Deconvolution of noisy radiological images

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Deconvolution of noisy radiological images

• Adrian Jannetta

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Medical image processing

• Image formation described by Poisson statistics
• Signal-to-noise ratio increases with radiation
  dose
• Radiological images are obtained under
  conflicting requirements
• ALARP principle
• X-ray machine design and performance
  considerations
• Radiological images are obtained in an inherently
  noisy environment
• Enhancement or Restoration?
• Spatial or frequency filtering, wavelets,
  deconvolution methods
• Restoration methods derive from an image
  degradation model and attempt to undo the
  effects blurring and noise.

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Focal spot size, magnification and blur
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Application 1 Mammography

• Focal spot size determines the blurring
• Fine focal spot produces less blurring, but
• Slower tube heat dissipation so smaller currents
  are used
• Longer exposures and chance of patient motion
  blur
• Geometry determines the image magnification
• Higher magnification allows detection of smaller
  microcalcifications, but
• More image blurring
• Modern X-ray units have evolved to live with
  these conflicting design and performance
  requirements.
• Alternative Deblurring, to obtain images as good
  as those which would be obtained with a perfect
  (ideal) focal spot

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The degradation/restoration model
True image
Observed image
Restored image
Geometric Unsharpness
Quantum noise
In spatial domain
In frequency domain
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The deconvolution problem
Solution?
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The deconvolution problem
Solution?
If H?0 then the restored image is devastated with
artefacts, even when H is well defined.
The answer is to use regularised deconvolution,
where constraints are placed on the acceptable
restoration.
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Maximum Entropy Method

• Maximum entropy method (MEM) is a suitable
  deconvolution technique.

• Guess a solution. Generate trial data using
  the forward map.
• Chi-Squared Goodness of Fit statistic for the
  observed data and trial data.
• When this is minimised then we have a good fit
  between our trial and observed images?
• No! It is equivalent to solving the matrix
  equation

h is ill conditioned for a given g there are
many not necessarily close together.
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Maximum Entropy Method

• We impose a constraint on the solution Choose
  the with the maximum entropy, S.

• (Choice of the entropy function is a result of
  treating the restoration process as a statistical
  inference problem).
• Numerical procedure is to minimise the objective
  function

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Mammography experiments

• Obtain images with conventional set-up
• 1.8 magnification, fine focal spot
• Typical Radiographic factors (28kV, 40mAs)
• Realistic scatter
• Obtain images taken with unconventional set-ups
• 1.8 magnification, broad focal spot
• 3.0 magnification, fine focal spot
• These unconventional modes are not used in
  practice blurring introduced is unacceptable
• Use MEM to restore these images
• Can we make 1.8 BF images as good as 1.8 FF?
• Can we reduce blurring in the 3.0FF case?

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TORMAM Phantom Scoring
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The system PSF
Brass foil with pinholes
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1.8FF Conventional Setup
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1.8BF Not used in practice
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Pixel luminance profiles
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1.8BF as good as 1.8FF?
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3.0FF Better shape resolution
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Image scores
Image features scored with 3,2,1,0 depending on
perceived visibility
Average scores of two experienced, independent
observers
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Discussion

• Better visibility of all features under all three
  set-ups.
• Improvement in the signal-to-noise ratio
• Improvement in spatial resolution
• General acceptance amongst radiologists that
  traditional (Fourier based) de-blurring
  techniques are of little value
• MEM deconvolution addresses issues of noise
  amplification and artefact introduction
• MEM offers a way of weakening the link between
  focal spot size and geometric blurring

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Paper

• Collaboration with RMPG at Newcastle General
  Hospital
• Paper submitted to Physics in Medicine and
  Biology in May 2004

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Application 2 Linear tomography

• X-ray tube and image receptor have linear but
  opposing movements
• Only a focal plane remains in focus regions
  above and below are blurred
• High pass filtering will remove blur (and low
  frequencies in the focal plane)
• Deconvolution models are a better way forward

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Linear tomography machine
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Simple 3-plane tomography model
Tomograph
Object
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Linear tomography model
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Simulated 3-plane restoration
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5 planes through a skull phantom
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What next?

• Magnification mammography
• Repeat, using a more complicated, realistic
  phantom
• Experiments with reduced radiation doses (higher
  levels of noise)

• Linear tomography
• Different image priors?
• Post processing with high frequency filters?
• Deconvolution of scatter
• To improve radiographic contrast

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The End

• Thank you