks were
classified into the reperfused group by the wavelet method.
Histopathologic features associated with the classification of
reperfusion by the wavelet method were infarct transmurality
(P=0.024) and degree of necrosis
(P=0.028).
Conclusions—Our clinical and experimental data suggest that the
wavelet method can be used to differentiate between viable
myocardium with recovery potential and definite myocardial
necrosis in the early postinfarction period.
Key Words: myocardial infarction • reperfusion • tissue
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Introduction
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Several studies have
demonstrated that myocardial infarction produces alterations in
myocardial tissue structure and composition,1
leading to changes in acoustical properties of the
myocardium. However, with standard 2-dimensional
echocardiographic examination, it is impossible to
differentiate nonfunctional infarcted myocardium with an
occluded infarct-related artery from reperfused, stunned, or
hibernating myocardium, which can recover either
spontaneously or after appropriate therapeutic interventions.
Furthermore, detection of a patent infarct-related artery by
coronary angiography is not sufficient evidence that
dysfunctional myocardium perfused by this artery is still
viable. Because the quality of standard ultrasound images precludes
accurate identification of myocardial reperfusion early in the course
of myocardial infarction, the search for additional sources of
information is still in progress.
We2 have previously shown that only a few
texture measures can be used for texture characterization of infarcted
myocardium and detection of reperfused
myocardium in the early postinfarction period. Among these,
measures calculated with the wavelet image decomposition method
revealed the best preliminary results3 and
therefore were selected for the current study. To the best of our
knowledge, no studies have assessed the application of the wavelet
transform method for detection of reperfused or viable
myocardium early after myocardial infarction.
The purposes of this study were as follows: (1) to establish the
relationship between texture properties of the infarcted
myocardium and patency of the infarct-related artery by use
of quantitative computer analysis of 2-dimensional
echocardiographic images with the wavelet-based method
for texture characterization; (2) to evaluate the relationship between
texture properties and myocardial viability, as assessed by follow-up
echocardiograms 6 months after infarction; and (3) to correlate
histopathologic changes after experimental infarction with the texture
measures.
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Methods
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Study Patients
The study group consisted of 18 patients with first acute
myocardial infarction (11 with a patent and 7 with an occluded
infarct-related artery) taken from our acute myocardial infarction
database.
Data Acquisition
We retrospectively analyzed 2-dimensional
echocardiographic images obtained 2 days, 1 week, and 3
weeks after infarction. All images were acquired on a commercially
available imaging system (Acuson 128) with a 2.5-MHz probe and
recorded on 0.5-in VHS videotapes. All recordings were made
by 2 echocardiographers; each was free to set the time-gain
compensation, gain, and adjustment during the recording to
optimize images visually. Depending on infarct location,
end-diastolic images from apical 4- and 2-chamber views
were used for data acquisition. Images recorded on videotapes were
digitized with 512x512 pixel and 256-gray-level resolution. As an
input into the texture analysis procedure, for each patient 5
samples of 16x16 pixels were taken from the infarcted area of the
myocardium and 5 from the area not affected by infarction
(Figure 1
). For this purpose, asynergic
segments were considered an infarcted zone. In a given patient, tissue
samples were taken from the same segments (initially assigned as
infarcted and normal). Samples were taken by the electrical engineer in
cooperation with experienced echocardiographers who were
blinded to patients' clinical and angiographic data. All texture
analysis and calculations were done by the engineer team,
without any knowledge of patients' history.
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Figure 1. Data acquisition. Transthoracic
echocardiogram, apical 4-chamber view. White and black squares
represent samples taken from the normal and infarcted
myocardium, respectively.
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Coronary Angiography
Coronary angiography was performed in all patients
before discharge. Perfusion of the infarct-related artery was assessed
by use of Thrombolysis In Myocardial Infarction (TIMI)
criteria.4 Successful reperfusion of the
infarct-related artery was defined as TIMI grade 3.
