Download Blind deblurring of spiral CT images

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 7, JULY 2003
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Blind Deblurring of Spiral CT Images
Ming Jiang*, Ge Wang, Fellow, IEEE, Margaret W. Skinner, Jay T. Rubinstein, Member, IEEE, and
Michael W. Vannier, Member, IEEE
Abstract—To discriminate fine anatomical features in the inner
ear, it has been desirable that spiral computed tomography (CT)
may perform beyond their current resolution limits with the aid
of digital image processing techniques. In this paper, we develop a
blind deblurring approach to enhance image resolution retrospectively without complete knowledge of the underlying point spread
function (PSF). An oblique CT image can be approximated as the
convolution of an isotropic Gaussian PSF and the actual cross section. Practically, the parameter of the PSF is often unavailable.
Hence, estimation of the parameter for the underlying PSF is crucially important for blind image deblurring. Based on the iterative
deblurring theory, we formulate an edge-to-noise ratio (ENR) to
characterize the image quality change due to deblurring. Our blind
deblurring algorithm estimates the parameter of the PSF by maximizing the ENR, and deblurs images. In the phantom studies, the
blind deblurring algorithm reduces image blurring by about 24%,
according to our blurring residual measure. Also, the blind deblurring algorithm works well in patient studies. After fully automatic
blind deblurring, the conspicuity of the submillimeter features of
the cochlea is substantially improved.
Index Terms—Blind deblurring/deconvolution, cochlear implantation, computed tomography (CT), edge-to-noise ratio (ENR), EM
algorithm, Gaussian blurring, spiral/helical CT.
Spiral/helical computed tomography (CT) is advantageous in
visualizing and measuring bony structures of the middle and
inner ear preoperatively and geometric features of implanted
metallic devices postoperatively [1]–[4]. However, CT scanners
cannot resolve many important temporal bone details, especially
those millimeter- or submillimeter-sized features of the middle
and inner ear. It has been well established that digital deblurring
is an effective strategy to enhance image resolution retrospectively [5]. However, the underlying point spread function (PSF)
of the CT scanner is often unavailable in practice. Therefore, we
are motivated to develop a blind deblurring approach for resolution improvement of spiral CT slices.
On a single-slice scanner, it was validated that spiral CT can
be modeled as a spatially invariant process with a three-dimensional Gaussian PSF [5]. Due to the introduction of multislice
systems, we recently conducted a similar experiment on a multislice scanner, and obtained the same conclusion. Consequently,
an arbitrary oblique cross section in an image volume can be
approximated as a convolution of an isotropic two-dimensional
Gaussian PSF and the actual cross section
(1)
I. INTRODUCTION
T
HE TEMPORAL bone is a set of complex paired structures on the skull base which contains the organ of hearing
among others [1]. Treatment of severe-to-profound hearing loss
often employs a multielectrode cochlear implant, inserted in the
temporal bone. For those with this degree of hearing loss in
both ears who derive little benefit from acoustic hearing aids,
the American Medical Association and the American Academy
of Otolaryngology-Head and Neck Surgery have recognized the
cochlear implant as the standard treatment.
Manuscript received April 19, 2001; revised January 11, 2003. This work
was supported in part by the National Institute of Health (NIH) under Grant
R01 DC03590, the National Basic Research Program of China under Grant
G1998030606 and the National Science Foundation of China (NSFC) under
Grant 60272018. The Associate Editor responsible for coordinating the review
of this paper and recommending its publication was R. Leahy. Asterisk indicates
corresponding author.
*M. Jiang is with LMAM, School of Mathematical Sciences, Peking
University, Beijing 100871, China. This work was performed while he was a
visiting professor with CT/Micro-CT Laboratory, Department of Radiology,
University of Iowa, Iowa City, IA 52242, USA (e-mail: [email protected],
[email protected]).
G. Wang is with CT/Micro-CT Laboratory, Department of Radiology, University of Iowa, Iowa City, IA 52242 USA.
M. W. Skinner is with the Department of Otolaryngology-Head & Neck
Surgery, Washington University, St. Louis, MO 63110 USA.
J. T. Rubinstein is with the Department of Otolaryngology, University of
Iowa, Iowa City, IA 52242 USA.
M. W. Vannier is with the Department of Radiology, University of Iowa, Iowa
City, IA 52242 USA.
