ABSTRACT 
 
Title of thesis: RADIATION DOSE REDUCTION STRATEGIES FOR 
INTRAOPERATIVE GUIDANCE AND NAVIGATION USING 
CT 
 
Avanti Shetye, Master of Science, 2007. 
Thesis directed by: Dr. Raj Shekhar 
Department of Electrical and Computer Engineering 
 
The advent of 64-slice computed tomography (CT) with high-speed scanning makes CT a 
highly attractive and powerful tool for navigating image-guided procedures. Interactive 
navigation needs scanning to be performed over extended time periods or even 
continuously. However, continuous CT is likely to expose the patient and the physician to 
potentially unsafe radiation levels. Before CT can be used appropriately for navigational 
purposes, the dose problem must be solved. Simple dose reduction is not adequate, 
because it degrades image quality. This study proposes two strategies for dose reduction; 
the first is the use of a statistical approach representing the stochastic nature of noisy 
projection data at low doses to lessen image degradation and the second, the modeling of 
local image deformations in a continuous scan. Taking advantage of modern CT scanners 
and specialized hardware, it may be possible to perform continuous CT scanning at 
acceptable radiation doses for intraoperative navigation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
RADIATION DOSE REDUCTION STRATEGIES FOR INTRAOPERATIVE 
GUIDANCE AND NAVIGATION USING CT 
 
 
By 
 
Avanti Satish Shetye 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the 
University of Maryland, College Park in partial fulfillment 
of the requirements for the degree of 
Master of Science 
2007 
 
 
 
 
 
 
 
 
 
 
 
 
Advisory committee: 
Professor Raj Shekhar, Chair 
Professor Rama Chellappa 
Professor Jonathan Simon
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Avanti Satish Shetye 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ii
Dedication 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
?To my dearest Aai and Pappa, and to the loving memory of my brother Yogendra...? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iii
Acknowledgements 
 
 
I extend my sincere appreciation toward my advisor, Dr. Raj Shekhar for giving me the 
wonderful opportunity of working in the field of medical imaging. Through his patient 
guidance, encouragement and innovative ideas, he created a dynamic environment in the 
lab that challenged me to accomplish my research pursuits and developed in me a deep 
respect for innovation. My interaction with him has made me confident to face challenges 
in my professional career with a positive attitude. Thank you Dr. Shekhar for all that you 
have done for me!! 
 
I thank Prof. Rama Chellappa and Dr. Jonathan Simon for agreeing to serve on my thesis 
committee and for sparing their invaluable time reviewing my manuscript. Special thanks 
to Prof. Andre Tits at the University of Maryland, Prof. Kenneth Lange at the UCLA and 
Dr. Jeffrey Fessler at the University of Michigan for their prompt responses to my 
research queries.  
 
I express my heartfelt gratitude toward Bulent Bayraktar, Adam Covitch and Abraham 
Cohn at Philips Medical Systems, Ohio and Pavan at the University of Maryland for their 
assistance in providing experimental data for this project. I thank my lab-members Will, 
Jianzhou, Vivek, Yash and Peng for sharing their thoughts and ideas on technical matters. 
 
On a personal note, I would like to thank my beautiful friends Rupali, Om, Pankaj, Arun, 
Nirmala and several others for being a wonderful support system during my days of 
distress. I would like to acknowledge the love and support of my sweetheart Tushar, who 
 iv
courageously endured all my eccentricities. Finally, I would like to acknowledge the love 
and blessings of my family over all these years: my parents Sudha and Satish Shetye, my 
late brother Yogendra, my aunts Smita Maushi and Pushpa Maushi, and my late 
grandparents, Bai Aaji, Baba Ajoba and Atya Aaji. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v
Table of contents 
 
Dedication............................................................................................................................ii 
Acknowledgements............................................................................................................iii 
Table of contents..................................................................................................................v 
List of figures......................................................................................................................vi 
1. Introduction and motivation........................................................................................ 1 
2. The reconstruction process .......................................................................................... 4 
2.1. Conventional approach to CT reconstruction .......................................................... 5 
2.2. Statistical approach to CT reconstruction................................................................ 6 
3. Dose reduction...............................................................................................................7 
3.1. MLEM Algorithm.................................................................................................... 7 
3.2. Local deformations .................................................................................................. 8 
3.3. Gradient descent optimization ............................................................................... 10 
4. Results .......................................................................................................................... 12 
4.1. MLEM reconstruction of Shepp-Logan phantom.................................................. 12 
4.2. MLEM reconstruction of abdominal phantom ...................................................... 13 
4.3. Metal artifact reduction.......................................................................................... 18 
4.4. Feasibility of a continuous CT scan (Further dose reduction)............................... 21 
5. Discussion..................................................................................................................... 33 
6. Scope for further investigation through the extension of MLEM algorithm........ 35 
References........................................................................................................................ 38 
 