Texture Analysis
For calculation of the texture measures, we performed an image
decomposition with filter banks derived from wavelet functions (Figure 2).3 5 After
thorough mathematical analysis,3 we
selected energy calculated from the vertical-edge image
(ENGLH) as the texture measure to be used
in further classification.
Classification
For each analyzed patient, 5 tissue samples each were
taken from the area not affected by infarction and from infarcted
myocardial segments. Energy was computed for each sample. As a
quantitative measure of dissimilarity between 2 tissue groups (ie,
between normal and infarcted tissue), we have proposed the distance
function (D):
where 
1 and
2 are the texture measure
mean values for the tissue samples taken from normal tissue and
infarcted area, respectively; n1 and
n2 are numbers of tissue samples taken from
normal tissue and infarcted area, respectively; and
C1 and C2 are
the texture measure variances for normal and infarcted tissue,
respectively.
When tissue samples taken from infarcted myocardium and
from areas not affected by infarction are composed from similar
textural patterns, the random variables
1 and
2 have similar
distributions, and the distance between them (value of the D
function) is very small. On the contrary, when analyzed samples
have definite dissimilarity, the variables
1 and
2 have significantly
different distributions, and the distance between them will have higher
values. Thus, in this case, D represents the
quantitative measure of similarity between normal and infarcted tissue.
With the automatically determined2 D cutoff
value of 5.5, infarcted myocardium was classified as
reperfused (
5.5) or nonreperfused (>5.5).
Validation of the Wavelet Method
To assess the applicability of the proposed texture measure and
energy difference cutoff value in differentiating patients with and
without reperfusion, we prospectively evaluated another group of 19
patients (10 with a patent and 9 with an occluded infarct-related
artery) using the same texture measure and the same D cutoff
value. To examine the impact of image quality and various storage
conditions, we analyzed images of 10 healthy volunteers and 10
patients (5 with a patent and 5 with an occluded infarct-related
artery) obtained directly from the echocardiograph and the
videotape (Appendix).
Assessment of Viability
Because we have previously shown6
that regional wall motion of the infarcted zone after
thrombolysis improves up to 3 months after infarction,
all patients underwent follow-up echocardiographic
study 6 months after infarction to evaluate the relationship between
texture properties and myocardial viability. For each study, wall
motion was graded as normal, hypokinetic, akinetic, or dyskinetic and
improvement, deterioration, or no change of regional wall motion of the
infarcted area was noted. Improvement in regional wall motion of the
analyzed segments in the infarcted zone over time was
considered evidence of the viability of these segments. It was
considered that viability was successfully predicted by the wavelet
method if the patient was classified into the reperfused group and
subsequent improvement in regional wall motion was noted on a follow-up
study.
Experimental Study
Finally, to assess the relationship between histopathology and
the texture measures, we evaluated 11 dogs with experimental myocardial
infarction. The left anterior descending coronary artery distal
to the first diagonal branch was ligated and tightened to occlude the
artery. Dogs were divided into 2 groups: those with permanent occlusion
of the left anterior descending artery (5 dogs) and those with
reperfusion after 60-minute occlusion (6 dogs). The
echocardiographic protocol was the same as for the
patients: 2-dimensional echocardiographic images were
obtained on day 2 and at 1 and 3 weeks after experimental infarction.
Images were captured directly from the echocardiograph and
were analyzed in the same manner as for the patients.
Classification of the infarcted segments as reperfused or nonreperfused
was done with the same cutoff value as for the patients. Two dogs (1
with permanent occlusion and 1 with reperfusion) died before the end of
the experiment and were excluded from the study analysis.