Digital Object Identifier 10.1109/TMI.2003.815075
is the
where
Gaussian function with standard deviation parameter ,
the noise term,
the oblique section of interest, i.e., the
is the actual cross section, which is the
blurred image, and
truth in the real world. An estimate of the real image is called
a restored or deblurred image.
In practice, the parameter is not precisely known for an arbitrary oblique cross section. Hence, we need a blind deblurring
approach to restore the real image. Blind deblurring/deconvolution is to recover an actual image without complete knowledge of the associated system PSF. Blind deblurring methods
were recently reviewed [6]–[8]. The blind deblurring methods
reviewed in [6], [7] require that the PSF and the actual image
must be irreducible. However, this critical assumption is invalid
in the Gaussian blurring case. The Gaussian PSF is reducible:
if
. This property might have
rendered the blind deblurring problem the most difficult. Even
in the noiseless case, the problem is well known as the ill-posed
inverse problem of heat transfer. Therefore, existing algorithms
for Gaussian blind deblurring have not been successful.
To appreciate this situation better, let us look at a popular
blind deblurring technique, also referred to as the double iteration scheme, developed by Holmes et al. [9]. As discussed in
[8], the convergence of this iteration scheme remains unknown;
the worse news is that, with an inappropriate initial guess, the
estimated PSF may converge to a function, making the deblurred image the same as the observed image . In [9], heuristic
constraints were added to incorporate some prior information
0278-0062/03$17.00 © 2003 IEEE
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 7, JULY 2003
about the PSF into the algorithm, but these means were not
effective.
There are Bayesian approaches that utilize prior information
about the image and the PSF, such as the total variation [10] and
other priors [11], [12]. These approaches introduce new problems of estimating the hyper-parameters. Furthermore, the convergence of the algorithms are not well understood [8]. In [13],
a spectrum domain approach was studied to deblur images obtained with Gaussian or Lorentzian PSFs. In this case, the PSF
is detected from one-dimensional (1-D) Fourier analysis of a selected profile in a blurred image. A noniterative image deblurring technique, “slow evolution constraint backward” (SECB),
uses this detected PSF to deblur the image. This approach only
works for a special class of images, and it requires much interactive work to adjust the parameters.
Our goal is to develop a blind deblurring algorithm to effectively restore Gaussian blurred CT images, especially images of
the temporal bone for cochlear implantation. Essentially, what
we need is a good estimate of the parameter . Then, we can
apply the established expectation-maximization (EM) deblurring algorithm [5]. To estimate the parameter , we believe that
the key is to analyze the edge and noise effects, based on the
classic results on edge and noise associated with EM iteration
[14]. We define an edge-to-noise ratio (ENR), and propose an
“ENR maximization principle” to estimate the optimal for
blind deblurring.
The outline of this paper is as follows. In Section II, we first
present the four key components of our approach: 1) Csiszár’s
axiomatic discrepancy measure; 2) the EM algorithm; 3) the
edge and noise effects with the EM algorithm; and 4) the ENR
maximization principle; then, we propose our blind deblurring
algorithm. In Section III, we describe the phantom and patient
data. In Section IV, we report numerical and experimental results. Primarily, the characteristics of the ENR is studied in extensive simulation to validate the proposed “ENR maximization
principle”. The behavior of the algorithm is also studied in the
case of noisy data. Then, the feasibility of our blind deblurring
algorithm is demonstrated in patient studies. In Section V, we
discuss relevant issues and future refinements of the methodology, and conclude the paper.
II. METHOD
A. Discrepancy Measure
For two nonnegative distributions and , the discrepancy
measure consistent with Csiszár’s axioms [15] is the -divergence, or generalized Kullback distance
(2)
where
is the pixel position in the image plane in our case.
This algorithm has a long successful history with various
important applications [16]–[18]. It is well known that the
algorithm converges in either the deterministic sense of the
-divergence or the statistical sense of the Poisson likelihood
its
[18], [19]. Additionally, given a positive initial guess
intermediate iterates are always nonnegative, and preserve the
. In this paper, we always
energy, i.e.,
use a positive constant image as the initial guess, whose value
is the mean of the input image.
The EM algorithm assumes nonnegative valued images, but
CT numbers in Hounsfield units (HU) can be negative. However,
the general blurring model still holds after real and observed
images are simultaneously offset by a constant. Specifically,
an appropriate positive constant, for example, 1024 HU, can be
added to a spiral CT image for nonnegativity. Then, deblurring
can be performed. After that, the same constant must be
subtracted from the deblurred image.
