SCATTER
CHARACTERISATION
Global optimisation: Locally Linear Embedding
Mixture of Poisson distributions model
DOI characterisation
Centroid
Locally Linear Embedding
(LLE)
Low
dimensional
manifold
prior
EM
Refinement
Maximum Likelihood Estimation
depth of interaction
secondary photons
parameters forward model
4-D PET / MR
DETECTOR MODEL
MULTI-MODALITY
motion parameter
ACTIVITY
Longitudinal joint registration and segmentation
Unknown non-rigid motion
MR-driven motion correction
Known non-rigid motion
no motion, warped (reference)
SINOGRAM
Unknown gidid motion
PARAMS UPTAKE
PARAMS MRI
ATLAS
DISTORTION
MRI
HIDDEN LABELS
RECONSTRUCTION
- COMPUTATIONAL COMPLEXITY
- NON-CONVEXITY
- STEP SIZE
- POSITIVITY
FACTORISATION
STATISTICAL ATLAS
EXPECTATION MAXIMISATION
EXPECTATION MAXIMISATION
SYNTHETIC FDG PET
FDG PET
LIMITED INFORMATION
10000 iterations 24800 instances
10000 iterations 1 instance
PROBLEM
SOLUTION
PROBLEM
- SMOOTNESS PRIOR
- EARLY TERMINATION
- HIGH VARIANCE
- NO CONVERGENCE
UNCERTAINTY:
- INCREASES IF NUMBER OF PHOTONS DECREASE
- INCREASES IF CONDITIONING NUMBER DECREASES
CONDITIONING NUMBER:
- TENDS TO ZERO: ILL-POSEDNESS
ILL-POSEDNESS:
- SMALL AMOUNT OF INFORMATION
X-Ray CT
PET (MR)
SOLUTION
SPECT
Model:
attenuation
photon counts
X-Ray source
Optimisation:
PET Model:
photon counts
back-projection
activity
PET-MRI
Optimisation:
projection
->
Positron Emission Tomography (PET):
Magnetic Resonance Imaging (MRI):
SPECT Model:
back-projection
photon counts
activity
projection
Single Photon Emission Computed Tomography (SPECT)
Optimisation:
NiftyRec
ATTENUATION
activity
MLEM attenuation from emission data
http://niftyrec.scienceontheweb.net
attenuation
Expectation Maximization
Activity
GENERATIVE MODELLING
Attenuation
Activity
Attenuation
UNCERTAINTY
4D Tomography
Stefano Pedemonte
CAUSAL MODELLING
SPECT
PET
X-Ray CT
Advisors:
- Prof. Sebastien Ourselin (UCL - CMIC)
- Prof. Simon Arridge (UCL - CMIC)
CONDITIONAL
INDEPENDENCIES
FACTORISATION
STRUCTURE
Laplace Approximation of the posterior distribution
3
Circulant Fisher Information Matrix
128 VOXELS: 4 x 10 CELLS
12
Sparse Fisher Information
Ray-traced Hessian
- characterisation of the uncertainty
- system design optimisation
- second order optimisation algorithms
SYSTEM DESIGN