Immediately after the echocardiographic examination at
3 weeks, dogs were killed, and the hearts were subjected to
histopathologic examination. An infarcted segment that was equidistant
from the center of infarction and from normal surrounding
myocardium was analyzed in both occluded and
reperfused dogs. Samples were paraffin-embedded and sections stained by
hematoxylin-eosin, Mason's trichrome, and elastica–Van Gieson. The
following histopathologic features were graded with a semiquantitative
scoring system: transmurality of an infarct, degree of necrosis, degree
of fibrosis (collagen content), and ratio of necrotic to preserved
capillaries. Transmurality was scored as 1 (infarct 50% of wall
thickness), 2 (infarct >50% of wall thickness), or 3 (100% of wall
thickness was infarcted). Degree of necrosis was graded by measuring
the extent of necrosis in 20 randomly chosen high-power fields (x400)
as follows: none (score=0) if there was no necrosis and mild (score=1),
moderate (score=2), or severe (score=3) if 33%, 66%, or >66%,
respectively, of the total area examined was necrotic. The
degree of fibrosis was graded with the same grading system: none
(score=0), mild (score=1), moderate (score=2), or severe (score=3). If
all capillaries within an examined area were preserved, the score was
0; if 33% of capillaries were necrotic, the score was 1; if 66%
of capillaries were necrotic, the score was 2; and if >66% of
capillaries were necrotic, they were scored as 3.
Statistical Analysis
Mann-Whitney U test was used to test the
differences in distance measures between patients with patent and
occluded infarct-related arteries, as well as to test the relationship
between classification results by the wavelet method and different
histopathologic features in the experimental study. Analysis of
distance measure changes over time was performed by 2-way ANOVA, and
the relationship between distance measure and wall motion of the
infarcted zone over time (with wall motion as a covariate) was
analyzed by repeated-measures ANOVA.
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Results
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Texture Properties of Infarcted Myocardium and Patency
of Infarct-Related Artery
Figures 3 and 4 show the application of the wavelet
method to nonreperfused and reperfused myocardial tissue, respectively.
With nonreperfused myocardium (Figure 3), a clear
difference between the normal (Figure 3a) and infarcted area (Figure 3b) can easily be seen. In all cases, the most prominent difference was
detected in the vertical-edge image
( f LH). However, no difference was
noted between the normal and infarcted area in reperfused
myocardium (Figure 4).
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Figure 3. a, Wavelet decomposition of normal
myocardium, taken from echocardiogram of a patient with an
occluded infarct-related artery. b, Wavelet decomposition of infarcted
myocardium, taken from echocardiogram of a patient with an
occluded infarct-related artery. Single image in first row
represents original texture image; in second row (from left)
are low-pass-filtered image
( f LL), vertical-edge image
( f LH), horizontal-edge image
( f HL), and corner image
( f HH).
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Figure 4. a, Wavelet decomposition of normal
myocardium, taken from echocardiogram of a patient with a
patent infarct-related artery. b, Wavelet decomposition of infarcted
myocardium, taken from echocardiogram of a patient with a
patent infarct-related artery. Explanation and abbreviations as in
Figure 3 .
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Differentiation of Patients With and Without Reperfusion
Distance measures for the study and validation groups are shown in
Table 1. Texture data for the energy
measure calculated from vertical-edge images, as well as the
relationship between classification results and perfusion status for
all patients, are shown in Tables 2 and 3. A significant decrease of the distance
measure over time occurred in reperfused
(
2=6.95, P=0.03) but not in
nonreperfused (2=0.88, P=0.65)
patients. Repeated-measures ANOVA that included all patients revealed
that regional wall motion changes over time had no impact on distance
measures (F=0.21, P=0.65). Sensitivity, specificity,
accuracy, and positive and negative predictive values of the wavelet
method for the detection of reperfusion in both the study and
validation groups are shown in Figure 5a and 5b.
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Figure 5. A, Detection of reperfusion by wavelet transform
method in study group. B, Detection of reperfusion in validation group.
C, Detection of viability by wavelet transform method in study group.
D, Detection of viability in validation group. Bars denote sensitivity
(SE), specificity (SP), accuracy (ACC), and positive (PPV) and negative
(NPV) predictive values of the method on day 2 and day 7 and at 3
weeks.
