Introducing 

Prezi AI.

Your new presentation assistant.

Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.

Loading…
Transcript

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 (reference)

frame-by-frame

with noise

4-D reconstruction

noiseless measurement

no motion, warped (reference)

SINOGRAM

Unknown gidid motion

joint

single frame

with motion

no 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

  • PARTIAL VOLUME EFFECT
  • 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

  • PHYSIOLOGICALLY-BASED

MODEL

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

Learn more about creating dynamic, engaging presentations with Prezi