Powerpoint template for scientific poster

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• Clinical input data (supplied by OHI)
• 4 normal subjects
• Short-axis oriented slices
• Static and Dynamic data OSEM reconstruction,
  stress/rest studies
• 128x128 image size (17 frames for dynamic data)
• Phantom input data
• allows objective MSE measure to quantify
  denoising performance
• noise only slices generated with H2O cylinder
  (free of localized uptake)
• noise fused with normal SA slices (smoothed with
  10mm FWHM Gaussian)
• The static data was denoised, then evaluated
  visually by experts at OHI. The dynamic data was
  denoised, then fitted to a one-compartment Rb-82
  model.

Wavelets
Physiological Model Output (OSEM stress,
Denoising Protocol 17)
Abstract
Note We assume an additive Gaussian noise model.
The denoising protocols require an estimate of
noise variance in the image. The robust median
estimator allows a data-driven estimate from the
noisy wavelet coefficients

• The methods we investigate are based on the
  current state of the art denoising methods using
  a wavelet representation. It is well-established
  in the literature that wavelet-based denoising
  can outperform Gaussian smoothing, separating
  signal from noise at multiple image scales.
• the discrete wavelet transform (DWT) is a signal
  representation whose members consist of shifted,
  dilated versions of a suitable basis function
• wavelets provide an inherent advantage when
  processing nonstationary signals (such as cardiac
  PET images) the inclusion of localized
  fine-scale functions in the signal basis allows
  one to better represent diagnostically
  significant detail
• the DWT can be realized efficiently as an
  iterated filter bank. The filter banks structure
  generates approximation coefficients and detail
  coefficients at each decomposition level.

Objectives Cardiac PET scans generated using
Rb-82 are a convenient, noninvasive method of
diagnosing coronary artery disease (CAD).
Unfortunately, the clinical value of such data
can be compromised by the inherent high degree of
noise, reducing image quality and introducing
bias into extracted quantitative measures, such
as myocardial perfusion. Denoising methods based
on the wavelet transform have shown potential to
outperform existing standard methods such as
Gaussian filtering due to their ability to
preserve detail while suppressing noise at
multiple scales. In this work, a hybrid scheme
comprising two recently-developed wavelet
denoising methods spatially adaptive
thresholding and cross scale regularization is
applied to the wavelet coefficient subbands of
dynamic Rb-82 PET data. Methods Dynamic
rest/stress Rb-82 PET scans were performed in 4
healthy volunteers (lt5 likelihood of CAD). FBP
and OSEM images were reconstructed with no
smoothing filter applied. A three-level wavelet
decomposition was performed using a spline-based
(discrete dyadic) three-dimensional wavelet
decomposition which fully exploits correlation
between image slices. Denoised images were
synthesized after applying spatially adaptive
thresholding on level 3, and cross scale
regularization of level 2 or levels 2 and 3. A
one-compartment model was then used to estimate
perfusion (K1) from the denoised dynamic images.
Image quality was compared visually to 3D
Gaussian smoothing, and was evaluated
quantitatively using the precision of the K1
perfusion estimates.   Results When applied as a
post-processing step to standard FBP and OSEM
reconstruction for subjects with a healthy
myocardium, the proposed denoising protocols give
a considerable improvement in image quality (as
confirmed with a visual assessment of the
denoised images by qualified PET experts). In
particular, the proposed methods appear to
preserve relevant image detail around the inner
myocardial wall/cavity and outer myocardial
boundaries when compared to its Gaussian-smoothed
counterpart. When the denoised data are fitted to
a one-compartment model to extract perfusion, we
observed a modest increase in K1 precision. In
addition, the use of a data-driven noise estimate
based on the wavelet coefficients of the input
data provides a mechanism of adaptivity, by which
more (or less) aggressive denoising is performed
where warranted. Conclusions This work supports
the value of continuing to investigate the
applicability of recent advances in wavelet-based
denoising to nuclear medicine images.
where M1k represents the wavelet modulus of the
coefficients at the first level of decomposition,
defined as
(with k being the index over all coefficients in
that subband).