 
 vi
List of Figures 
Figure 1: The geometry of a typical 3GCT scan: the x-ray tube and detectors rotate, with 
the axis of rotation running from the patient's head to toe [9]............................................ 4 
Figure 2: Schematic of a 4G CT scanner............................................................................ 5 
Figure 3: A 512 x 512 digital Shepp-Logan phantom. ..................................................... 14 
Figure 4: Visual comparison of reconstruction quality..................................................... 15 
Figure 5: PSNR comparison between FBP and MLEM. .................................................. 16 
Figure 6: FBP reconstruction (left) and MLEM reconstruction (right) of abdominal 
phantom at 200 mAs. ........................................................................................................ 16 
Figure 7: FBP reconstruction (left) and MLEM reconstruction (right) of abdominal 
phantom at 25 mAs. .......................................................................................................... 17 
Figure 8: PSNR comparison between FBP and MLEM for abdominal phantom............. 17 
Figure 9: Digital Shepp-Logan phantom with high attenuation pixel at location (190,295). 
(highlighted for clarity)..................................................................................................... 18 
Figure 10: Parallel beam sinogram of the digital phantom of Figure 9 with a high- 
intensity pixel (number of projections in degrees against number of detectors). ............. 19 
Figure 11: Metal artifact comparison................................................................................ 20 
Figure 12: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (1
st
 data set).......................................................................... 22 
Figure 13: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 12)........................................................................................................ 23 
Figure 14: Cost function as a function of the number of iterations for Figure 12. ........... 23 
Figure 15: PSNR as a function of number of iterations for Figure 12.............................. 24 
Figure 16: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (2nd data set). ...................................................................... 24 
Figure 17: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 16)........................................................................................................ 25 
Figure 18: Cost function as a function of the number of iterations for Figure 16. ........... 25 
Figure 19: PSNR as a function of number of iterations for Figure 16.............................. 26 
Figure 20: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (for abdominal phantom)..................................................... 26 
Figure 21: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 20)........................................................................................................ 27 
Figure 22: Cost function as a function of the number of iterations for Figure 20. ........... 27 
Figure 23: PSNR as a function of number of iterations for Figure 20.............................. 28 
Figure 24: Reduction of dose with fewer projections. Original deformed image (a), 
Reconstruction using 90 (b), 60 (c), 45 (d), 36 (e), 30 (f) projections.............................. 29 
Figure 25: Difference image of the original deformed image with: its initial estimate (a), 
its estimate after convergence using: 90 (b), 60 (c), 45 (d), 36 (e), 30 (f) projections. .... 30 
Figure 26: Convergence of the const function using various subsets of projections........ 31 
Figure 27: A zoomed-in version of Figure 26 from iteration 20. ..................................... 31 
 vii
Figure 28: PSNR as a function of the number of iterations for subsets of projections. 
Image quality is unchanged down to 30 projections......................................................... 32 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1
CHAPTER 1 
Introduction and motivation 
The method of choice for many surgical procedures has shifted from traditional open 
surgery to the use of less invasive means, a transition facilitated by the introduction of 
minimally invasive techniques more than a decade ago. Such procedures are often 
performed through 3 or 4 small skin ports (keyhole-size holes) instead of the 6- to 8-inch 
incisions required for traditional surgery [1]. The results are reduced trauma to the body, 
shorter recovery times and lower costs. However, the utility of such procedures is limited 
without a clear representation of the anatomy undergoing the procedure. The ability of 
the clinician will be greatly enhanced if three-dimensional (3D) visualization of this 
anatomy is available to guide such procedures [2]. 
 
Computed tomography (CT), a widely used diagnostic technique, is known to provide a 
highly accurate volumetric representation of the anatomy, with good contrast resolution. 
A CT scanner can create instantaneous 3D representations of the internal anatomy with 
good contrast resolution. This gives CT an edge over other imaging modalities in terms 
of continuous visualization of and navigation through structures. Some minimally 
invasive procedures utilize this benefit by acquiring a preoperative CT scan for guidance. 
This approach is limited, because it does not provide updated information on 
intraoperative anatomic deformations and deformations since the time of preoperative 
CT. A continuous CT-guided approach can represent intraoperative anatomy accurately, 
but such scanning is practical only if radiation is reduced to a minimal level with a high 
image reconstruction speed. Commercially available CT scanners employ a filtered 
 2
backprojection (FBP) technique for image reconstruction. Although useful in many 
imaging applications, the FBP technique does not allow dose reduction without 
significantly degrading image quality. Continuous CT with FBP reconstruction, then, 
would expose both patient and practitioner to elevated levels of radiation. FBP also 
causes streak artifacts when metal is in the field of view, for example during surgery.  
 
The motivation behind this study is to utilize the benefit of 3D visualization achieved 
through CT, but at a greatly reduced radiation dose without compromising image quality. 
Iterative techniques using maximum likelihood are proven to replicate Poisson statistics 
for positron emission tomography, single-photon emission computed tomography and CT 
[3]-[8]. Although statistical reconstruction is computationally expensive, the suboptimal 
FBP approach is certainly not an acceptable one for reconstructing noisy projection data. 
This study suggests two dose reduction strategies for developing a minimally invasive 
surgical system under a continuous CT guidance and elimination of metal artifacts 
resulting from surgical tools with the use of tracking tools. Our first strategy is the 
achievability of dose reduction through replacement of FBP with a statistical approach 
using maximum likelihood expectation maximization (MLEM) for image reconstruction. 
Our second strategy is the achievability of dose reduction for continuous CT through 
reduction in the number of projections using gradient descent optimization to iteratively 
model the local intraoperative anatomic deformations. 
 