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Viability
On a follow-up study 6 months after infarction, 9 patients in the
study group and 8 in the validation group showed improvement in
regional wall motion of infarcted segments over time or after
revascularization procedures (2 patients from the
study group and 4 from the validation group underwent CABG surgery),
indicating the presence of viable myocardium; each of them
had a patent infarct-related artery. Patients with an occluded
infarct-related artery showed no improvement in regional wall motion of
the infarcted segments. Sensitivity, specificity, accuracy, and
positive and negative predictive values of the wavelet method for
detection of viability in both the study and validation groups are
shown in Figure 5c and 5d. Detection of viability by observed regional
wall motion improvement and the wavelet method is shown in Table 4. On the other hand, nonviability was
correctly predicted in 17, 18, and 15 of 20 patients on day 2, on day
7, and at 3 weeks, respectively.
Experimental Study
Histopathologic findings are shown in Table 5. Texture measures calculated from
vertical-edge images, as well as the relationship between
classification results and perfusion status for all dogs, are shown in
Table 6. Sensitivity, specificity, and
accuracy of the wavelet method for the detection of reperfusion were
100%, 50%, and 78%, respectively, on day 2; 80%, 75%, and 78% at
1 week; and 80%, 100%, and 89% at 3 weeks. Histopathologic features
found to be related to classification results by the wavelet method
were transmurality of an infarct (P=0.024) and degree of
necrosis (P=0.028). However, the density of preserved
capillaries (P=0.18) and collagen content
(P=0.58) did not correlate with the classification
results.
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Discussion
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It has been reported that infarct-related artery patency has
numerous beneficial effects: it improves healing of the infarcted
tissue and prevents infarct expansion and left ventricular
remodeling,6 7 8 preserves viability of
hibernating myocardial segments,9 and increases
electrical stability.10 To plan management
strategy in the postinfarction period, it is important to determine
infarct-related artery patency and whether infarcted segments are
viable or dead. Although there are several noninvasive markers of
successful reperfusion, they are not specific and reliable enough to
enable definite conclusions to be reached.11
Coronary angiography yields an accurate assessment of vessel
patency but does not provide any information about infarcted tissue
properties. On the other hand, viability can be assessed by low-dose
dobutamine or dipyridamole
echocardiography, PET, or follow-up
echocardiographic or radionuclide ventriculography
studies (detecting functional improvement of previously asynergic
segments that occurs spontaneously or after
revascularization procedures). However, there is
still a need for an additional method that could provide valuable
information regarding myocardial perfusion and viability simply and
noninvasively; texture characterization of the affected
myocardium is an attractive approach.
In the image-processing field, a number of methods for texture
characterization have been developed over the
years.2 12 Some of these techniques have been
used in medicine for the assessment of different pathological
conditions of the myocardium.1 For
example, recently it has been shown that short-lasting myocardial
ischemia is associated with an abrupt increase in myocardial
echodensity detectable by videodensitometric analysis applied
to standard transthoracic echocardiographic
images.13 Also, it has been shown that the cyclic
variation of relative integrated backscatter can be used to diagnose
recent myocardial infarction.14 Additionally,
ultrasonic tissue characterization was used successfully for diagnosis
of acute myocardial infarction in the coronary care unit,
showing results comparable to standard 2-dimensional
echocardiography.15 However,
data are scarce regarding the application of texture characterization
for detection of the extent of irreversibly damaged
myocardium in humans. Furthermore, to the best of our
knowledge, the value of the wavelet transform method for assessment of
viability early after myocardial infarction has not been
established.
Our data demonstrate that in the majority of patients, no difference in
myocardial texture existed between normal segments and reperfused
infarcted segments, whereas a significant difference between normal
myocardium and nonreperfused infarcted segments was found.