C. Noise and Edge Effects
A classic study on the noise and edge effects of the EM algorithm were performed by Snyder et al. [14]. The following summary is edited based on [14] and supported by our results: The
images obtained with the EM algorithm can be quite encouraging initially. The estimates appear to have better resolution,
signal-to-noise ratio, and contrast. However, as the iteration
process goes on, some disturbing “artifacts” become evident.
Images appear to be more “noisy” as the successive estimates
approach the maximum-likelihood estimate of . At the same
time, sharp transitions or edges in the image become greatly
accentuated with substantial overshoots, much like the wellknown Gibbs phenomenon. The noise effect appears as large
peaks and valleys seemingly randomly distributed throughout
the image. The edge effect appears as ridges and valleys that
follow edges in the underlying image.
Snyder et al. demonstrated that deblurring with a sieve for
a blurred version of the ideal function effectively reduced both
noise and edge artifacts [14]. The only additional processing for
the regularized EM algorithm is that an EM estimate is postfiltered to obtain a desirable estimate. In other words, in the case
of Gaussian blurring we can improve the EM algorithm in the
following way. First, EM iterations are performed with a different Gaussian kernel. Then, the deblurred image is blurred by
be the real blurring value. Let
another Gaussian kernel. Let
, , and
are related by
(4)
are the kernel widths of the Gaussian PSFs
where , , and
called deblurring, sieve, and resolution widths, respectively. The
as follows:
algorithm then iterates with
B. EM Algorithm
Assume the linear space-invariant blurring model (1) in the
nonnegative space, the EM algorithm iterates as follows:
(3)
where
.
and
(5)
After
with
iterations, the final result is obtained by postfiltering
is the restored image at iteration
(6)
JIANG et al.: BLIND DEBLURRING OF SPIRAL CT IMAGES
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Although the choices of the sieve and resolution widths were
not dictated by any existing theory, the following qualitative
comments can be made:
• “The overshoot (at edges) is seen to be a weak function of
the sieve; in general, the overshoot increases slightly with
wider sieves” [14].
• “The overshoot is a strong function of the resolution
width; the overshoot decreases rapidly as the resolution-kernel width is increased” [14].
• “The overshoot increases with iteration number” [14].
• “An assumed density that is too narrow unintentionally results in an estimate of a blurred version of the radioactivity
distribution; an assumed density that is too wide introduces an unintentional sieve, and the estimate produced is
of the presieve intensity unless a postfilter corresponding
to the mismatch is applied; such an estimate can be quite
noisy in appearance” [14].
D. Edge-to-Noise Ratio
To quantify the noise effect, we use Csiszár’s axiomatic discrepancy measure. The noise effect is defined as the discrepancy
of a blurred image and its mean. We can estimate the mean as
where
is the image deblurred
by the EM algorithm with iterations and the deblurring .
The noise effect with respect to a deblurring and an iteration
number is, thus, expressed as
(7)
To quantify the edge effect, we compare a deblurred image
and an estimated mean
of the
blurred image
(8)
Heuristically, this measure characterizes changes near edges
after deblurring.
may result in
Choosing by simply maximizing
a deblurred image with exaggerated edges and unacceptable
noise, since the noise effect is not included in the object function. Clearly, we need a balance between the edge effect
and the noise effect
. This consideration leads to the
following “edge-to-noise ratio” (ENR, in the same spirit of the
signal-to-noise ratio)
(9)
Based on the ENR, we have the following.
ENR Maximization Principle: The optimal parameter
for deblurring should be so chosen that the
is
maximized.
E. Blind Deblurring Algorithm
Our algorithm consists of two stages: 1) preparation, and 2)
restoration. The first stage is to determine the parameters for the
second stage. The second stage applies the ENR maximization
principle to find the parameter and deblur an image. Specifically, we have the following.
ENR-Based Blind Deblurring Algorithm:
First Stage. Preparation:
Step 1.1. Initialization:
Design the phantom(s);
Specify the permissible range
[
] of ;
Choose an image deblurring
residual measure.
Step 1.2. Estimate the optimal iteration
number .
Second Stage. Restoration:
Step 2.1. Input a blurred image.
by
Step 2.2. Estimate the optimal
.
maximizing the
Step 2.3. Deblur the image with the
obtained in Step 2.2.