The reconstruction process is described in chapter 2 striking distinctions between two 
widely used approaches to CT reconstruction. The theory behind our dose reduction 
 3
strategies is outlined in chapter 3 followed by the results in chapter 4. Inferences from 
this study and some practical issues are discussed in chapter 5. Another novel method for 
dose reduction that combines the two strategies is currently under investigation and is 
presented in chapter 6. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4
CHAPTER 2 
The reconstruction process 
Inside a typical 3
rd
 generation (3G) CT scanner is a gantry that has an x-ray tube on one 
side and arc-shaped array of detectors mounted on the opposite side. The x-ray photons 
emitted by the tube are captured by the detectors after being attenuated through the object 
under consideration to generate projection data. Image reconstruction is the process of 
determining the attenuation coefficients at all locations in the cross-section of the object 
using available projection data. Several such closely spaced cross-sections are stacked 
together to generate a volumetric representation of the object. CT is frequently used for 
diagnostic purposes. A pictorial representation of a typical 3G CT scan is demonstrated in 
Figure 1. 
 
Figure 1: The geometry of a typical 3GCT scan: the x-ray tube and detectors rotate, with 
the axis of rotation running from the patient's head to toe [9]. 
 
 5
A typical 4
th
 generation (4G) scanner consisting of a stationary ring of detectors with a 
rotating x-ray source is shown in Figure 2 [10]. 
 
Figure 2: Schematic of a 4G CT scanner. 
2.1. Conventional approach to CT reconstruction 
 
FBP, the conventional approach to CT reconstruction, uses the Fourier slice theorem to 
arrive at a closed-form deterministic solution to finding attenuation coefficients. The 
underlying assumption behind this theorem is that each projection represents an 
independent measurement of the object. The details can be found in [11]. The advantage 
of FBP is that the process of reconstruction can be started as soon as the first projection 
has been measured, speeding up the process and reducing the requirements for storage. 
FBP reconstruction produces high-quality images at high radiation doses. However, the 
image quality begins to deteriorate as the x-ray dose is reduced. Dose reduction is a 
crucial requirement for the application of CT in interventional purposes, where patients 
and practitioners will be exposed to continuous radiation over the duration of surgery. 
 
 6
2.2. Statistical approach to CT reconstruction 
 
The process of photon generation in an x-ray tube can be approximated using the Poisson 
distribution. Iterative techniques such as MLEM capture the stochastic variations in 
photon counts accurately (unlike the deterministic FBP approach) yielding more accurate 
reconstructions at much lower radiation doses. Maximum likelihood has been shown to 
have excellent theoretical properties that model the statistical nature of CT in a realistic 
manner [7]. The objective of this algorithm is to maximize the complete likelihood of the 
photons entering each pixel along the projection ray, given the number of photons 
detected by the detector at the projection, parameterized by the current estimate of pixel 
intensities. The new estimate of the pixel intensity can be approximated to a closed-form 
solution. The original MLEM algorithm is presented in brief in the next chapter. For a 
detailed description of the original algorithm, the interested reader is referred to [7]. 
 
 
 
 
 
 
 
 
 
 
 7
CHAPTER 3 
Dose reduction 
3.1. MLEM Algorithm 
Our algorithm has been developed based on the Lange & Carson [7] framework. The 
concept is described for parallel beam geometry and can be extended easily to the fan 
beam case. The MLEM algorithm is part of our first dose reduction strategy. 
 
The number of photons detected by scanning air provides a fair approximation to the 
number of photons generated by the x-ray source. If W
i
 is the number of photons leaving 
the source, all W
i
 photons will be detected in the absence of an attenuating object. Then, 
in the presence of an attenuating object, if Y
i
 is the number of photons detected, by 
Beer?s law, each photon leaving the source has an equal probability of reaching the 
detector. This probability is expressed as: 
?
=
?
?
i
Jj
jij
l
i
ep
?
  ,                                                (1) 
where ij
l
 is the length of intersection of the i
th
 ray with the j
th
 pixel, 
j
?
is the intensity 
(i.e., attenuation coefficient) of the j
th
 pixel and 
i
J
 is the set of all pixels traversed by 
the i
th
 ray. 
 
Because Y
i
 follows a Poisson distribution, the entire log likelihood can be reduced to 
??
?
?
?
?
?
?
?
?
?
?
?+?
?
?=
?
?
?
i
iii
Jj
jiji
l
i
YWYlYeWYg
i
i
Jj
jij
!lnln),(ln ??
?
.            (2) 
 8
The strict concavity, which suggests the existence of a maximum of this likelihood, can 
be established by the non-negative definiteness of the matrix with elements 
?
?
?
?
?
=
i
iik
ik
Jk
Jkl
a
..........0
........
.                                            (3) 
 
In the MLEM algorithm, a reconstruction grid of uniform intensity is used as the initial 
estimate. Iterating on the reconstruction grid, the log likelihood is maximized and the 
maximizing image estimate is used as an initial estimate for the next iteration. The closed 
form solution at the 
th
n )1( + iteration is expressed as: 
( )
()
?
?
?
?+
+
?
=
Ji
ikikik
Ji
ikik
n
k
lNM
NM
i
2
1
1
? ,                                     (4) 
where 
ik
M and 
ik
N  are the expected number of photons entering and leaving pixel k and 
are determined using Beer?s law (Eq. 1). 
3.2. Local deformations 
 
