Wavelet-based Denoising of Cardiac PET Data

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Wavelet-based Denoising of Cardiac PET Data

• M.A.Sc. Thesis
• Geoffrey Green, B. Eng.(Electrical)
• Supervisors
• Dr. Aysegul Cuhadar (Carleton SCE)
• Dr. Rob deKemp (Cardiac PET Center, Ottawa Heart
  Institute)

January 11, 2005
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Outline of Presentation

• Problem Statement / Thesis Motivation
• Thesis Objective
• Thesis Contributions / Publications
• Background Information
• Cardiac anatomy
• PET and its use in cardiology
• Wavelets and wavelet-based denoising
• Spatially Adaptive Thresholding
• Cross Scale Regularization
• Denoising Experiments
• Representative Results
• Future Work

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Problem Statement / Thesis Motivation (1)

• PET images of the heart using 82Rb radiotracer
  are performed to observe and quantify uptake of
  blood flow to the heart muscle.
• Such myocardial perfusion measures can be used
  to diagnose coronary arterial disease and
  prescribe an appropriate treatment.
• 82Rb is used for several practical reasons
• no on-site cyclotron required
• short half life (76s) allows quick, repeated
  studies
• like potassium, selectively taken up in cardiac
  muscle tissue
• HOWEVER, the PET data that results from 82Rb is
  highly contaminated by noise, leading to
  erroneous uptake images and extracted
  physiological parameters that are biased.

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Problem Statement / Thesis Motivation (2)

• Clinical noise reduction protocol used at OHI
  involves filtering with a fixed-width Gaussian
  kernel, regardless of noise level.
• This method is not adaptive to images of
  differing quality, and tends to oversmooth
  smaller-scale image features.
• More effective noise suppression techniques
  would lead to more accurate images, and a
  subsequent decrease in the risk of misdiagnosis
  and inappropriate treatment.

RAW DATA
GAUSSIAN FILTERED
myocardium
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Published Results
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 1605-1608, 2004.
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Thesis Objective

• The goal of this thesis is to develop denoising
  methods that improve the quality of cardiac 82Rb
  PET scans, and illustrate their effectiveness and
  robustness when used to measure myocardial
  perfusion.
• 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 LPF methods, separating
  signal from noise at multiple image scales.

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Thesis Contributions

• We apply the following recently-developed
  wavelet denoising techniques to cardiac 82Rb PET
  data
• spatially adaptive (SA) thresholding
• cross-scale regularization (CSR)
• We investigate the relative effect that these
  methods have on the denoised result when they are
  applied
• individually (across multiple scales),
• in combination (across multiple scales), and
• to various image domains (2D and 3D)
• We propose a novel denoising protocol that
  comprises a hybrid of the above methods, and
  illustrate the improvement it offers when
  compared to the current clinical protocol.

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Background - Cardiac Anatomy
blood pool (cavity)
myocardium
slices
apex

• The left ventricle is modelled as a
  semi-ellipsoid, containing a muscular wall
  (myocardium) which surrounds a blood pool.
• When viewed from the apex along the axis of the
  ellipsoid, the myocardium appears as a ring.
• Forceful contraction of LV is vital for blood
  supply to body.

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Background - PET

• Used to observe and measure physiological
  processes in vivo.
• Patient is injected with a radioactive tracer,
  which is selectively taken up (in myocardium).
• As tracer nucleus decays, a positron is emitted
  and travels a short distance (mm) before
  colliding with an electron from a nearby atom,
  causing an annihilation
• This creates two 511keV gamma rays that are
  emitted at 180o, picked up by external detectors
• Image reconstruction algorithms form a spatial
  representation of tracer distribution, using
  either - filtered backprojection (FBP), or
• - ordered subset expectation maximization (OSEM)

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Background PET in cardiology

• Used for both qualitative (location of defect)
  and quantitative analysis

Quantitative
Qualitative
polar map
TAC
Input Function
reduced uptake in damaged area
Myocardial cells M(t)
K1
K2
compartmental model

• Performed under rest and stress conditions
• Quantitative analysis uses a time series of
  images (frames), extracted TACs as input into a
  compartmental model
• Nonlinear regression used to determine model
  parameters (e.g. K1) from measured PET data

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Background Wavelets (1)