Since the ENR depends on a deblurred image, the choice
of the iteration number is important to estimate the deblurring
kernel . In the first stage, we determine an optimal iteration
number in an average sense for a class of images. This task is
done in numerical simulation with an appropriately designed
phantom and an image deblurring residual measure. Note that
the phantom must be representative of the class of images to be
processed, and summarize our domain knowledge effectively.
In the second stage, the search for the optimal deblurring
is formulated as a 1-D maximization problem, given an itera] can be estimated based
tion number . The range [
on the data from CT quality assurance tests [5]. The choice of a
1-D maximization algorithm depends on the user’s preference.
” which
In this paper, we use the Matlab function “
is a combination of golden section search and parabolic interpolation. To compute the ENR, the algorithm needs to run the EM
algorithm for each value generated by the 1-D optimization
algorithm.
The first stage is a one-pass process. The parameters obtained
from the first stage can be repeatedly used in the second stage to
deblur images of the same class. In practice, results from Step
2.2 may be used in Step 2.3.
III. MATERIALS
A. Phantom of the Cochlea
Since our main interest is to deblur sectional CT images of the
temporal bone, especially the cochlea, we utilize an idealized
cross section of the human cochlea as shown in Fig. 1(a) [5]. The
upper image represents a horizontal histological section through
one cochlea, while the lower one represents a vertical section
through another cochlea. The phantom was made as follows.
Decalcified and celloidin embedded, grossly normal, right temporal bones from two adults were serially sectioned, one horizontally and the other vertically. The sections were then stained
with hematoxylin and eosin. A midmodiolar section from each
cochlea was projected at 40 times onto a drawing paper. Then, a
tracing of the three main structures was made, which are the
cochlea scalae, soft tissue and bone. A transparent precision
ruler (0.5 mm) was then projected onto the paper, and the tick
marks were traced to show the magnification factor. The draw-
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 7, JULY 2003
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 1. Original, blurred, and deblurred images of the phantom of the cochlea. (a) Original image. (b) Blurred image with
(c) = 0:4 and n = 30, (d) = 0:4 and n = 80, (e) = 0:4 and n = 120, and (f) = 0:4 and n = 140.
ings were then digitally scanned into Adobe Photoshop (Adobe
Systems Inc., Mountain View, CA), scaled to 0.1-mm square
pixels, and combined into one image of 100 100 pixels. Mean
CT numbers for fluid (perilymph and endolymph in the cochlear
scalae), soft tissue and bone were estimated from real spiral CT
scans as 443, 214, and 2384 HU, respectively, and then assigned to corresponding classes in the combined image.
B. Patient Data
The patient was scanned using a Toshiba Xpress/SX spiral
CT scanner (Toshiba Corp., Tokyo, Japan). The imaging protocol uses 1-mm collimation and 1-mm table feed per gantry
rotation. Images were reconstructed via half-scan interpolation
at 0.1-mm longitudinal interval. A 18-cm field of view (FOV) is
first used, and then restricted to a 51-mm FOV via direct reconstruction. As a result, isotropic voxels of 0.1 cubic millimeters
are obtained.
IV. RESULTS
In Section IV-A, we validate the ENR principle by computing
the ENR as a function of and in numerical simulation with
the phantom of the cochlea. The accuracy of the estimated
deblurring is also studied. In Section IV-B, we describe real
results on blind deblurring with patient data. Specific issues
], determination
include specification of a range [
of the optimal iteration number , and the computational time.
In Section IV-C, we study the robustness of the algorithm in
is
presence of image noise. In the following, the unit of
is [0.08, 0.6].
mm, and the range of
A. Validation
to
1) ENR Distributions: The ENR distributions with respect
and are computed via extensive numerical computation
= 0:4. Deblurred image with
and plotted for visualization and analysis. The process is as
follows.
1. For each
ranging from 0.1 to 0.5 mm
with step length 0.05 mm, the phantom
of the cochlea is blurred with the PSF
, producing
.
is added by
2. Each blurred image
.
Poisson noise, degrading to
is deblurred by the
3. Each image
from
EM algorithm with deblurring
0.08 to 0.6 mm with step length of
from
0.005 mm and iteration number
10 to 200 with step length of 5. The
.
results are
,
values are computed
4. For each
.
as
distributions are plotted.