In the context of minimally invasive surgery, if the anatomy were stationary, a 
preoperative scan would suffice. However, the anatomy is subject to change due to 
intervention and involuntary motion. Continuous (near real-time) guidance and 
navigation would require a CT scanner to be operated continually at very high frame 
acquisition rate. If the frame rate is significantly high, the imaged anatomy will have 
undergone only a slight redistribution of pixel intensities between successive frames. 
Starting with the final reconstructed image of the previous time-frame, a good estimate at 
 9
the current time-frame can be obtained by modeling the deformations between the current 
and the previous time-frames using available projection data for the current time-frame.  
 
A free form deformation (FFD) model of [12] using B-splines is used to model the local 
motion between successive time-frames. The underlying idea of FFDs is to deform an 
object by modifying the translation vectors of a coarse mesh of control points throughout 
the object. The resulting deformation when interpolated over the fine mesh of pixels 
yields a smooth and continuous deformation. B-splines provide a local control over 
deformation unlike thin-plate splines. The resulting FFD can be written as  
?? ++
=
3
0
3
0
,)()(),(
mjliml
vBuByxT ? , (5) 
where the image space is defined by a set { }YyXxyx <?<?=? 0,0|),( , ? denotes a 
mesh of 
yx
nn ? control points 
ji,
? separated by a uniform spacing ? , 
??
1/ ?=
x
nxi , 
? ?
1/ ?=
y
nyj , 
? ?
xx
nxnxu // ?=  and 
? ?yy
nynyv // ?=  and 
l
B  represents the 
th
l basis function of the B-spline 
6/)(
6/)1333()(
6/)463()(
6/)1()(
3
3
23
2
23
1
3
uuB
uuuuB
uuuB
uuB
o
=
+++?=
+?=
?=
.                                    (6) 
 
A large spacing of control points enables modeling of global non-rigid deformations and 
a small spacing of control points enables modeling of local non-rigid deformations. 
 
 10
3.3. Gradient descent optimization 
 
In a gradient descent minimization algorithm, steps are taken iteratively in the current 
direction of the negative gradient of the cost function )(
t
f ? . 
)(
1 ttt
f
t
????=?
?+
?
, (7) 
where ?  is a positive step-size parameter,
t
?  is a set of translations of the mesh of 
control points ( )
T
nn
yx
,2,11,1
,...,, ???  in the x- and y-direction at the 
th
t iteration, gradient 
)(
t
f
t
??
?
 denotes a vector of partial derivatives 
T
nn
ttt
yx
fff
?
?
?
?
?
?
?
?
?
??
?
??
?
??
,2,11,1
)(
,...,
)(
,
)(
???
and 
()
T
. denotes transpose. 
 
A Radon transform is always unique when sufficient samples of it are available. In two 
dimensions, if a sufficient set of Radon transform samples is known, then the Radon 
transform is adequately specified and the cross-section function comprising the pixel 
intensities can be determined by inverting the Radon transform [13]. Hence the cost 
function chosen for optimization is the sum of squared differences between scanner-
projection data of the deformed image and the Radon transform of the image estimate. 
(Note that the projection data is the radon transform of the actual deformed image).  
 
A good initial estimate of the image is provided by the final reconstructed image from the 
previous time-frame. The initial deformation vector 
t
?  for the coarse mesh of control 
points is set to 0 . The vector 
t
?  is updated using Eq. 7 in the current direction of the 
negative gradient of the cost function, thus improving its estimate iteratively. A smooth 
 11
continuous deformation is obtained from the vector 
t
?  through B-spline interpolation 
(Eq. 5 and 6). The image, used in the calculation of the cost function, is updated through 
bilinear interpolation of the previous image estimate using the current deformation 
vector.  
 
The step-size,
?
, is varied iteratively to avoid convergence to a local optimum solution. 
A good starting estimate for the step-size was empirically found to be 0.01. If the current 
value of cost function is better (less) than the previous value, the image is updated and 
step-size is increased by a factor of 10 for the next iteration. A small step-size leads to a 
slower convergence. So, to accelerate convergence, the step-size is adaptively changed 
depending on how well the current step-size performs. If the current value of cost 
function is worse than the previous one, the step size is reduced by half until a better 
estimate is obtained. The process is repeated until the terminating condition occurs. A 
terminating condition is said to have reached if the cost function changes by less than 0.5 
for 5 successive iterations, or if the number of iterations exceeds 200, whichever occurs 
first. To ensure convergence to global minimum, annealing techniques need to be 
investigated. 
 