In addition, the majority of patients classified as reperfused by the
wavelet method showed regional functional improvement on follow-up
studies, indicating that functional recovery of infarcted segments can
be predicted by this method. Therefore, it appeared that this method
had potential to detect viable myocardium early in the
postinfarction period, providing additional information compared with
serial observation of regional wall motion improvement over time.
Initial evaluation of the method and classification were based on the
perfusion status of the myocardium. It is reasonable to
expect that the majority of patients with reperfusion have different
amounts of viable myocardium in the infarct zone; however,
reperfused myocardium is not necessarily viable. To clarify
what we really detect by the wavelet method (ie, what is the
histopathologic correlate of the energy difference between reperfused
and nonreperfused myocardium detected by the wavelet
method), we conducted the experimental study. The analysis we
performed revealed that the histopathologic features that have a major
impact on accurate differentiation between reperfused and nonreperfused
myocardium by the wavelet method were infarct transmurality
and the degree of necrosis. Therefore, it appears that this method may
differentiate nontransmural infarcts with mild to moderate necrosis,
containing different amounts of viable myocardium, from
transmural, severely necrotic infarcts without viable tissue. Because
reperfused myocardium shows less necrosis and less
transmurality, on the basis of our experimental and clinical data, it
is more likely that the energy difference between reperfused and
nonreperfused segments detected by the wavelet method reflects
viability as a consequence of reperfusion but not the reperfusion
itself. There were patients with a patent vessel in whom akinesis
persisted throughout the study, and yet there was a reduction in energy
difference, suggesting myocardial viability. It may be assumed that
myocardial structure and composition in these patients were preserved
such that the differences in acoustic properties and texture between
infarcted and normal segments were not significant, indicating
presumably hibernating myocardial segments.
Technical Considerations
A method for successful characterization of myocardial tissue
changes caused by infarction must be sensitive to detect minor changes
in intracellular structure and myocardial fiber
orientation.1 In addition, it must be relatively
insensitive to the quality of the echocardiographic
equipment, variability of gain settings and adjustment, and the
expertise of technicians performing the 2-dimensional
echocardiographic study. Another disadvantage is the
relatively poor quality of ultrasound images.2 16
Through numerous experiments with the different texture measures, we
have concluded that for analysis of myocardial tissue, the
wavelet-based approach performs better than other
techniques.2 3 Furthermore, ultrasound noise is a
random phenomenon, mostly affecting a single image point. Therefore, of
all images obtained through wavelet decomposition, the corner image
f HH (representing the
highest frequencies) is the most sensitive to noise. Because we do not
use the energy ENGHH, the results are also
applicable in the presence of noise or any high-frequency, localized
distortion. An important reason for the good performance of the
proposed method is the unsupervised nature of the classification
scheme, in which the decision whether reperfusion occurred or not was
made by comparison of only the tissue samples taken from the same
image. Therefore, changes of the gain and processing settings
throughout the study could not affect the results. Additionally,
reperfusion was not determined from the numerical values of texture
measures directly but was expressed through the value of the distance
function, representing the similarity between normal and
infarcted tissue. By using this classification criterion, we have made
the algorithm insensitive to the acoustic variability of
analyzed images. There are several additional reasons why
wavelet-based texture analysis may be adequate for application
in this setting. It has been shown that the wavelet transform is a
powerful analytical tool for analyzing singularities in
processes.5 17 The visual difference between
normal and infarcted myocardial tissue is barely distinguishable
because of minor changes in intracellular structure; the wavelet
transform is appropriate for "zooming in" these differences. Also,
the wavelet transform represents an image decomposition into 4
different orientations (Figures 2 through 4), which is an excellent way
to study myocardial fiber orientation.
Study Limitations
Texture characterization is highly dependent on the selection of
texture description operators, as well as on the selection and quality
of images and myocardial texture samples. In standard ultrasound
images, the most important characteristics of a given picture, such as
brightness, contrast, or texture, change along the abscissa and
ordinate. Some of these inequalities can be removed by image-processing
techniques. However, in this application, during the selection of
representative tissue samples for 1 class, it is
strongly desirable to take image samples only from an isolated
myocardial region, without great changes in cursor positions. Otherwise
the variability between texture measures calculated for a single class
could affect classification results. Additionally, the proposed method
is based on comparison to the wall that is clearly uninvolved in
infarction, which would probably make its application more difficult in
patients suffering from multi-infarct coronary artery
disease.