5. The
0.2 and
Fig. 2 contains representative ENR profiles for
0.45 mm, respectively. Based on these data, it is observed that
for each of those fixed iteration numbers from 10 to 200, there
in the interval
exists a unique global maximum of
increases with
[0.08, 0.6], and the maximum of
the iteration number . The same observations can be made for
values under the above test conditions.
other blurring
2) Estimation Accuracy: Given the ENR distributions computed above, we can readily find the maximum as follows:
from 0.1 to 0.5 mm with
1. For each
step length 0.05 mm, and for each
from 10 to 200 with
iteration number
step length 5, find the maximum point
with
from 0.08 to 0.6
of
with step length 0.005 mm; the maximi-
JIANG et al.: BLIND DEBLURRING OF SPIRAL CT IMAGES
841
(a)
Fig. 2.
(b)
ENR distributions keyed to the true blurring kernel . (a) ENR distribution with respect to (a) and n for = 0:2 and (b) and n for = 0:45
zer is taken as an approximation to
the true maximum point of
in the interval [0.08, 0.6], denoted
.
as
2. The estimation error is defined as
(10)
3. The root-mean-squared error (RMSE) is
computed by
become evident. Hence, the iteration number
, which
is established above for the most accurate estimate of the true
blurring kernel , may not necessarily produce the best image
quality when it is used in the blind deblurring algorithm.
Because our goal is to develop a “completely” blind deblurring technique for image quality as good as possible, the following strategy is designed to find the optimal iteration number
. We use the RMSE to measure the image discrepancy of two
images. The RMSE measure is defined as
(12)
RMSE
RMSE
(11)
The results are presented in Fig. 3. In Fig. 3, it can be seen that
is smaller
for small iteration numbers the estimated
increases with the iteration
than the actual value ,
becomes
number , and for large iteration numbers ,
values tested except
,
greater than . For all the
there is an iteration number such that the estimation bias is close
to zero. Furthermore, the RMSE of the errors reaches a global
. Hence, there is no need for a larger iteraminimum at
tion number to produce an accurate estimate of .
B. Applications
1) Specification of the Permissible Interval for : Based
on our earlier experience [5] and recent literature, the in-plane
and through-plane Gaussian standard deviations are between
0.2–0.4 mm. Since those values are subject to change due to
many factors including the location of a region of interest, a
safe setting of the permissible deblurring interval should be
.
sufficiently large. Therefore, we set
2) Determination of the Optimal Iteration Number: There
are two reasons for an optimal iteration number. First, as demonstrated in Section IV-A, the estimated deblurring increases
with the iteration number. Second, as discussed in Section II-C,
as the iteration number increases, the noise and edge effects
for two images A and B. The following blurring residual is defined to measure the image quality change after deblurring a
blurred image:
RMSE
RMSE
(13)
and are the
where denotes the iteration number and
as defined in
phantom, its blurred version, and
is, the better
Section II-D, respectively. The smaller
the deblurred image quality. Different values are estimated
according to the ENR maximization principle with different
iteration numbers. Then, we choose the iteration number that
leads to the least blurring residual as the optimal iteration
number.
Fig. 4 shows the image blurring measures obtained from our
deblurring experiments using the phantom of the cochlea, where
0.2, 0.3, and 0.45,
15–70 with step length of 5,
real
and the blurring residuals are computed of the images deblurred
with values in Fig. 3. Then, the means of the blurring residuals
for each are obtained
Mean blurring residual
(14)
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 7, JULY 2003
(a)
(b)
(c)
(d)
Fig. 3. Estimation error e( ; n) and RMSE as functions of the iteration number n = 15 to 70 with step length of 5. Estimation errors for = 0:2, (b) =
0:3, and (c) = 0:45. (d) RMSE as a function of the iteration number n.
It can be observed in Fig. 4 that the iteration number
yields the least blurring residual for the class of images in our
application, and the mean blurring residual is reduced to about
76% by our blind deblurring algorithm. In other words, the reduction of image blurring is about 24%.
,
, and
3) Patient Studies: With the parameters
determined in Section IV-B1 and Section IV-B2, the blind deblurring algorithm can be directly applied to patient data. It is
found in our studies that the blind deblurring algorithm consistently produces excellent deblurring outcomes. As shown in
Figs. 5 and 6, anatomical features are substantially clarified.