 
 
 
 
 
 12
CHAPTER 4 
Results 
The reconstruction algorithms were applied to simulated data from the digital Shepp-
Logan phantom and to real projection data from an abdominal phantom representing real 
anatomy. The reconstruction quality was assessed using power signal-to-noise ratio 
(PSNR) calculated as: 
),(
)12(
log10
2
10
BAMSE
PSNR
bitdepth
?
= , and                                     (8) 
()
2
11
),(
MN
BA
BAMSE
M
i
N
j
ijij??
==
?
= ,                                          (9) 
Where M x N represents the number of pixels in image A and B, A
ij
 represents the 
intensity of (i,j)
th
 pixel of A and B
ij
 represents the intensity of (i,j)
th
 pixel of B. 
4.1. MLEM reconstruction of Shepp-Logan phantom 
 
A 512 x 512 digital Shepp-Logan phantom was generated in MATLAB and projection 
data was simulated using Beer?s law (Eq. 1). Expectation of noise in low-dose sinograms 
was estimated by fitting a Poisson distribution to the difference between sinograms of 
images obtained from the low-dose simulator at 200 mAs and at lower doses. This 
Poisson noise was scaled to the dynamic range of phantom and added to the simulated 
projections for the digital phantom to generate noisy data resembling low-dose (low tube 
current) projections, with the assumption that sinogram noise follows Poisson 
distribution. Reconstructions using the MLEM algorithm yielded better results in terms of 
 13
the PSNR values with the original phantom as the reference image than did 
corresponding reconstructions using FBP. 
 
The digital phantom used in our study is shown in Figure 3. Reconstructions at 11mAs 
using FBP and MLEM are shown in Figure 4(a) for a visual comparison. To test the 
reproducibility of our results, reconstructions at 15mAs using the same 2 methods are 
shown in Figure 4(b). At each of these doses, MLEM led to higher contrast resolution, 
mimicking that of the original image. PSNRs for these two algorithms at a range of dose 
levels are summarized in Table 1. A quantitative comparison of the reconstruction 
qualities achieved through FBP and MLEM is delineated by means of a plot in Figure 5. 
The comparison shows that MLEM outperforms FBP at any given dose level. Note that a 
tube current setting of 11mAs is the lowest achievable dose on a Siemens dose simulator. 
[Courtesy: Baltimore Veteran Affairs Medical Center, MD] 
4.2. MLEM reconstruction of abdominal phantom 
 
An abdominal phantom was scanned using a Philips Brilliance 40-slice CT scanner at 
120 kV and tube current varying at random from 25 to 250 mAs at the following scanner-
console settings. Axial scanning was done at 2-sec cycle time with standard resolution, 
16 x 2.5 mm collimation and slice thickness of 5 mm. The number of samples per view 
was 672 with 1160 views evenly spanned on a circular orbit of 360
o
. Raw un-
preprocessed fan beam data were extracted using scanner software and altered to parallel 
beam data. The PSNR values suggest that the image quality of MLEM reconstruction 
degrades less precipitously than that of FBP as the dose level is reduced from 250 to 25 
 14
mAs. Figure 6 and Figure 7 provide visual assessments of FBP and MLEM 
reconstructions. A quantitative assessment is detailed in Table 2 and shown in Figure 8. 
 
Figure 3: A 512 x 512 digital Shepp-Logan phantom. 
 
Table 1: 
PSNR comparison between FBP and MLEM for the Shepp-Logan phantom 
 
 
 
 
 
 
 
 
Dose (mAs) 
PSNR for FBP 
(dB) 
PSNR for 
MLEM (dB) 
11 30.08 36.98 
15 31.18 37.67 
20 32.73 38.56 
25 33.09 38.83 
30 33.97 39.50 
40 34.88 39.96 
50 35.86 40.13 
70 37.00 40.67 
85 37.26 40.90 
100 37.36 40.99 
150 38.56 41.07 
 15
 
(a) FBP reconstruction at 11 mAs (left) MLEM reconstruction at 11 mAs(right). 
 
 
(b) FBP reconstruction at 15 mAs (left) MLEM reconstruction at 15 mAs (right). 
Figure 4: Visual comparison of reconstruction quality. 
 
 16
25
30
35
40
45
050100150200
Radiation dose in mAs
P
S
N
R
 in
 d
B
FBP MLEM
 
Figure 5: PSNR comparison between FBP and MLEM. 
 
Figure 6: FBP reconstruction (left) and MLEM reconstruction (right) of abdominal 
phantom at 200 mAs. 
 17
 
 
Figure 7: FBP reconstruction (left) and MLEM reconstruction (right) of abdominal 
phantom at 25 mAs. 
 
31
32
33
34
35
36
37
38
39
40
41
250 200 150 100 85 70 60 50 40 30 25
Radiation dose in mAs
P
S
N
R
 in dB
FBP MLEM
 
Figure 8: PSNR comparison between FBP and MLEM for abdominal phantom. 
 
 
 18
Table 2: 
 PSNR comparison between FBP and MLEM for abdominal phantom 
Dose (mAs) 
PSNR for FBP 
(dB) 
PSNR for MLEM 
(dB) 
250 36.90 Inf 
200 36.63 39.75 
150 36.51 39.20 
100 36.46 37.85 
85 36.34 37.31 
70 36.30 36.93 
60 36.23 36.40 
50 36.19 36.37 
40 36.08 35.65 
30 35.97 34.79 
25 35.85 34.02 
4.3. Metal artifact reduction 
 
To demonstrate metal artifact reduction, a high-attenuation object was introduced in a 
512 x 512 digital Shepp-Logan phantom at pixel location (190, 295) shown in Figure 9. 
Figure 9: Digital Shepp-Logan phantom with high attenuation pixel at location 
(190,295). (highlighted for clarity). 
 