• Very active research area during the last 10
  years
• Wavelets provide an inherent advantage when
  denoising non-stationary signals, such as those
  found in cardiac PET imaging - the inclusion of
  localized fine scale functions in the basis
  allows one to better discern diagnostically
  significant details
• The DWT is a signal representation whose members
  consist of shifted, dilated versions of a chosen
  basis function
• The DWT is realized efficiently with an iterated
  filter bank, generating subbands of coefficients

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Background Wavelets (2)
Filter bank implementation of wavelet transform
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Approx. coeffs
Detail coefficients d1 d2
Level
1
2
3
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Approx. coeffs
Detail coefficients d1 d2
Level
1
2
3
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Background Wavelet based denoising
Overall denoising process
Noisy DWT coefficients
Denoised DWT coefficients
Noisy Image
Denoised Image
Inverse WT
Forward WT
Wavelet Coefficient Thresholding

• A multidimensional DWT which is meant to exploit
  the correlation within/between image slices
• Wavelet basis (3D discrete dyadic wavelet
  transform -Koren/Laine,1997) based on splines,
  which are well-suited to this class of images
• A translation-invariant wavelet representation,
  which reduces ringing effects in the
  reconstructed image
• The assumption is an additive Gaussian noise
  model

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Spatially Adaptive Thresholding

• Technique 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, sWk
• Feature area (e.g. edge) coefficient variance
  large, threshold set low in order to retain
  feature unchanged
• Background area coefficient variance small,
  threshold set high in order to suppress
  (noticeable) noise in that area

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Spatially Adaptive Thresholding 1D example
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Spatially Adaptive Thresholding 1D example
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Cross Scale Regularization

• Technique introduced by Jin, Angelini, Esser,
  Laine (2002)
• In the case of high noise levels (as in 82Rb
  PET), the most detailed subbands (i.e. 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 cross-scale coherence 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.
• Wavelet modulus of coefficients at the next most
  detailed subband (i.e. level 2) is used as a
  scaling factor for the level 1 coefficients.

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Cross Scale Regularization 1D example
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Denoising Experiments

• Phantom Input Data (since a priori tracer info
  is unknown)
• healthy, short-axis oriented slices
• simulated PET noise of varying types (merge
  phantom with clinical image that has no features
  present)

• Clinical Input Data (supplied by OHI)
• healthy, short-axis oriented slices
• Static OSEM/FBP reconstruction, stress/rest
  study
• Dynamic OSEM reconstruction, stress/rest study

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Denoising Experiments

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

• The denoising protocols require an estimate of
  noise variance in the image. Robust median
  estimator allows a data-driven estimate from the
  noisy wavelet coefficients

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Denoising Experiments

• Figures of Merit
• Phantom Data
• MSE
• Visual Assessment
• Clinical Data
• Visual Assessment - STATIC study
• Coefficient of Determination (R2) - DYNAMIC
  study
• Normalized K1 std. dev. - DYNAMIC study

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Selected Results - Phantom
MSE vs. Denoising Protocol for 3D Phantom Image
Gaussian
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Selected Results Static Clinical Data
Denoised Images 3D denoising, OSEM stress study
SA _at_ level 3, CSR _at_ level 2
SA _at_ level 3, CSR _at_ level 2,1
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Selected Results Dynamic Clinical Data
Model outputs vs. Denoising Protocol - 3D, OSEM
stress
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Future Work

• Development of a more sophisticated noise model
• Applicability to higher dimensions (including
  time) 4D, dynamic polar map
• Investigate denoising in sinogram domain
• Alternate signal basis (e.g. platelets,
  brushlets, curvelets)
• Application to other PET studies (e.g.
  ECG-gated, NH3 tracer)
• Statistical significance testing

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Denoising GUI

• In order to facilitate the investigation of
  parameter changes on the denoised results, a GUI
  was implemented.

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Wavelet-based Denoising of Cardiac PET Data

• M.A.Sc. Thesis
• Geoffrey Green, B. Eng.(Electrical)
• Supervisors
• Dr. Aysegul Cuhadar (Carleton SCE)
• Dr. Rob deKemp (Cardiac PET Center, Ottawa Heart
  Institute)

January 11, 2005
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Quantitative Results
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Quantitative Results
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Approx. coeffs
Detail coefficients d1 d2
Level
1
2
3