4) Computational Time: Our blind deblurring code is in
MatLab on a Windows 2000 Dell workstation with 1-GHz
Pentium III processor. The original data are converted from
Analyze format to raw binary data via Analyze™ [20]. The
total blind deblurring time is 1390 s for Fig. 6. It appears
that our algorithm is impractical at the first glance, but the
time is for a complete blind deblurring procedure without any
user’s interaction. Usually, it only takes 2–5 min to produce
satisfactory images, since the maximum of the ENR function is
easy to attain given the parabolic shape of the ENR functional
for a fixed (see Fig. 2).
C. Robustness
To evaluate the noise tolerance of our blind deblurring algorithm, we use the same phantom image , set the blurring
, generate the blurred image
, and add the
Gaussian noise with different standard deviations to . Then,
we estimate the optimal deblurring from the noisy image by
. Table I lists the
the ENR maximization principle with
noise level , estimated deblurring , estimation error , RMSE
measures of blurred image and deblurred image with respect to the phantom image , as well as blurring residuals
after blind deblurring. The noise level range from 0 to 80 HU is
selected based on clinical CT data.
It is found in Table I that for low noise levels the estimated
values are very close to the truth. Also, the estimated is fairly
stable with respect to the noise level change.
JIANG et al.: BLIND DEBLURRING OF SPIRAL CT IMAGES
843
(a)
(b)
(c)
(d)
Fig. 4. Image quality improvements as the percentage change of blurring in terms of RMSE. Blurring residuals for (a) = 0:2, (b) = 0:3, and (c) = 0:45.
(d) Means of the blurring residuals.
V. DISCUSSIONS AND CONCLUSION
In terms of the sieve and resolution widths, the value essuggests use of
timated by the ENR principle with
the resolution width larger than the sieve width, i.e., the deblurring width should be smaller than the blurring width. Based on
the studies on the effects of sieve and resolution widths [14], a
deblurring closer but smaller than the real is preferred for
better image quality. Fortunately, Fig. 3 shows that the estimated
are generally smaller than
deblurring values with
the real blurring . As a result, the EM algorithm converges
more rapidly, as pointed out by Snyder et al. “In general, we see
more rapid convergence of the EM algorithm when the width
of the resolution kernel exceeds the width of the sieve kernel”
[14, p. 236]. This is an additional merit of our blind deblurring
algorithm.
is not symmetric in its
Since the discrepancy measure
arguments, we can have alternative definitions of noise and edge
effects by swapping its arguments. Moreover, the discrepancy
can also be measured by the Euclidean distance. Although the
current ENR-based algorithm already performs well, the performance of other ratio measures is of interest for further study
[21].
The blind deblurring algorithm can be accelerated using
parallel computing techniques. One can search for the optimal
deblurring in several subintervals, and switch the searching
processes to other subintervals with appropriate signaling. The
present implementation is for proof-of-concept, and not optimized for speed. Even with simple parallel programming, the
blind deblurring time should be greatly reduced. Furthermore,
ordered-subset techniques may be applied in image and/or data
domains for major speed gains [22].
We emphasize that the ENR idea may be applicable to deblurring algorithms other than the EM algorithm. An essential
point we make in this paper is that a priori information about the
actual image and the quantification of the edge and noise effects
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(a)
Fig. 5. Blind deblurring of an image through the left temporal bone. (a) Original 200
and = 0:33.
(b)
2 300 CT image through the left cochlea. (b) Blind deblurred with n = 30
(a)
(b)
Fig. 6. Blind deblurring of an image in the region of the basal turn of the cochlea. (a) Original 300
(b) Blind deblurred with n = 30 and = 3:54.
2 260 CT image through the basal turn of the cochlea.
TABLE I
ESTIMATED DEBLURRING AT DIFFERENT NOISE LEVELS
JIANG et al.: BLIND DEBLURRING OF SPIRAL CT IMAGES
can be utilized to significantly improve the ill-posedness of the
blind deblurring problem.
In conclusion, we have developed a blind deblurring algorithm to improve spiral CT image resolution for cochlear implantation. This algorithm is based on the ENR maximization
principle, and proved to be remarkably effective in the case of
Gaussian blurring. The utility and robustness of our algorithm
are demonstrated in numerical simulation and patient studies.
Further studies are underway to extend and refine our methodology for various imaging applications.
ACKNOWLEDGMENT
The authors would like to thank T. Frei of the Department of
Radiology, University of Iowa, for technical assistance, and the
anonymous referees for important constructive comments.
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