The projection data simulated using Beer?s law (Eq. 1) was reconstructed using the 
MLEM algorithm, depicted in Figure 11 (b). With the prior knowledge of the location of 
 19
the high-attenuation object, the MLEM algorithm was able to accurately eliminate the 
FBP algorithm-generated streak artifacts as in Figure 11(a) by disregarding the 
projections passing through the pixels occupied by the metal to compute the likelihood. 
The approach becomes practical if a priori knowledge of the location of rigid metallic 
tools and their attenuation coefficients in the field of view of the scanner is available 
using specialized commercial tracking tools (such as those marketed by Polaris). 
 
 
Figure 10: Parallel beam sinogram of the digital phantom of Figure 9 with a high- 
intensity pixel (number of projections in degrees against number of detectors). 
 
 20
 
(a) Streak artifacts from the metal after reconstruction using FBP (highlighted for 
clarity). 
 
 
(b) Metal artifact reduction using MLEM and tracking information. 
Figure 11: Metal artifact comparison. 
 21
4.4. Feasibility of a continuous CT scan (Further dose reduction)  
 
To demonstrate our second strategy of dose reduction, the digital phantom was randomly 
deformed using the FFD B-spline technique (using Eq. 5 and 6) [12] and projections were 
generated using the Radon transform. Using the undeformed image as the initial estimate 
and sum of squared differences between radon transforms as the cost function, the image 
was iteratively updated through gradient descent optimization method (Eq. 7). For the 
abdominal phantom, a randomly deformed image of the original phantom was used as the 
initial estimate and the projection data from the original phantom was used to iteratively 
converge to the original image using gradient descent optimization. 
 
The number of projections used to compute the cost function was subsequently reduced 
and convergence was achieved without compromising the image quality in terms of 
PSNR. It was observed that using only a sixth of the original number of projections (30 
instead of 180) does not affect the reconstruction quality for a digital Shepp-Logan 
phantom.  
 
 
 22
            
Figure 12: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (1
st
 data set). 
 
A visual comparison (Figure 12, Figure 16 and Figure 20) shows that the optimized 
image matches the original deformed image. The difference images (Figure 13, Figure 17 
and Figure 21) provide a better visual assessment of the algorithm. Further, a quantitative 
assessment of the algorithm was studied through the convergence of the cost function 
plots of Figure 14, Figure 18 and Figure 22. The PSNR values of Figure 15, Figure 19 
and Figure 23 as a function of the number of iterations are monotonously increasing. 
 
 
 23
 
Figure 13: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 12) 
 
Figure 14: Cost function as a function of the number of iterations for Figure 12.  
(Note the convergence of the cost function). 
 
 
 24
0
10
20
30
40
50
60
1 21 41 61 81 101 121 141 161
Iterations
P
S
N
R (
d
B)
 
Figure 15: PSNR as a function of number of iterations for Figure 12.  
(Note the improvement of image quality in terms of PSNR as the number of iterations 
increases). 
 
 
Figure 16: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (2
nd
 data set). 
 
 25
        
 
 
Figure 17: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 16) 
 
 
Figure 18: Cost function as a function of the number of iterations for Figure 16. 
(Note the convergence of the cost function). 
 26
 
Figure 19: PSNR as a function of number of iterations for Figure 16.  
(Note the improvement of image quality in terms of PSNR as the number of iterations 
increases). 
 
 
Figure 20: Original deformed image (left) Recovered deformed image using gradient 
descent optimization (right) (for abdominal phantom). 
 
 
     
 
 27
            
Figure 21: Difference image of the original deformed image and its initial estimate (left), 
Difference image of the original deformed image and its estimate after convergence 
(right) (for Figure 20). 
 
 
Figure 22: Cost function as a function of the number of iterations for Figure 20. 
 28
 
 
Figure 23: PSNR as a function of number of iterations for Figure 20. 
 
The cost function, for a reduced subset of projections (evenly spaced over 180
o
), was 
minimized using gradient descent optimization. The number of projections used for the 
computation of the cost function was minimized from 180 to 30 for the digital phantom 
and from 1160 to 29 for the abdominal phantom. Visual assessments of the deformation 
recovery are provided in Figure 24 and Figure 25. The PSNR comparison (Figure 28) 
shows that the image quality remains virtually unchanged with the use of partial 
projections (from 180 down to 30). The quality degrades with further reduction of 
projections. The cost function (Figure 26 and Figure 27) also converges as the number of 
iterations increases.  
 29
     
    (a)                                                                 (b) 
     
    (c)                                                                 (d) 
     
    (e)                                                                  (f) 
Figure 24: Reduction of dose with fewer projections. Original deformed image (a), 
Reconstruction using 90 (b), 60 (c), 45 (d), 36 (e), 30 (f) projections. 
 
 30
                       
   (a)                                                                    (b) 
                
(c) (d) 
                  
    (e)                                                                   (f) 
Figure 25: Difference image of the original deformed image with: its initial estimate (a), 
its estimate after convergence using: 90 (b), 60 (c), 45 (d), 36 (e), 30 (f) projections. 
 
