Applications of wavelets in PET modelling

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Applications of wavelets in PET modelling

• - a literature survey

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Hammersmith, London Turkheimer et al. 1999-2000

• 3 articles of the subject
• theoretical framework of wavelets
• image reconstruction and image processing
• Dyadic wavelet transform (DWT) and translation
  invariant DWT (DWT-TI) techniques
• applications to dynamic PET-SPECT studies
• Parametric images kinetic and statistical
  modelling in wavelet space

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Denoising images with wavelets

• Wavelet transform of dynamic image
• Thresholding (e.g. SURE, universal, Bonferroni)
• Inverse transform

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Studies

• Low-resolution SPECT study
• Hoffman brain phantom
• DWT vs. DWT-TI in 2D
• High-resolution PET images
• FDG brain study
• universal thresholding vs. SURE thresholding
• Very high-resolution PET images
• 11CPK11195 study of peripheral
  benzodiazepine receptors in the brain
• high signal-to-noise ratio

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Image domain
Wavelet domain
WT(Dynamic image)
Wavelet transform
t
Kinetic modelling
Dynamic image
Parametric WT
Statistical thresholding
Inverse wavelet transform
Parametric WT thresholded
Parametric image
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Studies

• Synthetic dynamic study
• artificial data set with nonstationary noise
  field
• FDG dynamic PET study
• Patlak plot
• 11Craclopride PET dynamic study
• D2-receptor distribution in normal brain
• Logan plot vs. WT

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Image domain
Wavelet domain
WT multiple images
Wavelet transform
i
Statistical modelling
Multiple images
Parametric WT
Wavelet filter
Inverse wavelet transform
Filtered Parametric WT
Filtered parametric map
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Studies

• Randomization study
• null dataset with PET
• H215O activation/rest -gt two groups of
  simulated datasets
• Parametric study of cerebral blood flow response
  to word recognition
• 5 right-handed normal subjects
• Measuring the effect of depression on brain
  serotonin receptors with 11CWAY-100635
• WT vs. statistical parametric mapping

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Karolinska hospital, Stockholm Cselenyi et al.
2002

• Binding potential (BP) study with 11CFLB 457
• 4 methods
• traditional ROI analysis (reference data)
• pixel-based analysis
• 2 variants of wavelet-aided analyses
• Aim is to decrease the noise-sensitivity of a
  parameter estimation procedure with wavelet
  approach
• 10 healthy male subjects

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ROI analysis

• BP was estimated using the reference region
  version of Logans graphical analysis (reference
  regioncerebellar cortex)

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Pixel-by-Pixel analysis

• radioactivity of a pixel area under the curve
  (AUC) of the corresponding TAC
• Fitting is done with the same Logan analysis as
  in ROI-based version
• Final product parametric image of the density of
  dopamine D2 receptors in brain
• Anatomical standardisation
• Average BPs were determined in the same ROIs used
  with ROI-based analysis

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Wavelet-based estimation

• two-dimensional translation-invariant (2DTI) and
  three-dimensional (3-DWT) wavelet transform
• coefficients of the dynamic WT analysed in the
  same manner as in pixel-based approach except for
  the thresholding
• Final product parametric map of BP values
• Anatomical standardisation and averaging within
  ROIs done as in pixel-based analysis

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Results

• Compared to the ROI-based analyses, the BP values
  were
• 50 with pixel-based analysis (heterogeneous
  image)
• 78 with 2DTI
• 100 with 3-DWT

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References

• F. Turkheimer et al.Multiresolution Analysis of
  Emission Tomography Images in the Wavelet Domain,
  J Cereb. Blood Flow Metab. 191189-1208 (1999)
• F. Turkheimer et al.Modeling Dynamic PET-SPECT
  Studies in the Wavelet Domain, J Cereb. Blood
  Flow Metab. 20879-893 (2000)
• F. Turkheimer et al.Statistical Modeling of
  Positron Emission Tomography Images in Wavelet
  Space, J Cereb. Blood Flow Metab. 201610-1618
  (2000)
• Z. Cselenyi et al.Wavelet-Aided Parametric
  Mapping of Cerebral Dopamine D2 Receptors Using
  the High Affinity PET Radioligand 11CFLB 457,
  NeuroImage 1747-60 (2002)

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Other articles

• J.-W. Lin et al.Improving PET-Based
  Physiological Quantification Through Methods of
  Wavelet Denoising, IEEE trans. bio. eng. Vol48,
  No.2 (2001)
• P. Millet et al. Wavelet Analysis of Dynamic PET
  Data Applications to the Parametric Imaging of
  Benzodiazepine Receptor Concentration, NeuroImage
  11458-472 (2000)