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Conclusions
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Myocardial tissue characterization by use of wavelet image
decomposition represents a novel approach for noninvasive
assessment of viability of the infarcted myocardium in the
early postinfarction period. Our clinical and experimental data suggest
that this method can be used for early differentiation between viable
myocardium with recovery potential and definite myocardial
necrosis. However, additional studies are necessary to confirm these
findings.
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Appendix 1
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Impact of Storage Conditions on Texture Analysis
To check the sensitivity of texture measures to the image
quality, noise, and videotaping, we analyzed a group of 10
healthy volunteers, capturing the same images both directly from the
echocardiograph ("direct images") and the videotape
("video images"). We took 30 samples from the top to the bottom of
the image (from the same positions in both images) and calculated
ENGHL and texture
ENGLH measures. By comparing the values
obtained from video and direct images, we observed the following: (1)
In both images, the variance of the ENGHL
measure was higher than the variance of
ENGLH (proving the selection of this
measure as a more reliable descriptor). This result was expected
because the characteristic ultrasound pattern exhibits different
behavior along the path of the acoustic pulse, resulting in prominently
different distribution of horizontal edges along the y axis
of an image. (2) Because the videotaping induces some blurring, texture
measures calculated from video images had consistently smaller
values. (3) As a result of the speckle noise and other stochastic
problems, both ENGHL and
ENGLH measures had higher variance in
direct images. Due to the low-pass-filtering nature of the videotaping
procedure, the speckle pattern was not prominent in the group of video
images. After median filtering of the direct images, as a simple
technique for speckle removal, the texture measures variance is
decreased, and their behavior was identical to the behavior of texture
measures calculated from the video images. This result indicates the
applicability of the proposed method to images obtained directly from
the ultrasound machine (when preceded by noise-removal filtering).
To check the applicability of the proposed solution, we
analyzed a group of patients after myocardial infarction, also
using images from the videotape and identical images captured directly.
A total of 10 patients were analyzed, 5 with a patent and 5
with an occluded infarct-related artery. On video images with the
ENGLH texture measure and the same cutoff
value of 5.5, reperfusion was detected in 4 of 5 patients, and 5 of 5
were diagnosed as nonreperfused. By analyzing tissue samples taken from
the same positions in directly obtained images, we detected reperfusion
in 4 of 5 patients, whereas 3 of 5 were diagnosed as nonreperfused.
However, it was observed that the distance between normal and infarcted
tissue was consistently smaller in direct images. When a new
cutoff value for direct images of 3.5 was established, reperfusion was
detected in 4 of 5 patients, and 5 of 5 were diagnosed as
nonreperfused. Therefore, it appears that the method is generally
applicable, but processing parameters have to be modified
depending on the image type and quality.
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Acknowledgments
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The authors would like to thank Drena Berakovi, RN, and
Izabela Mi
kovi, RN, for assistance in the experimental
study; we greatly appreciate their support and enthusiasm. Also, we
thank Zoran Popovi, MD, for his thoughtful discussion.
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Footnotes
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Presented in part at the 69th Scientific Sessions of the American Heart Association, New Orleans, La, November 10–13, 1996, and at the XIXth European Congress of Cardiology, Stockholm, Sweden, August 24–28, 1997, and published in abstract form (Circulation. 1996;94[suppl I]:I-735).
Received September 24, 1997;
revision received March 11, 1998;
accepted April 20, 1998.
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Abstract
Introduction
and 
, respectively. At the output of the
filter bank are 4 decomposed images
(f2jLL,
f2jHL,
f2jLH,
and
f2jHH).