 
 31
0
2000
4000
6000
8000
10000
12000
1 21 41 61 81 101 121
Iterations
C
o
st
 f
unct
i
on
180 projections 45 projections 30 projections 20 projections
 
Figure 26: Convergence of the const function using various subsets of projections. 
 
 
 
0
50
100
150
200
250
300
350
400
21 41 61 81 101 121 141
Iterations
Cos
t
 f
unc
t
i
on
180 projections 45 projections 30 projections 20 projections
 
Figure 27: A zoomed-in version of Figure 26 from iteration 20. 
 32
0
5
10
15
20
25
30
35
40
45
1 214161811012
Iterations
PSN
R
 d
B
180 projections 45 projections 30 projections 20 projections
 
Figure 28: PSNR as a function of the number of iterations for subsets of projections. 
Image quality is unchanged down to 30 projections. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 33
CHAPTER 5 
Discussion 
We have demonstrated a reduction in radiation using the MLEM algorithm. The iterative 
MLEM algorithm incorporates the stochastic properties of x-ray photons while deriving a 
closed-form solution for attenuation coefficients. The image quality of MLEM was 
consistently better than that of the corresponding FBP reconstruction for all available 
doses for a digital phantom. For the abdominal phantom, the image quality degraded 
much faster for the FBP algorithm than the MLEM algorithm with a reduction in 
radiation dose. Although PSNR provides a good estimate of image quality for a digital 
phantom, it is not the best assessment measure for clinical images because of the absence 
of a standard reference for comparison. However, it shows the general trend of the quality 
of reconstruction these algorithms provide with respect to the dose value. A 
comparatively slow deterioration of image quality with decreased dose in the case of the 
MLEM algorithm could be used to study the feasibility of providing lower dose (tube 
current) settings on commercial scanners. PSNR does not correlate strongly with the 
subjective image quality ratings or observer task performance, limiting its utility in image 
quality assessment investigations [14]. Other assessment measures, such as the just 
noticeable difference (JND) [15] measure should be investigated in order to provide a 
more accurate comparison between MLEM and FBP.  
 
The second strategy for dose reduction uses a nonrigid transformation model to describe 
tissue motion in a continuous CT scan. The algorithm makes no assumption about the 
physical properties of the tissue. The experimental results have shown that the algorithm 
 34
was able to recover the deformed image using the complete set of the projection data. It 
has been possible to recover the deformed image using only partial subsets of the 
projection data without considerable change in image quality. Thus a reduction from 180 
to 30 projections, which amounts to a dose reduction by a factor of 6 for the digital 
phantom and a reduction from 1160 to 29 projections, which amounts to a dose reduction 
by a factor of 40 for the abdominal phantom was achieved. However, values for the 
initial estimate of the step size and the iterative scaling factor needs to be experimented 
with to determine their effects on the time for convergence. 
 
The integration of our algorithm in the clinical setting with the use of specialized tracking 
instruments and markers will successfully eliminate metal artifacts resulting from tools in 
the field of view. The use of such instruments in a clinical setting was successfully tested 
in an animal experiment as part of our Operating Room of the Future research. A new 
technique for dose reduction by modifying the MLEM algorithm is currently under 
experimentation. It is explained in the next chapter. 
 
Accurate and interactive navigation of image-guided procedures relies on high frame-rate 
intraoperative imaging and 3D visualization of the involved anatomy, such as that 
possible with 64-slice CT. Reduced dose will minimize risks associated with prolonged 
radiation exposure. The achievement of dose reduction, as presented here, establishes the 
feasibility of an innovative continuous CT-guided visualization and navigation system. 
This study provides proof-of-concept evidence for dose reduction in two dimensions 
using an approach that can be extended easily to three dimensions. 
 35
CHAPTER 6 
6. Scope for further investigation through the extension of MLEM  
Modified MLEM algorithm 
Our preliminary experiments conducted on the digital Shepp-Logan phantom have 
proved that the cost function of the MLEM algorithm is optimum when the applied 
deformation is equal to the actual synthetic deformation. 
Keeping the original MLEM framework, two more parameters have been added to limit 
the deformations between frames.  
 
()(){}()[]()[]{}
???
?+?+?=
?+?+=
j
jj
ij
jijij
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ijij
kkk
b?wa?wR - lN - e   N-M
yyxxYL
jij
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deformations 
k
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 36
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Simplifying results in 2 solutions given by 
 
()
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 37
() ()
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Solving for 
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k
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Dw
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)(8)(2)(2
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?
        (12) 
()(){ }DabswwDavgwwDavgww
Dw
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)(8)(2)(2
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ik
ikik
l
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avg
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2
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It is hypothesized that an appropriate selection of 
1
w and 
2
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value for 
k
x?  and
k
y? . 
 38
Thus a closed-form solution can be found for the intraoperative anatomic deformations 
for a coarse grid of pixels overlaid on the image. A B-spline interpolation, then, over the 
entire image would yield a smooth deformed image. We propose that a successful 
implementation of the modified MLEM algorithm would result in a dose reduction 
through the reduction in number of projections for our continuous CT application, a 
feasibility of which can only be determined through experimentation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 39
References 
[1] Cleaveland Clinic Foundation, ?Minimally Invasive Cardiovascular and Thoracic 
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Avanti Shetye 
Email: avshetye@gmail.com                                                                           Phone: 240-515-8469 
  
 
 
Education 
? University of Maryland, College Park, MD                  (Aug 2004-Feb 2007) 
M.S., Electrical & Computer Engineering 
? University of Mumbai, India                                        (Aug 2000-May 2004) 
B.E. (Hons.) Electrical & Electronics Engineering; Ranked 11/3000 in the 
University.  
 