• Spatially Adaptive Thresholding
• introduced by Chang,Yu,Vetterli (2000)
• attempts to distinguish features from background
  in wavelet domain, and adjusts threshold Tk
  accordingly.
• This is done by computing the local variance of
  the DWT coefficients, sW k, using a set of
  neighbouring coefficients h of size N with
• in a feature area (e.g. edge) the coefficient
  variance is large, so the threshold is set low in
  order to retain feature unchanged
• in a background area the coefficient variance
  is small, so the threshold set high in order to
  suppress (noticeable) noise in that area
• soft thresholding is performed on the denoised
  coefficients

Results
Filter Bank Implementation of Wavelet Transform
(3 level)
Input f n1,..,nD
1 W1
Static Phantom Data (OSEM stress noise), 3D
denoising
Gs(w1)
. . .
Level 1 detail coefficients
Conclusions
D W1
Gs(wD)
Level 2 detail coefficients

• For all experiments, we observed better results
  (both visual and quantitative) from using
  denoising techniques based on a 3D wavelet
  transform compared to those that use a 2D wavelet
  transform.
• The proposed denoising methods adapts to the
  amount of noise present in the input data. More
  aggressive denoising is performed when the PET
  data are very noisy, while less aggressive
  denoising is done where warranted. Our
  experiments show that such an approach leads to
  similar or marginal improvements in image quality
  compared to non-adaptive methods, with the added
  advantage that the noise estimate is data-driven.
  The denoising methods are useful for
  interpretation of Rb-82 images over a large range
  of image quality.
• Of the denoising protocols investigated, the
  most promising comprised a hybrid between SA and
  CSR methods, with the different methods performed
  across different levels of decomposition.
• This work supports the value of continuing to
  investigate the applicability of recent advances
  in wavelet-based denoising to nuclear medicine
  images.

1 W2
Gs(2w1)
Hs(w1)Hs(wD)
. . .
D W2
Level 3 detail coefficients
Gs(2wD)
1 W3
Hs(2w1)Hs(2wD)

• Cross Scale Regularization
• introduced by Jin, Angelini, Esser, Laine (2002)
• in the case of high noise levels (as in Rb-82
  PET), the most detailed subbands (e.g. level 1
  coefficients) are usually dominated by noise
  which cannot be easily removed using traditional
  thresholding schemes. To address this issue, a
  scheme is proposed that takes into account the
  cross-scale correlation of structured signals.
• the presence of strong image features produces
  large coefficients across multiple scales, so the
  edges in the higher level subbands (less
  contaminated by noise) are used as a oracle to
  select the location of important level 1 details.

Gs(4w1)
. . .
Static Clinical Data (OSEM stress), 3D denoising
D W3
Gs(4wD)
Approximation coefficients
Hs(4w1)Hs(4wD)
Future Work
Visualization of Wavelet Coefficients

• the wavelet modulus of coefficients at the next
  most detailed subband (normalized from 0-1) is
  used as a scaling factor.
• the regularization is performed on the wavelet
  modulus (the direction of the wavelet coefficient
  vector w remains unchanged).

• Investigate using a more sophisticated noise
  model with spatially varying parameters (possibly
  using the bootstrap method)
• Investigate whether it is possible to extend the
  denoising protocols to 4D (incorporating the
  time-varying nature of dynamic PET studies in the
  algorithm)
• Investigate whether these denoising protocols
  could be used to denoise data in the sinogram
  domain
• Investigate whether very recently introduced
  alternatives to wavelets (e.g. platelets,
  brushlets) that have shown to be suitable for
  medical imaging could be used in our denoising
  protocols

Detail coefficients d1 d2
Approx. coeffs
Level
Raw Image
Objectives
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• PET images of the heart using Rb-82 radiotracer
  uptake are performed to observe and quantify
  blood flow to the heart muscle (myocardium). Such
  myocardial perfusion measures can be used to
  diagnose and manage coronary artery disease.
• Rb-82 is used for several reasons
• no on-site cyclotron is required
• its short half-life (76s) allows quick, repeated
  studies,
• it is selectively taken up in cardiac muscle
  tissue
• Unfortunately, the PET data that results from
  Rb-82 is highly contaminated by noise, which may
  bias derived physiological parameters.
• Clinical noise reduction protocol used at the
  Ottawa Heart Institute (OHI) involves filtering
  with a fixed width Gaussian kernel (full width at
  half maximum, FWHM15mm), regardless of the noise
  level in the raw image. The FWHM parameter is
  designed for the worst case (i.e. noisiest
  scans), so this frequently results in significant
  oversmoothing of less noisy images.

Static Phantom Data (OSEM stress noise), 3D
denoising
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References

• We investigated a set of 17 denoising protocols
  in order to assess the effect of using SA/CSR
  techniques
• when applied to multiple decomposition levels
  independently and in combination
• when denoising was applied in various domains
  (2D vs. 3D)

S. G. Chang, B. Yu, and M. Vetterli. Spatially
adaptive wavelet thresholding with context
modeling for image denoising. IEEE Transactions
on Image Processing, 915221531, 2000. Y. Jin,
E. Angelini, P. Esser, and A. Laine. De-noising
SPECT/PET images using cross-scale
regularization. In Proceedings of the
International Conference on Medical Imaging and
Computer-Assisted Intervention (MICCAI),
Montreal, Canada, pages 3240, 2003. I. Koren and
A. Laine. Time-Frequency and Wavelet Transforms
in Biomedical Engineering, A discrete dyadic
wavelet transform for multidimensional feature
analysis. IEEE Press, Piscataway, NJ, USA,
1997. G. Green, A. Cuhadar, and R.A. deKemp.
Spatially adaptive wavelet thresholding of
rubidium-82 cardiac PET images. In EMBC 2004
Proceedings of the 26th International Conference,
IEEE Engineering in Medicine and Biology
Society, San Francisco, CA, USA, pages
16051608, 2004. J. Lin, A.F.Laine, and S.R.
Bergmann. Improving PET-based physiological
quantification through methods of wavelet
denoising. IEEE Transactions on Biomedical
Engineering, 48202212, 2001. Green, G.C. 2005.
Wavelet based Denoising of Cardiac PET Data.
M.A.Sc. Thesis, Carleton University, Ottawa, ON,
Canada.
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• Choice of Wavelet Basis - (discrete dyadic
  wavelet transform (DDWT) - Koren/Laine 1997)
• 2D and 3D DDWT exploits the correlation within
  and between PET image slices
• the transform is based on smooth spline
  functions, which are well-suited to this class of
  images
• the transform gives a translation-invariant
  wavelet representation, a feature that reduces
  oscillations and ringing artifacts in the
  reconstructed image

This method is not adaptive to images of
different quality more effective noise
suppression techniques would lead to more
accurate images, and a subsequent decrease in the
risk of misdiagnosis and inappropriate treatment.
Dynamic Clinical Data (OSEM stress noise), 3D
denoising
Methods
Raw Image
Gaussian denoised (FWHM15mm)
Overall Denoising Process
DENOISINGSTAGE Wavelet Coefficient Modification
(combinations of CSR, SA thresholding)
3D Inverse Wavelet Transform (3 level)
Noisy Image
Denoised Image
3D Wavelet Transform (3 level)

• For further information
• Please contact either
• Geoffrey Green (geoffgreen_at_ieee.org)
• Aysegul Cuhadar (cuhadar_at_sce.carleton.ca)
• Rob deKemp (radekemp_at_ottawaheart.ca)

Noisy DWT coefficients
Denoised DWT coefficients