Research Experience 
Graduate Research Assistant                                         (Jul 2005-Feb 2007) 
Imaging Technologies Laboratory, Diagnostic Imaging, University of Maryland 
Medical System (UMMS) 
Developing a statistical algorithm for computed tomography (CT) 
reconstruction using low radiation doses for continuous scanning and 
navigation. The motivation behind this research is to utilize the benefit of 3D 
visualization achieved through CT for interventional purposes, but at an 
innocuous radiation dose and without compromising image quality. [MATLAB, 
C/C++] 
 
Researcher                                                                      (Jan 2005- Jun 2005) 
Speech Communications Laboratory, University of Maryland, College Park 
Independently researched analyzing ?creakiness? in speech, one voice quality 
that can be used for speaker recognition, and submitted a 20 page report 
[MATLAB, Emacs, Xwin32] 
 
Publications 
? Avanti Shetye, Raj Shekhar, ?A statistical approach to high-quality CT 
reconstruction at low radiation doses for real-time guidance and 
navigation?, Medical Imaging: Image Processing, Proc. SPIE, 2007, 
accepted for publication 
? Avanti S. Shetye & Carol y. Espy-Wilson, ?Analysis of model and creaky 
voice quality variations?, Journal of the Acoustical Society of America, 
vol. 118, pp. 1965, 2005 
 
Projects  
Medical Imaging [In MATLAB]                                                         (Fall 2005) 
? Designed & implemented iterative & non-iterative algorithms for 
reconstruction of PET, SPECT, CT 
? Implemented Segmentation algorithm for Ultrasound images 
? Implemented rigid registration algorithm for MRI, CT 
 
 
Avanti Shetye 
Email: avshetye@gmail.com                                                                           Phone: 240-515-8469 
  
 
Image & Video Compression [In MATLAB]                                (Spring 2005) 
? Implemented JPEG & JPEG2000 compression schemes using DCT, EZW 
and EBCOT in sequential, hierarchical, lossless & progressive modes 
? Extended JPEG to MPEG2 video compression with SNR, spatial & 
temporal scalability  
 
Multimedia Signal Processing                                                       (Fall 2004) 
? Addressed fundamental multimedia issues on audio processing, speech 
recognition & synthesis, and image & video processing using state-of-the-
art technologies [MATLAB, C++, IBM via voice].  
? Developed an application for making Mapquest interactive and user-
friendly while driving with voice recognition and text-to-speech conversion 
[MS Speech SDK, C++]  
 
Undergraduate level projects 
? Designed and programmed a speech recognition & robotic application 
system aimed at assisting the physically challenged with operation of 
routine devices using speech [C]                                            (Spring 2004) 
? Designed a wireless transmitter using analog and digital devices with a 
potential to transmit over 250 meters                                           (Fall 2003) 
 
Relevant Coursework 
? Information theory & coding  ? Detection & Estimation theory 
? Multimedia Signal Processing ? Digital Image Processing 
? Medical Imaging & Imaging 
Analysis 
? Advanced DSP & adaptive filter 
design 
? Probability & Stochastic 
Processes in Communications & 
Control 
? Modeling, Analysis, & 
optimization of Embedded 
Software 
 
Academic Achievements  
? Sir Ratan Tata Trust Scholarship for academic excellence in sophomore 
and junior years of BE                                                                   (2002-03) 
? JRD Tata Trust Scholarship in the junior year of BE                          (2003) 
? National Talent Scholarship (N.T.S.) by the National Council of 
Educational Research and Training (Was in the top 750 out of more than a 
million students all over India)                                                            (1998) 
? Third position at the city level and twenty-second position at the State 
level (among more than 10,000 students) in academic Talent Search 
examinations                                                                             (1996-1998) 
 
Avanti Shetye 
Email: avshetye@gmail.com                                                                           Phone: 240-515-8469 
  
 
Skills 
? Software languages ? MATLAB, Pascal, C, C++, PHP  
? Assembly languages ? 8085, 8086, 80286, 80386, 8051, Pentium 
? Operating system ? MS DOS, WINDOWS 95/98/2000/NT/XP, UNIX 
? Applications ? MS Office Suite, Microsoft Visio, X-windows, Emacs, Adobe 
Photoshop, HTML, Dreamweaver, SQL, Crystal Reports, Praat 
  
Other Professional Activities 
? Student Member ? IEEE (The institute of Electrical and Electronics 
Engineers, Inc.)                                                                         (2005-2007) 
? Student Head of Electrical Engineering Department during the Technical 
Festival Technovanza of the senior year of BE                             (2003-04) 
? General Secretary, Electrical Engineers? Student Association (EESA) -
organized technical activities                                                         (2001-02) 
? EESA Librarian - Conceived & created the EESA library for Electrical 
Engineers                                                                                      (2001-02) 
 
Languages ? English (Fluent), French (Written language), Hindi (Fluent)